程序代写代做代考 scheme assembly Fortran algorithm interpreter Java flex gui python c++ database Lambda Calculus DNA javascript c# discrete mathematics Haskell cache compiler data structure decision tree computational biology chain Fundamentals of

Fundamentals of

Programming

Python

DR
AF

Richard L. Halterman
Southern Adventist University

January 18, 2018

Fundamentals of Python Programming

See the preface for the terms of use of this document.

Contents

1 The Context of Software Development 1

1.1 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Development Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Learning Programming with Python . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.4 Writing a Python Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.5 The Python Interactive Shell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.6 A Longer Python program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2 Values and Variables 13

2.1 Integer and String Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2 Variables and Assignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.3 Identifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.4 Floating-point Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.5 Control Codes within Strings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2.6 User Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.7 Controlling the print Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.8 String Formatting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

2.9 Multi-line Strings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

2.10 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3 Expressions and Arithmetic 43

3.1 Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.2 Mixed Type Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.3 Operator Precedence and Associativity . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.4 Formatting Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

CONTENTS ii

3.5 Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

3.6 Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.6.1 Syntax Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.6.2 Run-time Exceptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.6.3 Logic Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

3.7 Arithmetic Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.8 More Arithmetic Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.9 Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3.10 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

4 Conditional Execution 67

4.1 Boolean Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

4.2 Boolean Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

4.3 The Simple if Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

4.4 The if/else Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

4.5 Compound Boolean Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

4.6 The pass Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

4.7 Floating-point Equality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

4.8 Nested Conditionals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

4.9 Multi-way Decision Statements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

4.10 Multi-way Versus Sequential Conditionals . . . . . . . . . . . . . . . . . . . . . . . . . 97

4.11 Conditional Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

4.12 Errors in Conditional Statements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

4.13 Logic Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

4.14 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

5 Iteration 113

5.1 The while Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

5.2 Definite Loops vs. Indefinite Loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

5.3 The for Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

5.4 Nested Loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

5.5 Abnormal Loop Termination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

5.5.1 The break statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

5.5.2 The continue Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

5.6 while/else and for/else . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

CONTENTS iii

5.7 Infinite Loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

5.8 Iteration Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

5.8.1 Computing Square Root . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

5.8.2 Drawing a Tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

5.8.3 Printing Prime Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

5.8.4 Insisting on the Proper Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

5.9 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

6 Using Functions 157

6.1 Introduction to Using Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

6.2 Functions and Modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

6.3 The Built-in Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

6.4 Standard Mathematical Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

6.5 time Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

6.6 Random Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

6.7 System-specific Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

6.8 The eval and exec Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

6.9 Turtle Graphics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

6.10 Other Techniques for Importing Functions and Modules . . . . . . . . . . . . . . . . . . 185

6.11 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

7 Writing Functions 193

7.1 Function Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194

7.2 Parameter Passing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

7.3 Documenting Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

7.4 Function Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213

7.4.1 Better Organized Prime Generator . . . . . . . . . . . . . . . . . . . . . . . . . 213

7.4.2 Command Interpreter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215

7.4.3 Restricted Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216

7.4.4 Better Die Rolling Simulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218

7.4.5 Tree Drawing Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219

7.4.6 Floating-point Equality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220

7.5 Refactoring to Eliminate Code Duplication . . . . . . . . . . . . . . . . . . . . . . . . . 222

7.6 Custom Functions vs. Standard Functions . . . . . . . . . . . . . . . . . . . . . . . . . . 224

7.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227

CONTENTS iv

8 More on Functions 233

8.1 Global Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233

8.2 Default Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238

8.3 Introduction to Recursion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241

8.4 Making Functions Reusable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246

8.5 Functions as Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249

8.6 Separating Concerns with Pluggable Modules . . . . . . . . . . . . . . . . . . . . . . . . 253

8.7 Lambda Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273

8.8 Generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278

8.9 Local Function Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286

8.10 Decorators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292

8.11 Partial Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303

8.12 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306

9 Objects 311

9.1 Using Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311

9.2 String Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312

9.3 File Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316

9.4 Fraction Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323

9.5 Turtle Graphics Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325

9.6 Graphics with tkinter Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326

9.7 Other Standard Python Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332

9.8 Object Mutability and Aliasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332

9.9 Garbage Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336

9.10 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337

10 Lists 339

10.1 Using Lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341

10.2 List Traversal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345

10.3 Building Lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346

10.4 List Membership . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351

10.5 List Assignment and Equivalence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352

10.6 List Bounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357

10.7 Slicing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358

10.8 List Element Removal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361

CONTENTS v

10.9 Lists and Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362

10.10 List Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363

10.11 Prime Generation with a List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366

10.12 Command-line Arguments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368

10.13 List Comprehensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369

10.14 Multidimensional Lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375

10.15 Summary of List Creation Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384

10.16 Lists vs. Generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385

10.17 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385

11 Tuples, Dictionaries, and Sets 389

11.1 Tuples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389

11.2 Arbitrary Argument Lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393

11.3 Dictionaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398

11.4 Using Dictionaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402

11.5 Counting with Dictionaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404

11.6 Grouping with Dictionaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408

11.7 Keyword Arguments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411

11.8 Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414

11.9 Set Quantification with all and any . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415

11.10 Enumerating the Elements of a Data Structure . . . . . . . . . . . . . . . . . . . . . . . 419

11.11 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421

12 Handling Exceptions 425

12.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425

12.2 Common Standard Exceptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426

12.3 Handling Exceptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428

12.4 Handling Multiple Exceptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431

12.5 The Catch-all Handler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432

12.6 Catching Exception Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436

12.7 Exception Handling Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437

12.8 Raising Exceptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446

12.9 The try Statement’s Optional else Block . . . . . . . . . . . . . . . . . . . . . . . . . . 451

12.10 finally block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453

12.11 Using Exceptions Wisely . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457

CONTENTS vi

12.12 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 458

13 Custom Types 463

13.1 Circle Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463

13.2 Restricting Access to Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473

13.3 Rational Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474

13.4 Bank Account Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479

13.5 Stopwatch Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483

13.6 Traffic Light Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486

13.7 Automated Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492

13.8 Plotting Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497

13.9 Dynamic Content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 502

13.10 Class Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 506

13.11 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 507

14 Class Design: Composition and Inheritance 513

14.1 Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513

14.2 Class Inheritance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 518

14.3 Composition vs. Inheritance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537

14.4 Multiple Inheritance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 540

14.5 Unit Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558

14.6 Custom Exceptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563

14.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566

15 Algorithm Quality 567

15.1 Good Algorithms Versus Bad Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . 567

15.2 Sorting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 576

15.3 Flexible Sorting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 580

15.4 Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582

15.4.1 Linear Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582

15.4.2 Binary Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584

15.5 Recursion Revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593

15.6 List Permutations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 600

15.7 Randomly Permuting a List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 609

15.8 Reversing a List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614

CONTENTS vii

15.9 Memoization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615

15.10 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 628

16 Representing Relationships with Graphs 631

16.1 Introduction to Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 631

16.2 Implementing Graphs in Python . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635

16.3 Path Finding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635

16.4 Breadth-first Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 637

16.5 Depth-first Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 647

16.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654

Index 655

CONTENTS viii

Preface

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Chapter 1

The Context of Software Development

A computer program, from one perspective, is a sequence of instructions that dictate the flow of electri-
cal impulses within a computer system. These impulses affect the computer’s memory and interact with
the display screen, keyboard, mouse, and perhaps even other computers across a network in such a way
as to produce the “magic” that permits humans to perform useful tasks, solve high-level problems, and
play games. One program allows a computer to assume the role of a financial calculator, while another
transforms the machine into a worthy chess opponent. Note the two extremes here:

• at the lower, more concrete level electrical impulses alter the internal state of the computer, while

• at the higher, more abstract level computer users accomplish real-world work or derive actual plea-
sure.

So well is the higher-level illusion achieved that most computer users are oblivious to the lower-level
activity (the machinery under the hood, so to speak). Surprisingly, perhaps, most programmers today write
software at this higher, more abstract level also. An accomplished computer programmer can develop
sophisticated software with little or no interest or knowledge of the actual computer system upon which it
runs. Powerful software construction tools hide the lower-level details from programmers, allowing them
to solve problems in higher-level terms.

The concepts of computer programming are logical and mathematical in nature. In theory, computer
programs can be developed without the use of a computer. Programmers can discuss the viability of a
program and reason about its correctness and efficiency by examining abstract symbols that correspond
to the features of real-world programming languages but appear in no real-world programming language.
While such exercises can be very valuable, in practice computer programmers are not isolated from their
machines. Software is written to be used on real computer systems. Computing professionals known
as software engineers develop software to drive particular systems. These systems are defined by their
underlying hardware and operating system. Developers use concrete tools like compilers, debuggers, and
profilers. This chapter examines the context of software development, including computer systems and
tools.

1.1. SOFTWARE 2

1.1 Software

A computer program is an example of computer software. One can refer to a program as a piece of software
as if it were a tangible object, but software is actually quite intangible. It is stored on a medium. A hard
drive, a CD, a DVD, and a USB pen drive are all examples of media upon which software can reside. The
CD is not the software; the software is a pattern on the CD. In order to be used, software must be stored
in the computer’s memory. Typically computer programs are loaded into memory from a medium like the
computer’s hard disk. An electromagnetic pattern representing the program is stored on the computer’s hard
drive. This pattern of electronic symbols must be transferred to the computer’s memory before the program
can be executed. The program may have been installed on the hard disk from a CD or from the Internet. In
any case, the essence that was transferred from medium to medium was a pattern of electronic symbols that
direct the work of the computer system.

These patterns of electronic symbols are best represented as a sequence of zeroes and ones, digits from
the binary (base 2) number system. An example of a binary program sequence is

10001011011000010001000001001110

To the underlying computer hardware, specifically the processor, a zero here and three ones there might
mean that certain electrical signals should be sent to the graphics device so that it makes a certain part of
the display screen red. Unfortunately, only a minuscule number of people in the world would be able to
produce, by hand, the complete sequence of zeroes and ones that represent the program Microsoft Word
for an Intel-based computer running the Windows 8.1 operating system. Further, almost none of those who
could produce the binary sequence would claim to enjoy the task.

The Word program for older Mac OS X computers using a PowerPC processor works similarly to
the Windows version and indeed is produced by the same company, but the program is expressed in a
completely different sequence of zeroes and ones! The Intel Core i7 in the Windows machine accepts a
completely different binary language than the PowerPC processor in the older Mac. We say the processors
have their own machine language.

1.2 Development Tools

If very few humans can (or want) to speak the machine language of the computers’ processors and software
is expressed in this language, how has so much software been developed over the years?

Software can be represented by printed words and symbols that are easier for humans to manage than
binary sequences. Tools exist that automatically convert a higher-level description of what is to be done
into the required lower-level code. Higher-level programming languages like Python allow programmers to
express solutions to programming problems in terms that are much closer to a natural language like English.
Some examples of the more popular of the hundreds of higher-level programming languages that have been
devised over the past 60 years include FORTRAN, COBOL, Lisp, Haskell, C, Perl, C++, Java, and C#. Most
programmers today, especially those concerned with high-level applications, usually do not worry about the
details of underlying hardware platform and its machine language.

One might think that ideally such a conversion tool would accept a description in a natural language,
such as English, and produce the desired executable code. This is not possible today because natural
languages are quite complex compared to computer programming languages. Programs called compilers
that translate one computer language into another have been around for over 60 years, but natural language
processing is still an active area of artificial intelligence research. Natural languages, as they are used

1.2. DEVELOPMENT TOOLS 3

by most humans, are inherently ambiguous. To understand properly all but a very limited subset of a
natural language, a human (or artificially intelligent computer system) requires a vast amount of background
knowledge that is beyond the capabilities of today’s software. Fortunately, programming languages provide
a relatively simple structure with very strict rules for forming statements that can express a solution to any
problem that can be solved by a computer.

Consider the following program fragment written in the Python programming language:

subtotal = 25
tax = 3
total = subtotal + tax

While these three lines do constitute a proper Python program, they more likely are merely a small piece
of a larger program. The lines of text in this program fragment look similar to expressions in algebra.
We see no sequence of binary digits. Three words, subtotal, tax, and total, called variables, represent
information. Mathematicians have used variables for hundreds of years before the first digital computer
was built. In programming, a variable represents a value stored in the computer’s memory. Instead of some
cryptic binary instructions meant only for the processor, we see familiar-looking mathematical operators
(= and +). Since this program is expressed in the Python language, not machine language, no computer
processor can execute the program directly. A program called an interpreter translates the Python code into
machine code when a user runs the program. The higher-level language code is called source code. The
corresponding machine language code is called the target code. The interpreter translates the source code
into the target machine language.

The beauty of higher-level languages is this: the same Python source code can execute on different target
platforms. The target platform must have a Python interpreter available, but multiple Python interpreters
are available for all the major computing platforms. The human programmer therefore is free to think about
writing the solution to the problem in Python, not in a specific machine language.

Programmers have a variety of tools available to enhance the software development process. Some
common tools include:

• Editors. An editor allows the programmer to enter the program source code and save it to files.
Most programming editors increase programmer productivity by using colors to highlight language
features. The syntax of a language refers to the way pieces of the language are arranged to make
well-formed sentences. To illustrate, the sentence

The tall boy runs quickly to the door.

uses proper English syntax. By comparison, the sentence

Boy the tall runs door to quickly the.

is not correct syntactically. It uses the same words as the original sentence, but their arrangement
does not follow the rules of English.

Similarly, programming languages have strict syntax rules that programmers must follow to create
well-formed programs. Only well-formed programs are acceptable for translation into executable
machine code. Some syntax-aware editors can use colors or other special annotations to alert pro-
grammers of syntax errors during the editing process.

• Compilers. A compiler translates the source code to target code. The target code may be the machine
language for a particular platform or embedded device. The target code could be another source
language; for example, the earliest C++ compiler translated C++ into C, another higher-level language.
The resulting C code was then processed by a C compiler to produce an executable program. (C++

1.3. LEARNING PROGRAMMING WITH PYTHON 4

compilers today translate C++ directly into machine language.) Compilers translate the contents of a
source file and produce a file containing all the target code. Popular compiled languages include C,
C++, Java, C#.

• Interpreters. An interpreter is like a compiler, in that it translates higher-level source code into
target code (usually machine language). It works differently, however. While a compiler produces
an executable program that may run many times with no additional translation needed, an inter-
preter translates source code statements into machine language each time a user runs the program. A
compiled program does not need to be recompiled to run, but an interpreted program must be rein-
terpreted each time it executes. For this reason interpreted languages are often refered to as scripting
languages. The interpreter in essence reads the script, where the script is the source code of the
program. In general, compiled programs execute more quickly than interpreted programs because
the translation activity occurs only once. Interpreted programs, on the other hand, can run as is on
any platform with an appropriate interpreter; they do not need to be recompiled to run on a different
platform. Python, for example, is used mainly as an interpreted language, but compilers for it are
available. Interpreted languages are better suited for dynamic, explorative development which many
people feel is ideal for beginning programmers. Popular scripting languages include Python, Ruby,
Perl, and, for web browsers, Javascript.

• Debuggers. A debugger allows a programmer to more easily trace a program’s execution in order
to locate and correct errors in the program’s implementation. With a debugger, a developer can
simultaneously run a program and see which line in the source code is responsible for the program’s
current actions. The programmer can watch the values of variables and other program elements to see
if their values change as expected. Debuggers are valuable for locating errors (also called bugs) and
repairing programs that contain errors. (See Section 3.6 for more information about programming
errors.)

• Profilers. A profiler collects statistics about a program’s execution allowing developers to tune ap-
propriate parts of the program to improve its overall performance. A profiler indicates how many
times a portion of a program is executed during a particular run, and how long that portion takes to
execute. Developers also can use profilers for testing purposes to ensure all the code in a program is
actually being used somewhere during testing. This is known as coverage. It is common for software
to fail after its release because users exercise some part of the program that was not executed anytime
during testing. The main purpose of profiling is to find the parts of a program that can be improved
to make the program run faster.

Many developers use integrated development environments (IDEs). An IDE includes editors, debug-
gers, and other programming aids in one comprehensive program. Python IDEs include Wingware, En-
thought, and IDLE.

Despite the wide variety of tools (and tool vendors’ claims), the programming process for all but trivial
programs is not automatic. Good tools are valuable and certainly increase the productivity of developers,
but they cannot write software. There are no substitutes for sound logical thinking, creativity, common
sense, and, of course, programming experience.

1.3 Learning Programming with Python

Guido van Rossum created the Python programming language in the late 1980s. In contrast to other popular
languages such as C, C++, Java, and C#, Python strives to provide a simple but powerful syntax.

1.4. WRITING A PYTHON PROGRAM 5

Python is used for software development at companies and organizations such as Google, Yahoo, Face-
book, CERN, Industrial Light and Magic, and NASA. Experienced programmers can accomplish great
things with Python, but Python’s beauty is that it is accessible to beginning programmers and allows them
to tackle interesting problems more quickly than many other, more complex languages that have a steeper
learning curve.

More information about Python, including links to download the latest version for Microsoft Windows,
Mac OS X, and Linux, can be found at http://www.python.org.

In late 2008, Python 3.0 was released. Commonly called Python 3, the current version of Python is
incompatible with earlier versions of the language. Currently the Python world still is in transition between
Python 2 and Python 3. Many existing published books cover Python 2, but more Python 3 resources now
are becoming widely available. The code in this book is based on Python 3.

This book does not attempt to cover all the facets of the Python programming language. Experienced
programmers should look elsewhere for books that cover Python in much more detail. The focus here is on
introducing programming techniques and developing good habits. To that end, our approach avoids some
of the more esoteric features of Python and concentrates on the programming basics that transfer directly to
other imperative programming languages such as Java, C#, and C++. We stick with the basics and explore
more advanced features of Python only when necessary to handle the problem at hand.

1.4 Writing a Python Program

The text that makes up a Python program has a particular structure. The syntax must be correct, or the
interpreter will generate error messages and not execute the program. This section introduces Python by
providing a simple example program.

A program consists of one or more statements. A statement is an instruction that the interpreter executes.
The following statement invokes the print function to display a message:

print(“This is a simple Python program”)

We can use the statement in a program. Listing 1.1 (simple.py) is one of the simplest Python programs that
does something:

Listing 1.1: simple.py

print(“This is a simple Python program”)

We will use Wingware’s WingIDE 101 to develop our Python programs. This integrated development
environment is freely available from http://wingware.com/downloads/wingide-101, and its target au-
dience is beginning Python programmers. Its feature set and ease of use make WingIDE 101 an ideal
platform for exploring programming in Python.

The way you launch WingIDE 101 depends on your operating system and how it was installed. Fig-
ure 1.1 shows a screenshot of WingIDE 101 running on a Windows 8.1 computer. The IDE consists of a
menu bar at the top, along with a tool bar directly underneath it, and several sub-panes within the window.
The large, unlabeled pane in the upper left portion of the window is the editor pane in which we type in
our program’s source code. The versions of WingIDE 101 for Apple Mac OS X and Linux are similar in
appearance.

To begin entering our program, we will choose the New item from the File menu (File→New menu
sequence), as shown in Figure 1.2. This action produces a new editor pane for a file named Unititled-1.py.

http://www.python.org
http://wingware.com/downloads/wingide-101

1.4. WRITING A PYTHON PROGRAM 6

Figure 1.1 WingIDE 101 running under Microsoft Windows

Figure 1.2 The menu selection to create a new Python program.

1.4. WRITING A PYTHON PROGRAM 7

Figure 1.3 The new, untitled editor pane ready for code.

Figure 1.4 The code for the simple program after typed into the editor pane.

As Figure 1.3 shows, the file’s name appears in the editor’s tab at the top. (We will save the file with a
different name later.)

We now are ready to type in the code that constitutes the program. Figure 1.4 shows the text to type.

Next we will save the file. The menu sequence File→Save, also shown in Figure 1.5, produces the
dialog box shown in Figure 1.6 that allows us to select a folder and filename for our program. You should
name all Python programs with a .py extension.

The WingIDE-101 IDE provides two different ways to execute the program. We can run the program
by selecting the little green triangle under the menu bar, as shown in Figure 1.7. The pane labeled Python
Shell will display the program’s output. Figure 1.8 shows the results of running the program.

Another way to execute the program is via the Debug button on the menu, as shown in Figure 1.9.
When debugging the program, the executing program’s output appears in the Debug I/O pane as shown in
Figure 1.10.

Which the better choice, the Run option or the Debug option? As we will see later (see Section 5.7), the
debugging option provides developers more control over the program’s execution, so, during development,

Figure 1.5 Save the Python program

1.4. WRITING A PYTHON PROGRAM 8

Figure 1.6 The file save dialog allows the user to name the Python file and locate the file in a particular
folder.

Figure 1.7 Running the program

Figure 1.8 WingIDE 101 running under Microsoft Windows

Figure 1.9 Debugging the program

Figure 1.10 Debugger output

1.5. THE PYTHON INTERACTIVE SHELL 9

Figure 1.11 WingIDE 101 running under Microsoft Windows

we prefer the Debug option to the Run option.

When you are finished programming and wish to quit the IDE, follow the menu sequence File→Quit as
shown in Figure 1.11.

Listing 1.1 (simple.py) contains only one line of code:

print(“This is a simple Python program”)

This is a Python statement. A statement is a command that the interpreter executes. This statement
prints the message This is a simple Python program on the screen. A statement is the fundamental unit of
execution in a Python program. Statements may be grouped into larger chunks called blocks, and blocks can
make up more complex statements. Higher-order constructs such as functions and methods are composed
of blocks. The statement

print(“This is a simple Python program”)

makes use of a built in function named print. Python has a variety of different kinds of statements that we
can use to build programs, and the chapters that follow explore these various kinds of statements.

While integrated development environments like Wingware’s WingIDE-101 are useful for developing
Python programs, we can execute Python programs directly from a command line. In Microsoft Windows,
the command console (cmd.exe) and PowerShell offer command lines. In Apple Mac OS X, Linux, and
Unix, a terminal provides a command line. Figure 1.12 shows the Windows command shell running a
Python program. In all cases the user’s PATH environment variable must be set properly in order for the
operating system to find the Python interpreter to run the program.

Figure 1.8 shows that WingIDE 101 displays a program’s output as black text on a white background. In
order to better distinguish visually in this text program source code from program output, we will render the
program’s output with white text on a black background, as it would appear in the command line interpreter
under Windows as shown in Figure 1.12. This means we would show the output of Listing 1.1 (simple.py)
as

This is a simple Python program

1.5 The Python Interactive Shell

We created the program in Listing 1.1 (simple.py) and submitted it to the Python interpreter for execution.
We can interact with the interpreter directly, typing in Python statements and expressions for its immediate
execution. As we saw in Figure 1.8, the WingIDE 101 pane labeled Python Shell is where the executing
program directs its output. We also can type commands into the Python Shell pane, and the interpreter

1.5. THE PYTHON INTERACTIVE SHELL 10

Figure 1.12 Running a Python program from the command line

Figure 1.13 The interactive shell allows us to submit Python statements and expressions directly to the
interpreter

will attempt to execute them. Figure 1.13 shows how the interpreter responds when we enter the program
statement directly into the shell. The interpreter prompts the user for input with three greater-than symbols
(>>>). This means the user typed in the text on the line prefixed with >>>. Any lines without the >>> prefix
represent the interpreter’s output, or feedback, to the user.

We will find Python’s interactive interpreter invaluable for experimenting with various language con-
structs. We can discover many things about Python without ever writing a complete program.

We can execute the interactive Python interpreter directly from the command line, as Figure 1.14
demonstrates. This means not only can we execute Python programs apart from the WingIDE 101 de-
veloper environment, we also we can access Python’s interactive interpreter separately from WingIDE 101
if we so choose.

Figure 1.13 shows that the WingIDE 101 interpreter pane displays black text on a white background. In
order for readers of this text to better distinguish visually program source code from program output, we
will render the user’s direct interaction with the Python interpreter as black text on a light-gray background.
As an example, the following shows a possible interactive session with a user:

>>> print(“Hello!”)
Hello!

The interpreter prompt (>>>) prefixes all user input in the interactive shell. Lines that do not begin with the

1.6. A LONGER PYTHON PROGRAM 11

Figure 1.14 Running the Python interpreter from the command line

>>> prompt represent the interpreter’s response.

1.6 A Longer Python program

More interesting programs contain multiple statements. In Listing 1.2 (arrow.py), six print statements draw
an arrow on the screen:

Listing 1.2: arrow.py

print(” * “)
print(” *** “)
print(” ***** “)
print(” * “)
print(” * “)
print(” * “)

We wish the output of Listing 1.2 (arrow.py) to be

*
***

*****
*
*
*

If you try to enter each line one at a time into the interactive shell, the program’s output will be intermingled
with the statements you type. In this case the best approach is to type the program into an editor, save the
code you type to a file, and then execute the program. Most of the time we use an editor to enter and run
our Python programs. The interactive interpreter is most useful for experimenting with small snippets of
Python code.

1.7. EXERCISES 12

In Listing 1.2 (arrow.py) each print statement “draws” a horizontal slice of the arrow. All the horizontal
slices stacked on top of each other results in the picture of the arrow. The statements form a block of Python
code. It is important that no whitespace (spaces or tabs) come before the beginning of each statement. In
Python the indentation of statements is significant and the interpreter generates error messages for improper
indentation. If we try to put a single space before a statement in the interactive shell, we get

>>> print(‘hi’)
File ““, line 1

print(‘hi’)
ˆ

IndentationError: unexpected indent

The interpreter reports a similar error when we attempt to run a saved Python program if the code contains
such extraneous indentation.

1.7 Exercises

1. What is a compiler?

2. What is an interpreter?

3. How is a compiler similar to an interpreter? How are they different?

4. How is compiled or interpreted code different from source code?

5. What tool does a programmer use to produce Python source code?

6. What is necessary to execute a Python program?

7. List several advantages developing software in a higher-level language has over developing software
in machine language.

8. How can an IDE improve a programmer’s productivity?

9. What is the “official” Python IDE?

10. What is a statement in a Python program?

Chapter 2

Values and Variables

In this chapter we explore some building blocks that are used to develop Python programs. We experiment
with the following concepts:

• numeric values

• strings

• variables

• assignment

• identifiers

• reserved words

In the next chapter we will revisit some of these concepts in the context of other data types.

2.1 Integer and String Values

The number four (4) is an example of a numeric value. In mathematics, 4 is an integer value. Integers
are whole numbers, which means they have no fractional parts, and they can be positive, negative, or zero.
Examples of integers include 4, −19, 0, and−1005. In contrast, 4.5 is not an integer, since it is not a whole
number.

Python supports a number of numeric and nonnumeric values. In particular, Python programs can use
integer values. The Python statement

print(4)

prints the value 4. Notice that unlike Listing 1.1 (simple.py) and Listing 1.2 (arrow.py) no quotation marks
(“) appear in the statement. The value 4 is an example of an integer expression. Python supports other types
of expressions besides integer expressions. An expression is a basic building block of a Python statement.

The number 4 by itself is not a complete Python statement and, therefore, cannot be a program. The
interpreter, however, can evaluate a Python expression. You may type the enter 4 directly into the interactive
interpreter shell:

2.1. INTEGER AND STRING VALUES 14

Python 3.4.3 (v3.4.3:9b73f1c3e601, Feb 24 2015, 22:44:40)
[MSC v.1600 64 bit (AM
D64)] on win32
Type “help”, “copyright”, “credits” or “license” for more information.
>>> 4
4
>>>

The interactive shell attempts to evaluate both expressions and statements. In this case, the expression 4
evaluates to 4. The shell executes what is commonly called the read, eval, print loop. This means the
interactive shell’s sole activity consists of

1. reading the text entered by the user,

2. attempting to evaluate the user’s input in the context of what the user has entered up that point, and

3. printing its evaluation of the user’s input.

If the user enters a 4, the shell interprets it as a 4. If the user enters x = 10, a statement has has no overall
value itself, the shell prints nothing. If the user then enters x, the shell prints the evaluation of x, which is 10.
If the user next enters y, the shell reports a error because y has not been defined in a previous interaction.

Python uses the + symbol with integers to perform normal arithmetic addition, so the interactive shell
can serve as a handy adding machine:

>>> 3 + 4
7
>>> 1 + 2 + 4 + 10 + 3
20
>>> print(1 + 2 + 4 + 10 + 3)
20

The last line evaluated shows how we can use the + symbol to add values within a print statement that
could be part of a Python program.

Consider what happens if we use quote marks around an integer:

>>> 19
19
>>> “19”
’19’
>>> ’19’
’19’

Notice how the output of the interpreter is different. The expression “19” is an example of a string value.
A string is a sequence of characters. Strings most often contain nonnumeric characters:

>>> “Fred”
‘Fred’
>>> ‘Fred’
‘Fred’

Python recognizes both single quotes (‘) and double quotes (“) as valid ways to delimit a string value. The
word delimit means to determine the boundaries or limits of something. The left ‘ symbol determines the

2.1. INTEGER AND STRING VALUES 15

beginning of a string, and the right ‘ symbol that follows specifies the end of the string. If a single quote
marks the beginning of a string value, a single quote must delimit the end of the string. Similarly, the double
quotes, if used instead, must appear in pairs. You may not mix the two kinds of quotation marks when used
to delimit a particular string, as the following interactive sequence shows:

>>> ‘ABC’
‘ABC’
>>> “ABC”
‘ABC’
>>> ‘ABC”

File ““, line 1
‘ABC”

ˆ
SyntaxError: EOL while scanning string literal
>>> “ABC’

File ““, line 1
“ABC’

ˆ
SyntaxError: EOL while scanning string literal

The interpreter’s output always uses single quotes, but it accepts either single or double quotes as valid
input.

Consider the following interaction sequence:

>>> 19
19
>>> “19”
’19’
>>> ’19’
’19’
>>> “Fred”
‘Fred’
>>> ‘Fred’
‘Fred’
>>> Fred
Traceback (most recent call last):

File ““, line 1, in
NameError: name ‘Fred’ is not defined

Notice that with the missing quotation marks the interpreter does not accept the expression Fred.

It is important to note that the expressions 4 and ‘4’ are different. One is an integer expression and
the other is a string expression. All expressions in Python have a type. The type of an expression indicates
the kind of expression it is. An expression’s type is sometimes denoted as its class. At this point we have
considered only integers and strings. The built in type function reveals the type of any Python expression:

>>> type(4)

>>> type(‘4’)

Python associates the type name int with integer expressions and str with string expressions.

The built-in int function creates an actual integer object from a string that looks like an integer, and the
str function creates a string object from the digits that make up an integer:

2.1. INTEGER AND STRING VALUES 16

>>> 4
4
>>> str(4)
‘4’
>>> ‘5’
‘5’
>>> int(‘5’)
5

The expression str(4) evaluates to the string value ‘4’, and int(‘5’) evaluates to the integer value 5.
The int function applied to an integer evaluates simply to the value of the integer itself, and similarly str
applied to a string results in the same value as the original string:

>>> int(4)
4
>>> str(‘Judy’)
‘Judy’

As you might guess, there is little reason for a programmer to tansform an object into itself—the expression
int(4) is more easily expressed as 4, so the utility of the str and int functions will not become apparent
until we introduce variables (Section 2.2) and need to process user input (Section 2.6).

Any integer has a string representation, but not all strings have an integer equivalent:

>>> str(1024)
‘1024’
>>> int(‘wow’)
Traceback (most recent call last):

File ““, line 1, in
ValueError: invalid literal for int() with base 10: ‘wow’
>>> int(‘3.4’)
Traceback (most recent call last):

File ““, line 1, in
ValueError: invalid literal for int() with base 10: ‘3.4’

In Python, neither wow nor 3.4 represent valid integer expressions. In short, if the contents of the string
(the characters that make it up) look like a valid integer number, you safely can apply the int function to
produce the represented integer.

The plus operator (+) works differently for strings; consider:

>>> 5 + 10
15
>>> ‘5’ + ’10’
‘510’
>>> ‘abc’ + ‘xyz’
‘abcxyz’

As you can see, the result of the expression 5 + 10 is very different from ‘5’ + ’10’. The plus operator
splices two strings together in a process known as concatenation. Mixing the two types directly is not
allowed:

>>> ‘5’ + 10
Traceback (most recent call last):

2.2. VARIABLES AND ASSIGNMENT 17

File ““, line 1, in
TypeError: Can’t convert ‘int’ object to str implicitly
>>> 5 + ’10’
Traceback (most recent call last):

File ““, line 1, in
TypeError: unsupported operand type(s) for +: ‘int’ and ‘str’

but the int and str functions can help:

>>> 5 + int(’10’)
15
>>> ‘5’ + str(10)
‘510’

The type function can determine the type of the most complicated expressions:

>>> type(4)

>>> type(‘4’)

>>> type(4 + 7)

>>> type(‘4’ + ‘7’)

>>> type(int(‘3’) + int(4))

Commas may not appear in Python integer values. The number two thousand, four hundred sixty-eight
would be written 2468, not 2,468.

In mathematics, integers are unbounded; said another way, the set of mathematical integers is infinite. In
Python, integers may be arbitrarily large, but the larger the integer, the more memory required to represent
it. This means Python integers theoretically can be as large or as small as needed, but, since a computer
has a finite amount of memory (and the operating system may limit the amount of memory allowed for a
running program), in practice Python integers are bounded by available memory.

2.2 Variables and Assignment

In algebra, variables represent numbers. The same is true in Python, except Python variables also can
represent values other than numbers. Listing 2.1 (variable.py) uses a variable to store an integer value and
then prints the value of the variable.

Listing 2.1: variable.py

x = 10
print(x)

Listing 2.1 (variable.py) contains two statements:

• x = 10

2.2. VARIABLES AND ASSIGNMENT 18

This is an assignment statement. An assignment statement associates a value with a variable. The
key to an assignment statement is the symbol = which is known as the assignment operator. The
statement assigns the integer value 10 to the variable x. Said another way, this statement binds the
variable named x to the value 10. At this point the type of x is int because it is bound to an integer
value.

We may assign and reassign a variable as often as necessary. The type of a variable will change if it
is reassigned an expression of a different type.

• print(x)

This statement prints the variable x’s current value. Note that the lack of quotation marks here is very
important. If x has the value 10, the statement

print(x)

prints 10, the value of the variable x, but the statement

print(‘x’)

prints x, the message containing the single letter x.

The meaning of the assignment operator (=) is different from equality in mathematics. In mathematics,
= asserts that the expression on its left is equal to the expression on its right. In Python, = makes the variable
on its left take on the value of the expression on its right. It is best to read x = 5 as “x is assigned the value
5,” or “x gets the value 5.” This distinction is important since in mathematics equality is symmetric: if
x = 5, we know 5 = x. In Python this symmetry does not exist; the statement

5 = x

attempts to reassign the value of the literal integer value 5, but this cannot be done because 5 is always 5
and cannot be changed. Such a statement will produce an error.

>>> x = 5
>>> x
5
>>> 5 = x

File ““, line 1
SyntaxError: can’t assign to literal

We can reassign different values to a variable as needed, as Listing 2.2 (multipleassignment.py) shows.

Listing 2.2: multipleassignment.py

x = 10
print(x)
x = 20
print(x)
x = 30
print(x)

Observe that each print statement in Listing 2.2 (multipleassignment.py) is identical, but when the pro-
gram runs (as a program, not in the interactive shell) the print statements produce different results:

10
20
30

2.2. VARIABLES AND ASSIGNMENT 19

This program demonstrates that can we cannot always predict the behavior of a statement in isolation,
especially if that statement involves a variable. This is because the statement’s behavior may be dependent
on the assigned values of one or more variables that it uses.

The variable x in Listing 2.2 (multipleassignment.py) has type int, since x is bound to an integer value.
Listing 2.3 (multipleassignment2.py) is an enhancement of Listing 2.2 (multipleassignment.py) that provides
more descriptive print statements.

Listing 2.3: multipleassignment2.py

x = 10
print(‘x = ‘ + str(x))
x = 20
print(‘x = ‘ + str(x))
x = 30
print(‘x = ‘ + str(x))

Listing 2.3 (multipleassignment2.py) outputs

x = 10
x = 20
x = 30

Listing 2.3 (multipleassignment2.py) uses the str function to treat x as a string so the + operator will use
string concatenation:

print(‘x = ‘ + str(x))

The expression ‘x = ‘ + x would not be legal; as indicated in Section 2.1, the plus (+) operator may not
applied with mixed string and integer operands.

Listing 2.4 (multipleassignment3.py) provides a variation of Listing 2.3 (multipleassignment2.py) that
produces the same output.

Listing 2.4: multipleassignment3.py

x = 10
print(‘x =’, x)
x = 20
print(‘x =’, x)
x = 30
print(‘x =’, x)

This version of the print statement:

print(‘x =’, x)

illustrates the print function accepting two parameters. The first parameter is the string ‘x =’, and the
second parameter is the variable x bound to an integer value. The print function allows programmers to
pass multiple expressions to print, each separated by commas. The elements within the parentheses of the
print function comprise what is known as a comma-separated list. The print function prints each element
in the comma-separated list of parameters. The print function automatically prints a space between each
element in the list so the printed text elements do not run together.

A programmer may assign multiple variables in one statement using tuple assignment. Listing 2.5
(tupleassign.py) shows how:

2.2. VARIABLES AND ASSIGNMENT 20

Figure 2.1 Binding a variable to an object

a
2

Listing 2.5: tupleassign.py

x, y, z = 100, -45, 0
print(‘x =’, x, ‘ y =’, y, ‘ z =’, z)

The Listing 2.5 (tupleassign.py) program produces

x = 100 y = -45 z = 0

A tuple is a comma-separated list of expressions. If the variables total and s are defined, the expres-
sion total, 45, s, 0.3 represents a 4-tuple; that is, a tuple with composed of four elements. In the
assignment statement

x, y, z = 100, -45, 0

x, y, z is one tuple, and 100, -45, 0 is another tuple. Tuple assignment works as follows: The first
variable in the tuple on left side of the assignment operator is assigned the value of the first expression in
the tuple on the left side (effectively x = 100). Similarly, the second variable in the tuple on left side of
the assignment operator is assigned the value of the second expression in the tuple on the left side (in effect
y = -45). z gets the value 0.

Tuple assignment works only if the tuple on the left side of the assignment operator contains the same
number of elements as the tuple on the right side, as the following example illustrates:

>>> x, y, z = 45, 3
Traceback (most recent call last):

File ““, line 1, in
ValueError: need more than 2 values to unpack
>>> x, y, z = 45, 3, 23, 8
Traceback (most recent call last):

File ““, line 1, in
ValueError: too many values to unpack (expected 3)

A tuple is a kind of Python type, like int or float, and we explore tuples in more detail in Chapter 11.

An assignment statement binds a variable name to an object. We can visualize this process with boxes
and an arrow as shown in Figure 2.1.

One box represents the variable, so we name the box with the variable’s name. The arrow projecting
from the box points to the object to which the variable is bound. In this case the arrow points to another
box that contains the value 2. The second box represents a memory location that holds the internal binary
representation of the value 2.

2.2. VARIABLES AND ASSIGNMENT 21

Figure 2.2 How variable bindings change as a program runs: step 1

a
a = 2 2

Figure 2.3 How variable bindings change as a program runs: step 2

a = 2
b = 5

To see how variable bindings can change as the computer executes a sequence of assignment statements,
consider the following sequence of Python statements:

a = 2
b = 5
a = 3
a = b
b = 7

Figures 2.2–2.6 illustrate how the variable bindings change as the Python interpreter executes each of the
above statements. Importantly, the statement

a = b

means that a and b both are bound to the same numeric object. Observe that later reassigning b does not
affect a’s value.

Figure 2.4 How variable bindings change as a program runs: step 3

a = 2
b = 5
a = 3

2.2. VARIABLES AND ASSIGNMENT 22

Figure 2.5 How variable bindings change as a program runs: step 4

a = 2
b = 5
a = 3
a = b

b
5

Figure 2.6 How variable bindings change as a program runs: step 5

a = 2
b = 5
a = 3
a = b
b = 7

2.2. VARIABLES AND ASSIGNMENT 23

Not only may a variable’s value change during its use within an executing program; the type of a variable
can change as well. Consider Listing 2.6 (changeabletype.py).

Listing 2.6: changeabletype.py

a = 10
print(‘First, variable a has value’, a, ‘and type’, type(a))
a = ‘ABC’
print(‘Now, variable a has value’, a, ‘and type’, type(a))

Listing 2.6 (changeabletype.py) produces the following output:

First, variable a has value 10 and type
Now, variable a has value ABC and type

Programmers infrequently perform assignments that change a variable’s type. A variable should have
a specific meaning within a program, and its meaning should not change during the program’s execution.
While not always the case, sometimes when a variable’s type changes its meaning changes as well.

A variable that has not been assigned is an undefined variable or unbound variable. Any attempt to use
an undefined variable is an error, as the following sequence from Python’s interactive shell shows:

>>> x = 2
>>> x
2
>>> y
Traceback (most recent call last):

File ““, line 1, in
NameError: name ‘y’ is not defined

The assignment statement binds 2 to the variable x, and after that the interpreter can evaluate x. The
interpreter cannot evaluate the variable y, so it reports an error.

In rare circumstances we may want to undefine a previously defined variable. The del statement does
that, as the following interactive sequence illustrates:

>>> x = 2
>>> x
2
>>> del x
>>> x
Traceback (most recent call last):

File ““, line 1, in
NameError: name ‘x’ is not defined

The del keyword stands for delete, and so del deletes or removes a variable’s definition from the current
interpreter session or from an executing Python program. Figure 2.7 illustrates the definition and subsequent
deletion of variable x. If variables a, b, and c currently are defined, the statement

del a, b, c

undefines all three variables in one statement.

2.3. IDENTIFIERS 24

Figure 2.7 Definition and subsequent deletion of variable x

x = 2
x

x = 2
del x

x
2

2.3 Identifiers

While mathematicians are content with giving their variables one-letter names like x, programmers should
use longer, more descriptive variable names. Names such as sum, height, and sub_total are much better
than the equally permissible s, h, and st. A variable’s name should be related to its purpose within the
program. Good variable names make programs more readable by humans. Since programs often contain
many variables, well-chosen variable names can render an otherwise obscure collection of symbols more
understandable.

Python has strict rules for variable names. A variable name is one example of an identifier. An identifier
is a word used to name things. One of the things an identifier can name is a variable. We will see in later
chapters that identifiers name other things such as functions, classes, and methods. Identifiers have the
following form:

• An identifiers must contain at least one character.

• The first character of an identifiers must be an alphabetic letter (upper or lower case) or the underscore

ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz_

• The remaining characters (if any) may be alphabetic characters (upper or lower case), the underscore,
or a digit

ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz_0123456789

• No other characters (including spaces) are permitted in identifiers.

• A reserved word cannot be used as an identifier (see Table 2.1).

Examples of valid Python identifiers include

• x

• x2

• total

• port_22

2.3. IDENTIFIERS 25

Table 2.1 Python keywords
and del from None try
as elif global nonlocal True
assert else if not while
break except import or with
class False in pass yield
continue finally is raise
def for lambda return

• FLAG.

None of the following words are valid identifiers:

• sub-total (dash is not a legal symbol in an identifier)

• first entry (space is not a legal symbol in an identifier)

• 4all (begins with a digit)

• *2 (the asterisk is not a legal symbol in an identifier)

• class (class is a reserved word)

Python reserves a number of words for special use that could otherwise be used as identifiers. Called
reserved words or keywords, these words are special and are used to define the structure of Python programs
and statements. Table 2.1 lists all the Python reserved words. The purposes of many of these reserved words
are revealed throughout this book.

None of the reserved words in Table 2.1 may be used as identifiers. Fortunately, if you accidentally
attempt to use one of the reserved words as a variable name within a program, the interpreter will issue an
error:

>>> class = 15
File ““, line 1

class = 15
ˆ

SyntaxError: invalid syntax

(see Section 3.6 for more on interpreter generated errors).

To this point we have avoided keywords completely in our programs. This means there is nothing special
about the names print, int, str, or type, other than they happen to be the names of built-in functions.
We are free to reassign these names and use them as variables. Consider the following interactive sequence
that reassigns the name print to mean something new:

>>> print(‘Our good friend print’)
Our good friend print
>>> print

>>> type(print)

>>> print = 77

2.4. FLOATING-POINT NUMBERS 26

>>> print
77
>>> print(‘Our good friend print’)
Traceback (most recent call last):

File ““, line 1, in
TypeError: ‘int’ object is not callable
>>> type(print)

Here we used the name print as a variable. In so doing it lost its original behavior as a function to print
the console. While we can reassign the names print, str, type, etc., it generally is not a good idea to do
so.

Not only can we reassign a function name, but Python allows us to assign a variable to a function.

>>> my_print = print
>>> my_print(‘hello from my_print!’)
hello from my_print!

After binding the variable my_print to print we can use my_print in exactly as we would use the built-in
print function.

Python is a case-sensitive language. This means that capitalization matters. if is a reserved word, but
none of If, IF, or iF is a reserved word. Identifiers also are case sensitive; the variable called Name is
different from the variable called name. Note that three of the reserved words (False, None, and True) are
capitalized.

Programmers generally avoid distinguishing between two variables in the same context merely by dif-
ferences in capitalization. Doing so is more likely to confuse human readers. For the same reason, it is
considered poor practice to give a variable the same name as a reserved word with one or more of its letters
capitalized.

The most important thing to remember about a variable’s name is that it should be well chosen. A
variable’s name should reflect the variable’s purpose within the program. For example, consider a program
controlling a point-of-sale terminal (also known as an electronic cash register). The variable keeping track
of the total cost of goods purchased might be named total or total_cost. Variable names such as a67_99
and fred would be poor choices for such an application.

2.4 Floating-point Numbers

Many computational tasks require numbers that have fractional parts. For example, to compute the area of
a circle given the circle’s radius, we use the value π, or approximately 3.14159. Python supports such non-
integer numbers, and they are called floating-point numbers. The name implies that during mathematical
calculations the decimal point can move or “float” to various positions within the number to maintain the
proper number of significant digits. The Python name for the floating-point type is float. Consider the
following interactive session:

>>> x = 5.62
>>> x
5.62
>>> type(x)

2.4. FLOATING-POINT NUMBERS 27

Table 2.2 Characteristics of Floating-point Numbers
Title Storage Smallest Magnitude Largest Magnitude Minimum Precision
float 64 bits 2.22507×10−308 1.79769×10+308 15 digits

The range of floating-points values (smallest value to largest value, both positive and negative) and precision
(the number of digits available) depends of the Python implementation for a particular machine. Table 2.2
provides some information about floating point values as commonly implemented on most computer sys-
tems. Floating point numbers can be both positive and negative.

As you can see from Table 2.2, unlike Python integers which can be arbitrarily large (or, for negatives,
arbitrarily small), floating-point numbers have definite bounds.

Listing 2.7 (pi-print.py) prints an approximation of the mathematical value π.

Listing 2.7: pi-print.py

pi = 3.14159
print(“Pi =”, pi)
print(“or”, 3.14, “for short”)

The first line in Listing 2.7 (pi-print.py) assigns an approximation of π to the variable named pi, and the
second line prints its value. The last line prints some text along with a literal floating-point value. Any
literal numeric value with a decimal point in a Python program automatically has the type float. This
means the Python literal 2.0 is a float, not an int, even though mathematically we would classify it as an
integer.

Floating-point numbers are an approximation of mathematical real numbers. The range of floating-point
numbers is limited, since each value requires a fixed amount of memory. Floating-point numbers differ from
integers in another, very important way. An integer has an exact representation. This is not true necessarily
for a floating-point number. Consider the real number π. The mathematical constant π is an irrational
number which means it contains an infinite number of digits with no pattern that repeats. Since π contains
an infinite number of digits, a Python program can only approximate π’s value. Because of the limited
number of digits available to floating-point numbers, Python cannot represent exactly even some numbers
with a finite number of digits; for example, the number 23.3123400654033989 contains too many digits
for the float type. As the following interaction sequence shows, Python stores 23.3123400654033989 as
23.312340065403397:

>>> x = 23.3123400654033989
>>> x
23.312340065403397

An example of the problems that can arise due to the inexact nature of floating-point numbers is demon-
strated later in Listing 3.2 (imprecise.py).

We can express floating-point numbers in scientific notation. Since most programming editors do not
provide superscripting and special symbols like×, Python slightly alters the normal scientific notation. The
number 6.022×1023 is written 6.022e23. The number to the left of the e (we can use capital E as well) is
the mantissa, and the number to the right of the e is the exponent of 10. As another example, −5.1 × 10−4
is expressed in Python as -5.1e-4. Listing 2.8 (scientificnotation.py) prints some scientific constants using
scientific notation.

2.4. FLOATING-POINT NUMBERS 28

Listing 2.8: scientificnotation.py

avogadros_number = 6.022e23
c = 2.998e8
print(“Avogadro’s number =”, avogadros_number)
print(“Speed of light =”, c)

The type of any literal expressed scientific notation always has type float; for example, the Python expres-
sion 2e3 is a float, even though conceptually we may consider it the same as integer the 2,000.

Unlike floating-point numbers, integers are whole numbers and cannot store fractional quantities. We
can convert a floating-point to an integer in two fundamentally different ways:

• Rounding adds or subtracts a fractional amount as necessary to produce the integer closest to the
original floating-point value.

• Truncation simply drops the fractional part of the floating-point number, thus keeping whole number
part that remains.

We can see how rounding and truncation differ in Python’s interactive shell:

>>> 28.71
28.71
>>> int(28.71)
28
>>> round(28.71)
29
>>> round(19.47)
19
>>> int(19.47)
19

As we can see, truncation always “rounds down,” while rounding behaves as we would expect.

We also can use the round function to round a floating-point number to a specified number of decimal
places. The round function accepts an optional argument that produces a floating-point rounded to fewer
decimal places. The additional argument must be an integer and specifies the desired number of decimal
places to round. In the shell we see

>>> x
93.34836
>>> round(x)
93
>>> round(x, 2)
93.35
>>> round(x, 3)
93.348
>>> round(x, 0)
93.0
>>> round(x, 1)
93.3
>>> type(round(x))

>>> type(round(x, 1))

2.4. FLOATING-POINT NUMBERS 29

>>> type(round(x, 0))

As we can see, the single-argument version of round produces an integer result, but the two-argument
version produces a floating-point result.

The second argument to the round function may be a negative integer:

>>> x = 28793.54836
>>> round(x)
28794
>>> round(x, 1)
28793.5
>>> round(x, 2)
28793.55
>>> round(x, 0)
28794.0
>>> round(x, 1)
28793.5
>>> round(x, -1)
28790.0
>>> round(x, -2)
28800.0
>>> round(x, -3)
29000.0

The expression round(n, r) rounds floating-point expression n to the 10−r decimal digit; for example,
round(n, -2) rounds floating-point value n to the hundreds place (102). Similarly, round(n, 3) rounds
floating-point value n to the thousandths place (10−3).

The round function can be useful for integer values as well. If the first argument to round is an integer,
and the second argument to round is a negative integer, the second argument specifies the number decimal
places to the left of the decimal point to round. Consider the following experiments:

>>> round(65535)
65535
>>> round(65535, 0)
65535
>>> round(65535, 1)
65535
>>> round(65535, 2)
65535
>>> round(65535, -1)
65540
>>> round(65535, -2)
65500
>>> round(65535, -3)
66000
>>> round(65535, -4)
70000
>>> round(65535, -5)
100000
>>> round(65535, -6)
0

2.5. CONTROL CODES WITHIN STRINGS 30

In all of these cases the round function produced an integer result. As you can see, if the second argument
is a nonnegative integer, the round function evaluates to the original value.

2.5 Control Codes within Strings

The characters that can appear within strings include letters of the alphabet (A-Z, a-z), digits (0-9), punctu-
ation (., :, ,, etc.), and other printable symbols (#, &, %, etc.). In addition to these “normal” characters, we
may embed special characters known as control codes. Control codes control the way the console window
or a printer renders text. The backslash symbol (\) signifies that the character that follows it is a control
code, not a literal character. The string ‘\n’ thus contains a single control code. The backslash is known
as the escape symbol, and in this case we say the n symbol is escaped. The \n control code represents
the newline control code which moves the text cursor down to the next line in the console window. Other
control codes include \t for tab, \f for a form feed (or page eject) on a printer, \b for backspace, and \a
for alert (or bell). The \b and \a do not produce the desired results in the interactive shell, but they work
properly in a command shell. Listing 2.9 (specialchars.py) prints some strings containing some of these
control codes.

Listing 2.9: specialchars.py

print(‘A\nB\nC’)
print(‘D\tE\tF’)
print(‘WX\bYZ’)
print(‘1\a2\a3\a4\a5\a6′)

When executed in a command shell, Listing 2.9 (specialchars.py) produces

A
B
C
D E F
WYZ
123456

On many systems, the computer’s speaker beeps five times when printing the last line.

A string with a single quotation mark at the beginning must be terminated with a single quote; sim-
ilarly, A string with a double quotation mark at the beginning must be terminated with a double quote.
A single-quote string may have embedded double quotes, and a double-quote string may have embedded
single quotes. If you wish to embed a single quote mark within a single-quote string, you can use the
backslash to escape the single quote (\’). An unprotected single quote mark would terminate the string.
Similarly, you may protect a double quote mark in a double-quote string with a backslash (\”). Listing 2.10
(escapequotes.py) shows the various ways in which quotation marks may be embedded within string liter-
als.

Listing 2.10: escapequotes.py

print(“Did you know that ‘word’ is a word?”)
print(‘Did you know that “word” is a word?’)
print(‘Did you know that \’word\’ is a word?’)
print(“Did you know that \”word\” is a word?”)

The output of Listing 2.10 (escapequotes.py) is

2.6. USER INPUT 31

Did you know that ‘word’ is a word?
Did you know that “word” is a word?
Did you know that ‘word’ is a word?
Did you know that “word” is a word?

Since the backslash serves as the escape symbol, in order to embed a literal backslash within a string
you must use two backslashes in succession. Listing 2.11 (printpath.py) prints a string with embedded
backslashes.

Listing 2.11: printpath.py

filename = ‘C:\\Users\\rick’
print(filename)

Listing 2.11 (printpath.py) displays

C:\Users\rick

2.6 User Input

The print function enables a Python program to display textual information to the user. Programs may use
the input function to obtain information from the user. The simplest use of the input function assigns a
string to a variable:

x = input()

The parentheses are empty because the input function does not require any information to do its job.
Listing 2.12 (usinginput.py) demonstrates that the input function produces a string value.

Listing 2.12: usinginput.py

print(‘Please enter some text:’)
x = input()
print(‘Text entered:’, x)
print(‘Type:’, type(x))

The following shows a sample run of Listing 2.12 (usinginput.py):

Please enter some text:
My name is Rick
Text entered: My name is Rick
Type:

The second line shown in the output is entered by the user, and the program prints the first, third, and fourth
lines. After the program prints the message Please enter some text:, the program’s execution stops and
waits for the user to type some text using the keyboard. The user can type, backspace to make changes, and
type some more. The text the user types is not committed until the user presses the enter (or return) key.

Quite often we want to perform calculations and need to get numbers from the user. The input function
produces only strings, but we can use the int function to convert a properly formed string of digits into an
integer. Listing 2.13 (addintegers.py) shows how to obtain an integer from the user.

2.6. USER INPUT 32

Listing 2.13: addintegers.py

print(‘Please enter an integer value:’)
x = input()
print(‘Please enter another integer value:’)
y = input()
num1 = int(x)
num2 = int(y)
print(num1, ‘+’, num2, ‘=’, num1 + num2)

A sample run of Listing 2.13 (addintegers.py) shows

Please enter an integer value:
2
Please enter another integer value:
17
2 + 17 = 19

Lines two and four represent user input, while the program generates the other lines. The program halts
after printing the first line and does not continue until the user provides the input. After the program prints
the second message it again pauses to accept the user’s second entry.

Since user input almost always requires a message to the user about the expected input, the input
function optionally accepts a string that it prints just before the program stops to wait for the user to respond.
The statement

x = input(‘Please enter some text: ‘)

prints the message Please enter some text: and then waits to receive the user’s input to assign to x. We can
express Listing 2.13 (addintegers.py) more compactly using this form of the input function as shown in
Listing 2.14 (addintegers2.py).

Listing 2.14: addintegers2.py

x = input(‘Please enter an integer value: ‘)
y = input(‘Please enter another integer value: ‘)
num1 = int(x)
num2 = int(y)
print(num1, ‘+’, num2, ‘=’, num1 + num2)

Listing 2.15 (addintegers3.py) is even shorter. It combines the input and int functions into one statement.

Listing 2.15: addintegers3.py

num1 = int(input(‘Please enter an integer value: ‘))
num2 = int(input(‘Please enter another integer value: ‘))
print(num1, ‘+’, num2, ‘=’, num1 + num2)

In Listing 2.15 (addintegers3.py) the expression

int(input(‘Please enter an integer value: ‘))

uses a technique known as functional composition. The result of the input function is passed directly to
the int function instead of using the intermediate variables shown in Listing 2.14 (addintegers2.py). We
frequently will use functional composition to make our program code simpler.

2.6. USER INPUT 33

Be careful about code such as

num = int(input(‘Please enter a number: ‘))

This statement expects the user to enter an integer value. If the user types 3, for example, all is well. The
variable num then will refer to the integer object 3. The int function can convert the string ‘3’ to the integer
value 3. The word number is ambiguous, however, so the user might attempt to enter 3.4. In this case the
input statement would return the string ‘3.4’. The int function cannot convert the string ‘3.4’ to an
integer directly, even though it can convert the floating-point number 3.4 to the integer 3. The following
interactive sequence demonstrates:

>>> num = int(input(‘Please enter a number: ‘))
Please enter a number: 3
>>> num
3
>>> num = int(input(‘Please enter a number: ‘))
Please enter a number: 3.4
Traceback (most recent call last):

File ““, line 1, in
ValueError: invalid literal for int() with base 10: ‘3.4’
>>> int(3.4)
3
>>> int(‘3.4’)
Traceback (most recent call last):

File ““, line 1, in
ValueError: invalid literal for int() with base 10: ‘3.4’

This example reveals that the int can convert a string to an integer only if the string looks exactly like an
integer.

We could be more specific and simply request an integer value from the user. If we really want an integer
from the user but want to tolerate decimal places, we could use an additional function in our composition
of functions, as in the following:

>>> num = int(float(input(‘Please enter a number: ‘)))
Please enter a number: 3
>>> num
3
>>> num = int(float(input(‘Please enter a number: ‘)))
Please enter a number: 3.4
>>> num
3

The assignment statement here uses the input function to obtain the number from the user as a string. It
then uses the float function to convert the received string to a floating-point number. Finally it converts
the floating-point number to an integer via the int function. What if you wish to round the user’s input
value instead of truncating it? The following function composition would work in that case:

>>> num = round(float(input(‘Please enter a number: ‘)))
Please enter a number: 3.7
>>> num
4

2.7. CONTROLLING THE PRINT FUNCTION 34

2.7 Controlling the print Function

In Listing 2.13 (addintegers.py) we would prefer that the cursor remain at the end of the printed line so
when the user types a value it appears on the same line as the message prompting for the values. When the
user presses the enter key to complete the input, the cursor automatically will move down to the next line.
The print function as we have seen so far always prints a line of text, and then the cursor moves down
to the next line so any future printing appears on the next line. The print statement accepts an additional
argument that allows the cursor to remain on the same line as the printed text:

print(‘Please enter an integer value:’, end=”)

The expression end=” is known as a keyword argument. The term keyword here means something dif-
ferent from the term keyword used to mean a reserved word. We defer a complete explanation of keyword
arguments until we have explored more of the Python language. For now it is sufficient to know that a print
function call of this form will cause the cursor to remain on the same line as the printed text. Without this
keyword argument, the cursor moves down to the next line after printing the text.

The print statement

print(‘Please enter an integer value: ‘, end=”)

means “Print the message Please enter an integer value:, and then terminate the line with nothing rather
than the normal \n newline code.” Another way to achieve the same result is

print(end=’Please enter an integer value: ‘)

This statement means “Print nothing, and then terminate the line with the string ‘Please enter an integer value:’
rather than the normal \n newline code. The behavior of the two statements is indistinguishable.

The statement

print(‘Please enter an integer value:’)

is an abbreviated form of the statement

print(‘Please enter an integer value:’, end=’\n’)

that is, the default ending for a line of printed text is the string ‘\n’, the newline control code. Similarly,
the statement

print()

is a shorter way to express

print(end=’\n’)

Observe closely the output of Listing 2.16 (printingexample.py).

Listing 2.16: printingexample.py

print(‘A’, end=”)
print(‘B’, end=”)
print(‘C’, end=”)
print()
print(‘X’)
print(‘Y’)
print(‘Z’)

2.8. STRING FORMATTING 35

Listing 2.16 (printingexample.py) displays

ABC
X
Y
Z

The statement

print()

essentially moves the cursor down to next line.

Sometimes it is convenient to divide the output of a single line of printed text over several Python
statements. As an example, we may want to compute part of a complicated calculation, print an intermediate
result, finish the calculation, and print the final answer with the output all appearing on one line of text. The
end keyword argument allows us to do so.

Another keyword argument allows us to control how the print function visually separates the argu-
ments it displays. By default, the print function places a single space in between the items it prints. print
uses a keyword argument named sep to specify the string to use insert between items. The name sep stands
for separator. The default value of sep is the string ‘ ‘, a string containing a single space. Listing 2.17
(printsep.py) shows the sep keyword customizes print’s behavior.

Listing 2.17: printsep.py

w, x, y, z = 10, 15, 20, 25
print(w, x, y, z)
print(w, x, y, z, sep=’,’)
print(w, x, y, z, sep=”)
print(w, x, y, z, sep=’:’)
print(w, x, y, z, sep=’—–‘)

The output of Listing 2.17 (printsep.py) is

10 15 20 25
10,15,20,25
10152025
10:15:20:25
10—–15—–20—–25

The first of the output shows print’s default method of using a single space between printed items. The
second output line uses commas as separators. The third line runs the items together with an empty string
separator. The fifth line shows that the separating string may consist of multiple characters.

2.8 String Formatting

Consider Listing 2.18 (powers10left.py) which prints the first few powers of 10.

Listing 2.18: powers10left.py

print(0, 10**0)
print(1, 10**1)

2.8. STRING FORMATTING 36

print(2, 10**2)
print(3, 10**3)
print(4, 10**4)
print(5, 10**5)
print(6, 10**6)
print(7, 10**7)
print(8, 10**8)
print(9, 10**9)
print(10, 10**10)
print(11, 10**11)
print(12, 10**12)
print(13, 10**13)
print(14, 10**14)
print(15, 10**15)

Listing 2.18 (powers10left.py) prints

0 1
1 10
2 100
3 1000
4 10000
5 100000
6 1000000
7 10000000
8 100000000
9 1000000000
10 10000000000
11 100000000000
12 1000000000000
13 10000000000000
14 100000000000000
15 1000000000000000

Observe that each number is left justified.

Next, consider Listing 2.19 (powers10left2.py) which again prints the first few powers of 10, albeit in
most complicated way.

Listing 2.19: powers10left2.py

print(‘{0} {1}’.format(0, 10**0))
print(‘{0} {1}’.format(1, 10**1))
print(‘{0} {1}’.format(2, 10**2))
print(‘{0} {1}’.format(3, 10**3))
print(‘{0} {1}’.format(4, 10**4))
print(‘{0} {1}’.format(5, 10**5))
print(‘{0} {1}’.format(6, 10**6))
print(‘{0} {1}’.format(7, 10**7))
print(‘{0} {1}’.format(8, 10**8))
print(‘{0} {1}’.format(9, 10**9))
print(‘{0} {1}’.format(10, 10**10))
print(‘{0} {1}’.format(11, 10**11))
print(‘{0} {1}’.format(12, 10**12))
print(‘{0} {1}’.format(13, 10**13))

2.8. STRING FORMATTING 37

print(‘{0} {1}’.format(14, 10**14))
print(‘{0} {1}’.format(15, 10**15))

Listing 2.19 (powers10left2.py) produces output identical to Listing 2.18 (powers10left.py):

0 1
1 10
2 100
3 1000
4 10000
5 100000
6 1000000
7 10000000
8 100000000
9 1000000000
10 10000000000
11 100000000000
12 1000000000000
13 10000000000000
14 100000000000000
15 1000000000000000

The third print statement in Listing 2.19 (powers10left2.py) prints the expression

‘{0} {1}’.format(2, 10**2)

This expression has two main parts:

• ‘{0} {1}’: This is known as the formatting string. It is a Python string because it is a sequence of
characters enclosed with quotes. Notice that the program at no time prints the literal string {0} {1}.
This formatting string serves as a pattern that the second part of the expression will use. {0} and {1}
are placeholders, known as positional parameters, to be replaced by other objects. This formatting
string, therefore, represents two objects separated by a single space.

• format(2, 10**2): This part provides arguments to be substituted into the formatting string. The
first argument, 2, will take the position of the {0} positional parameter in the formatting string. The
value of the second argument, 10**2, which is 100, will replace the {1} positional parameter.

The format operation matches the 2 with the position marked by {0} and the 10**2 with the position
marked by {1}. This somewhat complicated expression evaluates to the simple string ‘2 100’. The print
function then prints this string as the first line of the program’s output.

In the statement

print(‘{0} {1}’.format(7, 10**7))

the expression to print, namely

‘{0} {1}’.format(7, 10**7)

becomes ’7 10000000’, since 7 replaces {0} and 107 = 10000000 replaces {1}. Figure 2.8 shows how the
arguments of format substitute for the positional parameters in the formatting string.

Listing 2.19 (powers10left2.py) provides no advantage over Listing 2.18 (powers10left.py), and it is
more complicated. Is the extra effort of string formatting ever useful? Observe that in both programs each

2.8. STRING FORMATTING 38

Figure 2.8 Placeholder substitution within a formatting string

‘{0} {1}’.format(7, 10**7)

10000000

‘7 10000000’

‘a{0}b{1}c{0}d’.format(‘x’, ‘y’) ‘axbycxd’

‘x’

‘y’

number printed is left justified. Ordinarily we want numeric values appearing in a column to be right-
justified so they align on the right instead of the left. A positional parameter in the format string provides
options for right-justifying the object that takes its place. Listing 2.20 (powers10right.py) uses a string
formatter with enhanced positional parameters to right justify the values it prints.

Listing 2.20: powers10right.py

print(‘{0:>3} {1:>16}’.format(0, 10**0))
print(‘{0:>3} {1:>16}’.format(1, 10**1))
print(‘{0:>3} {1:>16}’.format(2, 10**2))
print(‘{0:>3} {1:>16}’.format(3, 10**3))
print(‘{0:>3} {1:>16}’.format(4, 10**4))
print(‘{0:>3} {1:>16}’.format(5, 10**5))
print(‘{0:>3} {1:>16}’.format(6, 10**6))
print(‘{0:>3} {1:>16}’.format(7, 10**7))
print(‘{0:>3} {1:>16}’.format(8, 10**8))
print(‘{0:>3} {1:>16}’.format(9, 10**9))
print(‘{0:>3} {1:>16}’.format(10, 10**10))
print(‘{0:>3} {1:>16}’.format(11, 10**11))
print(‘{0:>3} {1:>16}’.format(12, 10**12))
print(‘{0:>3} {1:>16}’.format(13, 10**13))
print(‘{0:>3} {1:>16}’.format(14, 10**14))
print(‘{0:>3} {1:>16}’.format(15, 10**15))

Listing 2.20 (powers10right.py) prints

0 1
1 10

2.9. MULTI-LINE STRINGS 39

2 100
3 1000
4 10000
5 100000
6 1000000
7 10000000
8 100000000
9 1000000000

10 10000000000
11 100000000000
12 1000000000000
13 10000000000000
14 100000000000000
15 1000000000000000

The positional parameter {0:>3} means “right-justify the first argument to format within a width of
three characters.” Similarly, the {1:>16} positional parameter indicates that format’s second argument is
to be right justified within 16 places. This is exactly what we need to properly align the two columns of
numbers.

The format string can contain arbitrary text amongst the positional parameters. Consider the following
interactive sequence:

>>> print(‘$${0}//{1}&&{0}ˆ ˆ ˆ{2}abc’.format(6, ‘Fred’, 4.7))
$$6//Fred&&6ˆ ˆ ˆ4.7abc

Note how the resulting string is formatted exactly like the format string, including spaces. The only dif-
ference is the format arguments replace all the positional parameters. Also notice that we may repeat a
positional parameter multiple times within a formatting string.

2.9 Multi-line Strings

A Python string ordinarily spans a single line of text. The following statement is illegal:

x = ‘This is a long string with
several words’

A string literal that begins with a ‘ or ” must be terminated with its matching ‘ or ” on the same line in
which it begins. As we saw in Section 2.5), we can add newline control codes to produce line breaks within
the string:

x = ‘This is a long string with\nseveral words’

This technique, however, obscures the programmer’s view of the string within the source code. Python
provides way to represent a string’s layout more naturally within source code, using triple quotes. The triple
quotes (”’ or “””) delimit strings that can span multiple lines in the source code. Consider Listing 2.21
(multilinestring.py) that uses a multi-line string.

Listing 2.21: multilinestring.py

x = ”’
This is a multi-line

2.10. EXERCISES 40

string that goes on
for three lines!
”’
print(x)

Listing 2.21 (multilinestring.py) displays

This is a multi-line
string that goes on

for three lines!

Observe that the multi-line string obeys indentation and line breaks—essentially reproducing the same
formatting as in the source code. For a fancier example, consider the following two-dimensional rendition
of a three-dimensional cube, rendered with characters:

Listing 2.22: charactercube.py

x = ”’
A cube has 8 corners:

7——8
/| /|
3——4 |
| | | |
| 5—-|-6
|/ |/
1——2

”’
print(x)

Listing 2.22 (charactercube.py) displays

A cube has 8 corners:

7——8
/| /|
3——4 |
| | | |
| 5—-|-6
|/ |/
1——2

The “picture” in the source code looks like the picture on the screen.

We will see in Section 7.3 how Python’s multi-line strings play a major role in source code documenta-
tion.

2.10 Exercises

1. Will the following lines of code print the same thing? Explain why or why not.

2.10. EXERCISES 41

x = 6
print(6)
print(“6”)

2. Will the following lines of code print the same thing? Explain why or why not.

x = 7
print(x)
print(“x”)

3. What is the largest floating-point value available on your system?

4. What is the smallest floating-point value available on your system?

5. What happens if you attempt to use a variable within a program, and that variable has not been
assigned a value?

6. What is wrong with the following statement that attempts to assign the value ten to variable x?

10 = x

7. Once a variable has been properly assigned can its value be changed?

8. In Python can you assign more than one variable in a single statement?

9. Classify each of the following as either a legal or illegal Python identifier:

(a) fred

(b) if

(d) -4

(e) sum_total

(f) sumTotal

(g) sum-total

(h) sum total

(i) sumtotal

(j) While

(k) x2

(l) Private

(m) public

(n) $16

(o) xTwo

(p) _static

(q) _4

(r) ___

(s) 10%

(t) a27834

2.10. EXERCISES 42

(u) wilma’s

10. What can you do if a variable name you would like to use is the same as a reserved word?

11. How is the value 2.45×10−5 expressed as a Python literal?

12. How can you express the literal value 0.0000000000000000000000000449 as a much more compact
Python literal?

13. How can you express the literal value 56992341200000000000000000000000000000 as a much more
compact Python literal?

14. Can a Python programmer do anything to ensure that a variable’s value can never be changed after
its initial assignment?

15. Is “i” a string literal or variable?

16. What is the difference between the following two strings? ‘n’ and ‘\n’?

17. Write a Python program containing exactly one print statement that produces the following output:

A
B
C
D
E
F

18. Write a Python program that simply emits a beep sound when run.

Chapter 3

Expressions and Arithmetic

This chapter uses the Python numeric types introduced in Chapter 2 to build expressions and perform
arithmetic. Some other important concepts are covered—user input, comments, and dealing with errors.

3.1 Expressions

A literal value like 34 and a variable like x are examples of simple expressions. We can use operators to
combine values and variables and form more complex expressions. In Section 2.1 we saw how we can use
the + operator to add integers and concatenate strings. Listing 3.1 (adder.py) shows we can use the addition
operator (+) to add two integers provided by the user.

Listing 3.1: adder.py

value1 = int(input(‘Please enter a number: ‘))
value2 = int(input(‘Please enter another number: ‘))
sum = value1 + value2
print(value1, ‘+’, value2, ‘=’, sum)

To review, in Listing 3.1 (adder.py):

• value1 = int(input(‘Please enter a number: ‘))

This statement prompts the user to enter some information. After displaying the prompt string Please
enter an integer value:, this statement causes the program’s execution to stop and wait for the user to
type in some text and then press the enter key. The string produced by the input function is passed
off to the int function which produces an integer value to assign to the variable value1. If the user
types the sequence 431 and then presses the enter key, value1 is assigned the integer 431.

• value2 = int(input(‘Please enter another number: ‘))

This statement is similar to the first statement.

• sum = value1 + value2;

This is an assignment statement because is contains the assignment operator (=). The variable sum
appears to the left of the assignment operator, so sum will receive a value when this statement exe-
cutes. To the right of the assignment operator is an arithmetic expression involving two variables and

3.1. EXPRESSIONS 44

Table 3.1 Commonly used Python arithmetic binary operators
Expression Meaning

x + y x added to y, if x and y are numbers
x concatenated to y, if x and y are strings

x – y x take away y, if x and y are numbers
x * y x times y, if x and y are numbers

x concatenated with itself y times, if x is a string and y is an integer
y concatenated with itself x times, if y is a string and x is an integer

x / y x divided by y, if x and y are numbers
x // y Floor of x divided by y, if x and y are numbers
x % y Remainder of x divided by y, if x and y are numbers
x ** y x raised to y power, if x and y are numbers

the addition operator. The expression is evaluated by adding together the values bound to the two
variables. Once the addition expression’s value has been determined, that value is assigned to the sum
variable.

• print(value1, ‘+’, value2, ‘=’, sum)

This statement prints the values of the three variables with some additional decoration to make the
output clear about what it is showing.

All expressions have a value. The process of determining the expression’s value is called evaluation.
Evaluating simple expressions is easy. The literal value 54 evaluates to 54. The value of a variable named x
is the value stored in the memory location bound to x. The value of a more complex expression is found by
evaluating the smaller expressions that make it up and combining them with operators to form potentially
new values.

Table 3.1 contains the most commonly used Python arithmetic operators. The common arithmetic
operations, addition, subtraction, multiplication, division, and power behave in the expected way. The
// and % operators are not common arithmetic operators in everyday practice, but they are very useful in
programming. The // operator is called integer division, and the % operator is the modulus or remainder
operator. 25/3 is 8.3333. Three does not divide into 25 evenly. In fact, three goes into 25 eight times with a
remainder of one. Here, eight is the quotient, and one is the remainder. 25//3 is 8 (the quotient), and 25%3
is 1 (the remainder).

All these operators are classified as binary operators because they operate on two operands. In the
statement

x = y + z

on the right side of the assignment operator is an addition expression y + z. The two operands of the +
operator are y and z.

Two operators, + and -, can be used as unary operators. A unary operator has only one operand. The –
unary operator expects a single numeric expression (literal number, variable, or more complicated numeric
expression within parentheses) immediately to its right; it computes the additive inverse of its operand.
If the operand is positive (greater than zero), the result is a negative value of the same magnitude; if the
operand is negative (less than zero), the result is a positive value of the same magnitude. Zero is unaffected.
For example, the following code sequence

x, y, z = 3, -4, 0

3.1. EXPRESSIONS 45

x = -x
y = -y
z = -z
print(x, y, z)

within a program would print

-3 4 0

The following statement

print(-(4 – 5))

within a program would print

The unary + operator is present only for completeness; when applied to a numeric value, variable, or
expression, the resulting value is no different from the original value of its operand. Omitting the unary +
operator from the following statement

x = +y

does not change its behavior.

All the arithmetic operators are subject to the limitations of the data types on which they operate; for
example, consider the following interaction sequence:

>>> 2.0**10
1024.0
>>> 2.0**100
1.2676506002282294e+30
>>> 2.0**1000
1.0715086071862673e+301
>>> 2.0**10000
Traceback (most recent call last):

File ““, line 1, in
OverflowError: (34, ‘Result too large’)

The expression 2.0**10000 will not evaluate to the correct answer since the correct answer falls outside
the range of Python’s floating point values.

When we apply the +, -, *, //, %, or ** operators to two integers, the result is an integer. The statement

print(25//4, 4//25)

prints

6 0

The // operator produces an integer result when used with integers. In the first case above 25 divided by 4
is 6 with a remainder of 1, and in the second case 4 divided by 25 is 0 with a remainder of 4. Since integers
are whole numbers, the // operator discards any fractional part of the answer. The process of discarding
the fractional part of a number leaving only the whole number part is called truncation. Truncation is not
rounding; for example, 13 divided by 5 is 2.6, but 2.6 truncates to 2.

3.1. EXPRESSIONS 46

Figure 3.1 Integer division and modulus

4)25

-24

6 25//4

25%4

Truncation simply removes any fractional part of the value. It does not round.
Both 10.01 and 10.999 truncate to 10.

The modulus operator (%) computes the remainder of integer division; thus,

print(25%4, 4%25)

prints

1 4

since 25 divided by 4 is 6 with a remainder of 1, and 4 divided by 25 is 0 with a remainder of 4. Figure 3.1
shows the relationship between integer division and modulus.

The modulus operator is more useful than it may first appear. Listing 3.9 (timeconv.py) shows how it
can be used to convert a given number of seconds to hours, minutes, and seconds.

The / operator applied to two integers produces a floating-point result. The statement

print(25/4, 4/25)

prints

6.25 0.16

These results are what we would expect from a hand-held calculator. Floating-point arithmetic always
produces a floating-point result.

Recall from Section 2.4 that integers can be represented exactly, but floating-point numbers are im-
precise approximations of real numbers. Listing 3.2 (imprecise.py) clearly demonstrates the weakness of
floating point numbers.

Listing 3.2: imprecise.py

3.1. EXPRESSIONS 47

one = 1.0
one_third = 1.0/3.0
zero = one – one_third – one_third – one_third

print(‘one =’, one, ‘ one_third =’, one_third, ‘ zero =’, zero)

one = 1.0 one_third = 0.3333333333333333 zero = 1.1102230246251565e-16

The reported result is 1.1102230246251565 × 10−16, or 0.00000000000000011102230246251565, While
this number is very small, with real numbers we get

1−
1
3
−

1
3
−

1
3
= 0

Floating-point numbers are not real numbers, so the result of 1.0/3.0 cannot be represented exactly without
infinite precision. In the decimal (base 10) number system, one-third is a repeating fraction, so it has an
infinite number of digits. Even simple nonrepeating decimal numbers can be a problem. One-tenth (0.1) is
obviously nonrepeating, so we can express it exactly with a finite number of digits. As it turns out, since
numbers within computers are stored in binary (base 2) form, even one-tenth cannot be represented exactly
with floating-point numbers, as Listing 3.3 (imprecise10.py) illustrates.

Listing 3.3: imprecise10.py

one = 1.0
one_tenth = 1.0/10.0
zero = one – one_tenth – one_tenth – one_tenth \

– one_tenth – one_tenth – one_tenth \
– one_tenth – one_tenth – one_tenth \
– one_tenth

print(‘one =’, one, ‘ one_tenth =’, one_tenth, ‘ zero =’, zero)

The program’s output is

one = 1.0 one_tenth = 0.1 zero = 1.3877787807814457e-16

Surely the reported answer (1.3877787807814457× 10−16) is close to the correct answer (zero). If you
round our answer to the one-hundred trillionth place (15 places behind the decimal point), it is correct.

In Listing 3.3 (imprecise10.py) lines 3–6 make up a single Python statement. If that single statement
that performs nine subtractions were written on one line, it would flow well off the page or off the editing
window. Ordinarily a Python statement ends at the end of the source code line. A programmer may break
up a very long line over two or more lines by using the backslash (\) symbol at the end of an incomplete
line. When the interpreter is processing a line that ends with a \, it automatically joins the line that follows.
The interpreter thus sees a very long but complete Python statement.

The Python interpreter also automatically joins long statements spread over multiple lines in the source
code if it dectects an opening parenthesis (, square bracket [, or curly brace { that is unmatched by its
corresponding closing symbol. The following is a legal Python statement spread over two lines in the
source code:

x = (int(input(‘Please enter an integer’))
+ (y – 2) + 16) * 2

3.1. EXPRESSIONS 48

The last closing parenthesis on the second line matches the first opening parenthesis on the first line. No
backslash symbol is required at the end of the first line. The interpreter will begin scanning the first line,
matching closing parentheses with opening parentheses. When it gets to the end of the line and has not
detected a closing parenthesis to match an earlier opening parenthesis, the interpreter assumes it must appear
on a subsequent line, and so continues scanning until it completes the long statement. If the interpreter does
not find expected closing parenthesis in a program, it issues a error. In the Python interactive shell, the
interpreter keeps waiting until the user complies or otherwise types something that causes an error:

>>> y = 10
>>> x = (int(input(‘Please enter an integer: ‘))
… + (y – 2) + 16
…
…
…
…
…
… ) * 2
Please enter an integer: 3
>>> x
54

Since computers represent floating-point values internally in binary form, if we choose a binary frac-

tional power, the mathematics will work out precisely. Python can represent the fraction
1
4
= 0.25 = 2−2

exactly. Listing 3.4 (precise4.py) illustrates.

Listing 3.4: precise4.py

one = 1.0
one_fourth = 1.0/4.0
zero = one – one_fourth – one_fourth – one_fourth – one_fourth
print(‘one =’, one, ‘ one-fourth =’, one_fourth, ‘ zero =’, zero)

Listing 3.4 (precise4.py) behaves much better than the previous examples:

ne = 1.0 one-fourth = 0.25 zero = 0.0

Our computed zero actually is zero.

When should you use integers and when should you use floating-point numbers? A good rule of thumb
is this: use integers to count things and use floating-point numbers for quantities obtained from a measuring
device. As examples, we can measure length with a ruler or a laser range finder; we can measure volume
with a graduated cylinder or a flow meter; we can measure mass with a spring scale or triple-beam balance.
In all of these cases, the accuracy of the measured quantity is limited by the accuracy of the measuring
device and the competence of the person or system performing the measurement. Environmental factors
such as temperature or air density can affect some measurements. In general, the degree of inexactness of
such measured quantities is far greater than that of the floating-point values that represent them.

Despite their inexactness, floating-point numbers are used every day throughout the world to solve so-
phisticated scientific and engineering problems. The limitations of floating-point numbers are unavoidable
since values with infinite characteristics cannot be represented in a finite way. Floating-point numbers
provide a good trade-off of precision for practicality.

3.2. MIXED TYPE EXPRESSIONS 49

3.2 Mixed Type Expressions

Expressions may contain mixed integer and floating-point elements; for example, in the following program
fragment

x = 4
y = 10.2
sum = x + y

x is an integer and y is a floating-point number. What type is the expression x + y? Except in the case of
the / operator, arithmetic expressions that involve only integers produce an integer result. All arithmetic
operators applied to floating-point numbers produce a floating-point result. When an operator has mixed
operands—one operand an integer and the other a floating-point number—the interpreter treats the integer
operand as floating-point number and performs floating-point arithmetic. This means x + y is a floating-
point expression, and the assignment will make the variable sum bind to a floating-point value.

3.3 Operator Precedence and Associativity

When different operators appear in the same expression, the normal rules of arithmetic apply. All Python
operators have a precedence and associativity:

• Precedence—when an expression contains two different kinds of operators, which should be applied
first?

• Associativity—when an expression contains two operators with the same precedence, which should
be applied first?

To see how precedence works, consider the expression

2 + 3 * 4

Should it be interpreted as

(2 + 3) * 4

(that is, 20), or rather is

2 + (3 * 4)

(that is, 14) the correct interpretation? As in normal arithmetic, multiplication and division in Python have
equal importance and are performed before addition and subtraction. We say multiplication and division
have precedence over addition and subtraction. In the expression

2 + 3 * 4

the multiplication is performed before addition, since multiplication has precedence over addition. The
result is 14. The multiplicative operators (*, /, //, and %) have equal precedence with each other, and the
additive operators (binary + and -) have equal precedence with each other. The multiplicative operators
have precedence over the additive operators.

As in standard arithmetic, a Python programmer can use parentheses to override the precedence rules
and force addition to be performed before multiplication. The expression

3.3. OPERATOR PRECEDENCE AND ASSOCIATIVITY 50

Table 3.2 Operator precedence and associativity. The operators in each row have a higher precedence than
the operators below it. Operators within a row have the same precedence.

Arity Operators Associativity
Binary ** Right
Unary +, –
Binary *, /, //, % Left
Binary +, – Left
Binary = Right

(2 + 3) * 4

evaluates to 20. The parentheses in a Python arithmetic expression may be arranged and nested in any ways
that are acceptable in standard arithmetic.

To see how associativity works, consider the expression

2 – 3 – 4

The two operators are the same, so they have equal precedence. Should the first subtraction operator be
applied before the second, as in

(2 – 3) – 4

(that is, −5), or rather is

2 – (3 – 4)

(that is, 3) the correct interpretation? The former (−5) is the correct interpretation. We say that the subtrac-
tion operator is left associative, and the evaluation is left to right. This interpretation agrees with standard
arithmetic rules. All binary operators except assignment are left associative.

As in the case of precedence, we can use parentheses to override the natural associativity within an
expression.

The unary operators have a higher precedence than the binary operators, and the unary operators are
right associative. This means the statements

print(-3 + 2)
print(-(3 + 2))

which display

-1
-5

behave as expected.

Table 3.2 shows the precedence and associativity rules for some Python operators.

The assignment operator is a different kind of operator from the arithmetic operators. Programmers
use the assignment operator only to build assignment statements. Python does not allow the assignment
operator to be part of a larger expression or part of another statement. As such, the notions of precedence
and associativity do not apply in the context of the assignment operator. Python does, however, support a
special kind of assignment statement called chained assignment. The code

3.4. FORMATTING EXPRESSIONS 51

w = x = y = z

assigns the value of the rightmost variable (in this case z) to all the other variables (w, x, and y) to its left.
To initialize several variables to zero in one statement, you can write

sum = count = 0

which is slightly shorter than tuple assignment:

sum, count = 0, 0

3.4 Formatting Expressions

Python offers considerable flexibility for formatting arithmetic expressions; for example, suppose a program
is using the variables x and y to hold data, and we wish to use those variables within a mathematical
expression like the following from algebra:

3x+2y−5

Unlike algebra, Python has no implicit multiplication. This means we must write 3x as 3*x. We may not
omit the * operator.

We can print the value of the complete expression above as follows:

print(3*x + 2*y – 5)

This formatting is preferred, as it follows closely the style used in mathematics. The following is equally
acceptable to the Python interpreter:

print(3*x+2*y-5)

Note the lack of spaces. Most agree that this formatting, while legal Python, is less readable by humans.
Since people develop and read source code, human readability is important. Some suggest that spaces be
used around all binary operators, as in the following:

print(3 * x + 2 * y – 5)

In this case such a practice reduces the readability, since it make it appear as the operators have equal
precedence (which they do not—spacing in an expression does not influence operator precedence). The
first way we wrote the expression natrually grouped together the factors within a term, just as is common
in algebra. The following is computationally equivalent in Python but misleading and should be avoided:

print(3 * x+2 * y-5)

Again, spacing does not affect operator precedence, but this formatting makes it appear that the addition
and the subtraction will take place before the multiplication. Psychologically, the lack of space makes it
appear that + and – “bind” their operands more tightly than does *. This is not true, and this statement is
easily misinterpreted by a human reader.

The bottom line is that you should strive to format your Python source code in a way that enhances
human readability. Why is this important? Teams of programmers develop commercial software. They
must be able to review and revise code written by others. Any coding techniques that make it easier for
people to read and understand each other’s code greatly facilitates the development process.

If you really need to add and subtract in the expression above before performing the multiplications,
you can use parentheses to override the normal precedence rules, as in:

3.5. COMMENTS 52

print(3 * (x + 2) * (y – 5))

The following formatting:

print(3*(x + 2)*(y – 5))

better presents the expression as it you would find it in a algebra book.

3.5 Comments

Good programmers annotate their code by inserting remarks that explain the purpose of a section of code or
why they chose to write a section of code the way they did. These notes are meant for human readers, not
the interpreter. It is common in industry for programs to be reviewed for correctness by other programmers
or technical managers. Well-chosen identifiers (see Section 2.3) and comments can aid this assessment
process. Also, in practice, teams of programmers develop software. A different programmer may be
required to finish or fix a part of the program written by someone else. Well-written comments can help
others understand new code quicker and increase their productivity modifying old or unfinished code. While
it may seem difficult to believe, even the same programmer working on her own code months later can have
a difficult time remembering what various parts do. Comments can help greatly.

Any text contained within comments is ignored by the Python interpreter. The # symbol begins a
comment in the source code. The comment is in effect until the end of the line of code:

# Compute the average of the values
avg = sum / number

The first line here is a comment that explains what the statement that follows it is supposed to do. The
comment begins with the # symbol and continues until the end of that line. The interpreter will ignore the
# symbol and the contents of the rest of the line. You also may append a short comment to the end of a
statement:

avg = sum / number # Compute the average of the values

Here, an executable statement and the comment appear on the same line. The interpreter will read the
assignment statement, but it will ignore the comment.

How are comments best used? Avoid making a remark about the obvious; for example:

result = 0 # Assign the value zero to the variable named result

The effect of this statement is clear to anyone with even minimal Python programming experience. Thus, the
audience of the comments should be taken into account; generally, “routine” activities require no remarks.
Even though the effect of the above statement is clear, its purpose may need a comment. For example:

result = 0 # Ensures ‘result’ has a well-defined minimum value

This remark may be crucial for readers to completely understand how a particular part of a program works.
In general, programmers are not prone to providing too many comments. When in doubt, add a remark.
The extra time it takes to write good comments is well worth the effort.

3.6. ERRORS 53

3.6 Errors

Beginning programmers make mistakes writing programs because of inexperience in programming in gen-
eral or due to unfamiliarity with a programming language. Seasoned programmers make mistakes due to
carelessness or because the proposed solution to a problem is faulty and the correct implementation of an
incorrect solution will not produce a correct program.

In Python, there are three general kinds of errors: syntax errors, run-time exceptions, and logic errors.

3.6.1 Syntax Errors

The interpreter is designed to execute all valid Python programs. The interpreter reads the Python source
file and translates it into a executable form. This is the translation phase. If the interpreter detects an
invalid program statement during the translation phase, it will terminate the program’s execution and report
an error. Such errors result from the programmer’s misuse of the language. A syntax error is a common
error that the interpreter can detect when attempting to translate a Python statement into machine language.
For example, in English one can say

The boy walks quickly.

This sentence uses correct syntax. However, the sentence

The boy walk quickly.

is not correct syntactically: the number of the subject (singular form) disagrees with the number of the verb
(plural form). It contains a syntax error. It violates a grammatical rule of the English language. Similarly,
the Python statement

x = y + 2

is syntactically correct because it obeys the rules for the structure of an assignment statement described in
Section 2.2. However, consider replacing this assignment statement with a slightly modified version:

y + 2 = x

If a statement like this one appears in a program, the interpreter will issue an error message; Listing 3.5
(error.py) attempts such an assignment.

Listing 3.5: error.py

y = 5
x = y + 2
y + 2 = x

When runningListing 3.5 (error.py) the interpreter displays

File “error.py”, line 3
y + 2 = x
ˆ

SyntaxError: can’t assign to operator

3.6. ERRORS 54

The syntax of Python does not allow an expression like y + 2 to appear on the left side of the assignment
operator.

Other common syntax errors arise from simple typographical errors like mismatched parentheses

>>> x = )3 + 4)
File ““, line 1

x = )3 + 4)
ˆ

SyntaxError: invalid syntax

or mismatched string quotes

>>> x = ‘hello”
File ““, line 1

x = ‘hello”
ˆ

SyntaxError: EOL while scanning string literal

or faulty indentation.

>>> x = 2
>>> y = 5

File ““, line 1
y = 5
ˆ

IndentationError: unexpected indent

These examples illustrate just a few of the ways programmers can write ill-formed code.

The interpreter detects syntax errors before it begins running the program, and so it will not execute any
parts of a program that contains syntax errors.

3.6.2 Run-time Exceptions

A syntactically correct Python program still can have problems. Some language errors depend on the
context of the program’s execution. Such errors are called run-time exceptions or run-time errors. We say
the interpreter raises an exception. Run-time exceptions arise after the interpreter’s translation phase and
during the program’s execution phase.

The interpreter may issue an exception for a syntactically correct statement like

x = y + 2

if the variable y has yet to be assigned; for example, if the statement appears at line 12 and by that point y
has not been assigned, we are informed:

>>> x = y + 2
Traceback (most recent call last):

File “error.py”, line 12, in
NameError: name ‘y’ is not defined

Consider Listing 3.6 (dividedanger.py) which contains an error that manifests itself only in one particular
situation.

3.6. ERRORS 55

Listing 3.6: dividedanger.py

# File dividedanger.py

# Get two integers from the user
print(‘Please enter two numbers to divide.’)
dividend = int(input(‘Please enter the dividend: ‘))
divisor = int(input(‘Please enter the divisor: ‘))
# Divide them and report the result
print(dividend, ‘/’, divisor, “=”, dividend/divisor)

The expression

dividend/divisor

is potentially dangerous. If the user enters, for example, 32 and 4, the program works nicely

Please enter two numbers to divide.
Please enter the dividend: 32
Please enter the divisor: 4
32 / 4 = 8.0

If the user instead types the numbers 32 and 0, the program reports an error and terminates:

Please enter two numbers to divide.
Please enter the dividend: 32
Please enter the divisor: 0
Traceback (most recent call last):

File “C:\Users\rick\Desktop\changeable.py”, line 8, in
print(dividend, ‘/’, divisor, “=”, dividend/divisor)

ZeroDivisionError: division by zero

Division by zero is undefined in mathematics, and division by zero in Python is illegal.

As another example, consider Listing 3.7 (halve.py).

Listing 3.7: halve.py

# Get a number from the user
value = int(input(‘Please enter a number to cut in half: ‘))
# Report the result
print(value/2)

Some sample runs of Listing 3.7 (halve.py) reveal

Please enter a number to cut in half: 100
50.0

and

Please enter a number to cut in half: 19.41
9.705

So far, so good, but what if the user does not follow the on-screen instructions?

3.6. ERRORS 56

Please enter a number to cut in half: Bobby
Traceback (most recent call last):

File “C:\Users\rick\Desktop\changeable.py”, line 122, in
value = int(input(‘Please enter a number to cut in half: ‘))

File ““, line 1, in
NameError: name ‘Bobby’ is not defined

Please enter a number to cut in half: ‘Bobby’
Traceback (most recent call last):

File “C:\Users\rick\Desktop\changeable.py”, line 124, in
print(value/2)

TypeError: unsupported operand type(s) for /: ‘str’ and ‘int’

Since the programmer cannot predict what the user will provide as input, this program is doomed
eventually. Fortunately, in Chapter 12 we will examine techniques that allow programmers to avoid these
kinds of problems.

The interpreter detects syntax errors immediately. Syntax errors never make it out of the translation
phase. Sometimes run-time exceptions do not reveal themselves immediately. The interpreter issues a
run-time exception only when it attempts to execute the faulty statement. In Chapter 4 we will see how to
write programs that optionally execute some statements only under certain conditions. If those conditions
do not arise during testing, the faulty code does not get a chance to execute. This means the error may lie
undetected until a user stumbles upon it after the software is deployed. Run-time exceptions, therefore, are
more troublesome than syntax errors.

3.6.3 Logic Errors

The interpreter can detect syntax errors during the translation phase and uncover run-time exceptions during
the execution phase. Both kinds of problems represent violations of the Python language. Such errors are
the easiest to repair because the interpreter indicates the exact location within the source code where it
detected the problem.

Consider the effects of replacing the expression

dividend/divisor

in Listing 3.6 (dividedanger.py) with the expression:

divisor/dividend

The program runs, and unless the user enters a value of zero for the dividend, the interpreter will report no
errors. However, the answer it computes is not correct in general. The only time the program will print
the correct answer is when dividend equals divisor. The program contains an error, but the interpreter is
unable detect the problem. An error of this type is known as a logic error.

Listing 3.11 (faultytempconv.py) is an example of a program that contains a logic error. Listing 3.11
(faultytempconv.py) runs without the interpreter reporting any errors, but it produces incorrect results.

Beginning programmers tend to struggle early on with syntax and run-time errors due to their unfamil-
iarity with the language. The interpreter’s error messages are actually the programmer’s best friend. As the
programmer gains experience with the language and the programs written become more complicated, the

3.7. ARITHMETIC EXAMPLES 57

number of non-logic errors decrease or are trivially fixed and the number of logic errors increase. Unfortu-
nately, the interpreter is powerless to provide any insight into the nature and location of logic errors. Logic
errors, therefore, tend to be the most difficult to find and repair. Programmers frequently use tools such as
debuggers to help them locate and fix logic errors, but these tools are far from automatic in their operation.

Undiscovered run-time errors and logic errors that lurk in software are commonly called bugs. The
interpreter reports execution errors (exceptions) only when the conditions are right that reveal those errors.
The interpreter is of no help at all with logic errors. Such bugs are the major source of frustration for de-
velopers. The frustration often arises because in complex programs the bugs sometimes reveal themselves
only in certain situations that are difficult to reproduce exactly during testing. You will discover this frus-
tration as your programs become more complicated. The good news is that programming experience and
the disciplined application of good programming techniques can help reduce the number of logic errors.
The bad news is that since software development in an inherently human intellectual pursuit, logic errors
are inevitable. Accidentally introducing and later finding and eliminating logic errors is an integral part of
the programming process.

3.7 Arithmetic Examples

Suppose we wish to convert temperature from degrees Fahrenheit to degrees Celsius. The following formula
provides the necessary mathematics:

◦C =
5
9
× (◦F−32)

Listing 3.8 (tempconv.py) implements the conversion in Python.

Listing 3.8: tempconv.py

# File tempconv.py
# Author: Rick Halterman
# Last modified: August 22, 2014
# Converts degrees Fahrenheit to degrees Celsius
# Based on the formula found at
# http://en.wikipedia.org/wiki/Conversion_of_units_of_temperature

# Prompt user for temperature to convert and read the supplied value
degreesF = float(input(‘Enter the temperature in degrees F: ‘))
# Perform the conversion
degreesC = 5/9*(degreesF – 32)
# Report the result
print(degreesF, ‘degrees F =’, degreesC, ‘degrees C’)

Listing 3.8 (tempconv.py) contains comments that give an overview of the program’s purpose and pro-
vide some details about its construction. Comments also document each step explaining the code’s logic.
Some sample runs show how the program behaves:

Enter the temperature in degrees F: 212
212 degrees F = 100.0 degrees C

Enter the temperature in degrees F: 32
32 degrees F = 0.0 degrees C

3.7. ARITHMETIC EXAMPLES 58

Enter the temperature in degrees F: -40
-40 degrees F = -40.0 degrees C

Listing 3.9 (timeconv.py) uses integer division and modulus to split up a given number of seconds to
hours, minutes, and seconds.

Listing 3.9: timeconv.py

# File timeconv.py

# Get the number of seconds
seconds = int(input(“Please enter the number of seconds:”))
# First, compute the number of hours in the given number of seconds
# Note: integer division with possible truncation
hours = seconds // 3600 # 3600 seconds = 1 hours
# Compute the remaining seconds after the hours are accounted for
seconds = seconds % 3600
# Next, compute the number of minutes in the remaining number of seconds
minutes = seconds // 60 # 60 seconds = 1 minute
# Compute the remaining seconds after the minutes are accounted for
seconds = seconds % 60
# Report the results
print(hours, “hr,”, minutes, “min,”, seconds, “sec”)

If the user enters 10000, the program prints 2 hr, 46 min, 40 sec. Notice the assignments to the
seconds variable, such as

seconds = seconds % 3600

The right side of the assignment operator (=) is first evaluated. The statement assigns back to the seconds
variable the remainder of seconds divided by 3,600. This statement can alter the value of seconds if the
current value of seconds is greater than 3,600. A similar statement that occurs frequently in programs is
one like

x = x + 1

This statement increments the variable x to make it one bigger. A statement like this one provides fur-
ther evidence that the Python assignment operator does not mean mathematical equality. The following
statement from mathematics

x = x+1

surely is never true; a number cannot be equal to one more than itself. If that were the case, I would deposit
one dollar in the bank and then insist that I really had two dollars in the bank, since a number is equal to
one more than itself. That two dollars would become $3.00, then $4.00, etc., and soon I would be rich. In
Python, however, this statement simply means “add one to x’s current value and update x with the result.”

A variation on Listing 3.9 (timeconv.py), Listing 3.10 (enhancedtimeconv.py) performs the same logic
to compute the time components (hours, minutes, and seconds), but it uses simpler arithmetic to pro-
duce a slightly different output—instead of printing 11,045 seconds as 3 hr, 4 min, 5 sec, Listing 3.10
(enhancedtimeconv.py) displays it as 3:04:05. It is trivial to modify Listing 3.9 (timeconv.py) so that it
would print 3:4:5, but Listing 3.10 (enhancedtimeconv.py) includes some extra arithmetic to put leading
zeroes in front of single-digit values for minutes and seconds as is done on digital clock displays.

3.8. MORE ARITHMETIC OPERATORS 59

Listing 3.10: enhancedtimeconv.py

# File enhancedtimeconv.py

Listing 3.10 (enhancedtimeconv.py) uses the fact that if x is a one- or two-digit number, x % 10 is the tens
digit of x. If x % 10 is zero, x is necessarily a one-digit number.

3.8 More Arithmetic Operators

As Listing 3.10 (enhancedtimeconv.py) demonstrates, an executing program can alter a variable’s value by
performing some arithmetic on its current value. A variable may increase by one or decrease by five. The
statement

x = x + 1

increments x by one, making it one bigger than it was before this statement was executed. Python has a
shorter statement that accomplishes the same effect:

x += 1

This is the increment statement. A similar decrement statement is available:

x -= 1 # Same as x = x – 1

Python provides a more general way of simplifying a statement that modifies a variable through simple
arithmetic. For example, the statement

x = x + 5

can be shorted to

3.8. MORE ARITHMETIC OPERATORS 60

x += 5

This statement means “increase x by five.” Any statement of the form

x op= exp

where

• x is a variable.

• op= is an arithmetic operator combined with the assignment operator; for our purposes, the ones most
useful to us are +=, -=, *=, /=, //=, and %=.

• exp is an expression compatible with the variable x.

Arithmetic reassignment statements of this form are equivalent to

x = x op exp

This means the statement

x *= y + z

is equivalent to

x = x * (y + z)

The version using the arithmetic assignment does not require parentheses. The arithmetic assignment is
especially handy if we need to modify a variable with a long name; consider

temporary_filename_length = temporary_filename_length / (y + z)

versus

temporary_filename_length /= y + z

Do not accidentally reverse the order of the symbols for the arithmetic assignment operators, like in the
statement

x =+ 5

Notice that the + and = symbols have been reversed. The compiler interprets this statement as if it had been
written

x = +5

that is, assignment and the unary operator. This assigns exactly five to x instead of increasing it by five.

Similarly,

x =- 3

would assign −3 to x instead of decreasing x by three.

3.9. ALGORITHMS 61

3.9 Algorithms

Have you ever tried to explain to someone how to perform a reasonably complex task? The task could
involve how to make a loaf of bread from scratch, how to get to the zoo from city hall, or how to factor
an algebraic expression. Were you able to explain all the steps perfectly without omitting any important
details critical to the task’s solution? Were you frustrated because the person wanting to perform the task
obviously was misunderstanding some of the steps in the process, and you believed you were making
everything perfectly clear? Have you ever attempted to follow a recipe for your favorite dish only to
discover that some of the instructions were unclear or ambiguous? Have you ever faithfully followed the
travel directions provided by a friend and, in the end, found yourself nowhere near the intended destination?

Often it is easy to envision the steps to complete a task but hard to communicate precisely to someone
else how to perform those steps. We may have completed the task many times, or we even may be an expert
on completing the task. The problem is that someone who has never completed the task requires exact,
detailed, unambiguous, and complete instructions to complete the task successfully.

Because many real-world tasks involve a number of factors, people sometimes get lucky and can com-
plete a complex task given less-than-perfect instructions. A person often can use experience and common
sense to handle ambiguous or incomplete instructions. If fact, humans are so good at dealing with “fuzzy”
knowledge that in most instances the effort to produce excruciatingly detailed instructions to complete a
task is not worth the effort.

When a computer executes the instructions found in software, it has no cumulative experience and no
common sense. It is a slave that dutifully executes the instructions it receives. While executing a program a
computer cannot fill in the gaps in instructions that a human naturally might be able to do. Further, unlike
with humans, executing the same program over and over does not improve the computer’s ability to perform
the task. The computer has no understanding.

An algorithm is a finite sequence of steps, each step taking a finite length of time, that solves a problem
or computes a result. A computer program is one example of an algorithm, as is a recipe to make lasagna.
In both of these examples, the order of the steps matter. In the case of lasagna, the noodles must be cooked
in boiling water before they are layered into the filling to be baked. It would be inappropriate to place the
raw noodles into the pan with all the other ingredients, bake it, and then later remove the already baked
noodles to cook them in boiling water separately. In the same way, the ordering of steps is very important
in a computer program. While this point may be obvious, consider the following sound argument:

1. The relationship between degrees Celsius and degrees Fahrenheit can be expressed as

◦C =
5
9
× (◦F−32)

2. Given a temperature in degrees Fahrenheit, the corresponding temperature in degrees Celsius can be
computed.

Armed with this knowledge, Listing 3.11 (faultytempconv.py) follows directly.

Listing 3.11: faultytempconv.py

# File faultytempconv.py

# Establish some variables
degreesF, degreesC = 0, 0
# Define the relationship between F and C

3.10. EXERCISES 62

degreesC = 5/9*(degreesF – 32)
# Prompt user for degrees F
degreesF = float(input(‘Enter the temperature in degrees F: ‘))
# Report the result
print(degreesF, “degrees F =’, degreesC, ‘degrees C’)

Unfortunately, when run the program always displays

-17.7778

regardless of the input provided. The English description provided above is correct. The formula is imple-
mented faithfully. The problem lies simply in statement ordering. The statement

degreesC = 5/9*(degreesF – 32)

is an assignment statement, not a definition of a relationship that exists throughout the program. At the
point of the assignment, degreesF has the value of zero. The program assigns variable degreesC before it
receives degreesF’s value from the user.

As another example, suppose x and y are two variables in some program. How would we interchange
the values of the two variables? We want x to have y’s original value and y to have x’s original value. This
code may seem reasonable:

x = y
y = x

The problem with this section of code is that after the first statement is executed, x and y both have the same
value (y’s original value). The second assignment is superfluous and does nothing to change the values of
x or y. The solution requires a third variable to remember the original value of one the variables before it is
reassigned. The correct code to swap the values is

temp = x
x = y
y = temp

We can use tuple assignment (see Section 2.2) to make the swap even simpler:

x, y = y, x

These small examples emphasize the fact that we must specify algorithms precisely. Informal notions
about how to solve a problem can be valuable in the early stages of program design, but the coded program
requires a correct detailed description of the solution.

The algorithms we have seen so far have been simple. Statement 1, followed by Statement 2, etc. until
every statement in the program has been executed. Chapters 4 and 5 introduce some language constructs that
permit optional and repetitive execution of some statements. These constructs allow us to build programs
that do much more interesting things, but the algorithms that take advantage of them are more complex. We
must not lose sight of the fact that a complicated algorithm that is 99% correct is not correct. An algorithm’s
design and implementation can be derailed by inattention to the smallest of details.

3.10 Exercises

1. Is the literal 4 a valid Python expression?

3.10. EXERCISES 63

2. Is the variable x a valid Python expression?

3. Is x + 4 a valid Python expression?

4. What affect does the unary + operator have when applied to a numeric expression?

5. Sort the following binary operators in order of high to low precedence: +, -, *, //, /, %, =.

6. Given the following assignment:

x = 2

Indicate what each of the following Python statements would print.

(a) print(“x”)

(b) print(‘x’)

(d) print(“x + 1”)

(e) print(‘x’ + 1)

(f) print(x + 1)

7. Given the following assignments:

i1 = 2
i2 = 5
i3 = -3
d1 = 2.0
d2 = 5.0
d3 = -0.5

Evaluate each of the following Python expressions.

(a) i1 + i2

(b) i1 / i2

(d) i2 / i1

(e) i2 // i1

(f) i1 * i3

(g) d1 + d2

(h) d1 / d2

(i) d2 / d1

(j) d3 * d1

(k) d1 + i2

(l) i1 / d2

(m) d2 / i1

(n) i2 / d1

(o) i1/i2*d1

(p) d1*i1/i2

3.10. EXERCISES 64

(q) d1/d2*i1

(r) i1*d1/d2

(s) i2/i1*d1

(t) d1*i2/i1

(u) d2/d1*i1

(v) i1*d2/d1

8. What is printed by the following statement:

#print(5/3)

9. Given the following assignments:

i1 = 2
i2 = 5
i3 = -3
d1 = 2.0
d2 = 5.0
d3 = -0.5

Evaluate each of the following Python expressions.

(a) i1 + (i2 * i3)

(b) i1 * (i2 + i3)

(d) i1 // (i2 + i3)

(e) i1 / i2 + i3

(f) i1 // i2 + i3

(g) 3 + 4 + 5 / 3

(h) 3 + 4 + 5 // 3

(i) (3 + 4 + 5) / 3

(j) (3 + 4 + 5) // 3

(k) d1 + (d2 * d3)

(l) d1 + d2 * d3

(m) d1 / d2 – d3

(n) d1 / (d2 – d3)

(o) d1 + d2 + d3 / 3

(p) (d1 + d2 + d3) / 3

(q) d1 + d2 + (d3 / 3)

(r) 3 * (d1 + d2) * (d1 – d3)

10. What symbol signifies the beginning of a comment in Python?

11. How do Python comments end?

12. Which is better, too many comments or too few comments?

3.10. EXERCISES 65

13. What is the purpose of comments?

14. Why is human readability such an important consideration?

15. What circumstances can cause each of the following run-time errors to arise?

• NameError

• ValueError

• ZeroDivisionError

• IndentationError

• OverflowError

• SyntaxError

• TypeError

Hint: Try some of following activities in the interpreter or within a Python program:

• print a variable that has not been assigned

• convert the string ‘two’ to an integer

• add an integer to a string

• assign to a variable named end-point

• experiment adding spaces and tabs at various places in the code of an error-free Python program

• compute raise a floating-point number to a large power, as in 1.510,000.

16. Consider the following program which contains some errors. You may assume that the comments
within the program accurately describe the program’s intended behavior.

# Get two numbers from the user
n1 = float(input()) # 1
n2 = float(input()) # 2
# Compute sum of the two numbers
print(n1 + n2) # 3
# Compute average of the two numbers
print(n1+n2/2) # 4
# Assign some variables
d1 = d2 = 0 # 5
# Compute a quotient
print(n1/d1) # 6
# Compute a product
n1*n2 = d1 # 7
# Print result
print(d1) # 8

For each line listed in the comments, indicate whether or not an interpreter error, run-time exception,
or logic error is present. Not all lines contain an error.

17. Write the shortest way to express each of the following statements.

(a) x = x + 1

(b) x = x / 2

3.10. EXERCISES 66

(d) x = x + y

(e) x = x – (y + 7)

(f) x = 2*x

(g) number_of_closed_cases = number_of_closed_cases + 2*ncc

18. What is printed by the following code fragment?

x1 = 2
x2 = 2
x1 += 1
x2 -= 1
print(x1)
print(x2)

Why does the output appear as it does?

19. Consider the following program that attempts to compute the circumference of a circle given the
radius entered by the user. Given a circle’s radius, r, the circle’s circumference, C is given by the
formula:

C = 2πr

r = 0
PI = 3.14159
# Formula for the area of a circle given its radius
C = 2*PI*r
# Get the radius from the user
r = float(input(“Please enter the circle’s radius: “))
# Print the circumference
print(“Circumference is”, C)

(a) The program does not produce the intended result. Why?

(b) How can it be repaired so that it works correctly?

20. Write a Python program that …

21. Write a Python program that …

Chapter 4

Conditional Execution

All the programs in the preceding chapters execute exactly the same statements regardless of the input, if
any, provided to them. They follow a linear sequence: Statement 1, Statement 2, etc. until the last statement
is executed and the program terminates. Linear programs like these are very limited in the problems they
can solve. This chapter introduces constructs that allow program statements to be optionally executed,
depending on the context of the program’s execution.

4.1 Boolean Expressions

Arithmetic expressions evaluate to numeric values; a Boolean expression, sometimes called a predicate,
may have only one of two possible values: false or true. The term Boolean comes from the name of the
British mathematician George Boole. A branch of discrete mathematics called Boolean algebra is dedicated
to the study of the properties and the manipulation of logical expressions. While on the surface Boolean
expressions may appear very limited compared to numeric expressions, they are essential for building more
interesting and useful programs.

The simplest Boolean expressions in Python are True and False. In a Python interactive shell we see:

>>> True
True
>>> False
False
>>> type(True)

>>> type(False)

We see that bool is the name of the class representing Python’s Boolean expressions. Listing 4.1 (boolvars.py)
is a simple program that shows how Boolean variables can be used.

Listing 4.1: boolvars.py

# Assign some Boolean variables
a = True

4.2. BOOLEAN EXPRESSIONS 68

Table 4.1 The Python relational operators
Expression Meaning

x == y True if x = y (mathematical equality, not assignment); otherwise, false
x < y True if x < y; otherwise, false x <= y True if x≤ y; otherwise, false x > y True if x > y; otherwise, false
x >= y True if x≥ y; otherwise, false
x != y True if x 6= y; otherwise, false

Table 4.2 Examples of some Simple Relational Expressions
Expression Value
10 < 20 True 10 >= 20 False
x < 100 True if x is less than 100; otherwise, False x != y True unless x and y are equal b = False print('a =', a, ' b =', b) # Reassign a a = False print('a =', a, ' b =', b) Listing 4.1 (boolvars.py) produces a = True b = False a = False b = False 4.2 Boolean Expressions We have seen that the simplest Boolean expressions are False and True, the Python Boolean literals. A Boolean variable is also a Boolean expression. An expression comparing numeric expressions for equal- ity or inequality is also a Boolean expression. The simplest kinds of Boolean expressions use relational operators to compare two expressions. Table 4.1 lists the relational operators available in Python. Table 4.2 shows some simple Boolean expressions with their associated values. An expression like 10 < 20 is legal but of little use, since 10 < 20 is always true; the expression True is equivalent, simpler, and less likely to confuse human readers. Since variables can change their values during a program’s execution, Boolean expressions are most useful when their truth values depend on the values of one or more variables. In the Python interactive shell we see: >>> x = 10
>>> x
10
>>> x < 10 ©2017 Richard L. Halterman Draft date: January 18, 2018 4.3. THE SIMPLE IF STATEMENT 69 False >>> x <= 10 True >>> x == 10
True
>>> x >= 10
True
>>> x > 10
False
>>> x < 100 True >>> x < 5 False The first input in the shell binds the variable x to the value 10. The other expressions experiment with the relational operators. Exactly matching their mathematical representations, the following expressions all are equivalent: • x < 10 • 10 > x

• !(x >= 10)

• !(10 <= x) The relational operators are binary operators and are all left associative. They all have a lower prece- dence than any of the arithmetic operators; therefore, Python evaluates the expression x + 2 < y / 10 as if parentheses were placed as so: (x + 2) < (y / 10) 4.3 The Simple if Statement The Boolean expressions described in Section 4.2 at first may seem arcane and of little use in practical programs. In reality, Boolean expressions are essential for a program to be able to adapt its behavior at run time. Most truly useful and practical programs would be impossible without the availability of Boolean expressions. The execution errors mentioned in Section 3.6 arise from logic errors. One way that Listing 3.6 (dividedanger.py) can fail is when the user enters a zero for the divisor. Fortunately, programmers can take steps to ensure that division by zero does not occur. Listing 4.2 (betterdivision.py) shows how it might be done. Listing 4.2: betterdivision.py # File betterdivision.py # Get two integers from the user ©2017 Richard L. Halterman Draft date: January 18, 2018 4.3. THE SIMPLE IF STATEMENT 70 print('Please enter two numbers to divide.') dividend = int(input('Please enter the first number to divide: ')) divisor = int(input('Please enter the second number to divide: ')) # If possible, divide them and report the result if divisor != 0: print(dividend, '/', divisor, "=", dividend/divisor) The program may not always execute the print statement. In the following run Please enter two numbers to divide. Please enter the first number to divide: 32 Please enter the second number to divide: 8 32 / 8 = 4.0 the program executes the print statement, but if the user enters a zero as the second number: Please enter two numbers to divide. Please enter the first number to divide: 32 Please enter the second number to divide: 0 the program prints nothing after the user enters the values. The last non-indented line in Listing 4.2 (betterdivision.py) begins with the reserved word if. The if statement optionally executes the indented section of code. In this case, the if statement executes the print statement only if the variable divisor’s value is not zero. The Boolean expression divisor != 0 determines whether or not the program will execute the statement in the indented block. If divisor is not zero, the program prints the message; otherwise, the program displays nothing after the provides the input. Figure 4.1 shows how program execution flows through the if statement. of Listing 4.2 (betterdivision.py). The general form of the if statement is: condition block if : • The reserved word if begins a if statement. • The condition is a Boolean expression that determines whether or not the body will be executed. A colon (:) must follow the condition. • The block is a block of one or more statements to be executed if the condition is true. The statements within the block must all be indented the same number of spaces from the left. The block within an ©2017 Richard L. Halterman Draft date: January 18, 2018 4.3. THE SIMPLE IF STATEMENT 71 Figure 4.1 if flowchart do the division and print result Is divisor ≠ 0? yes no ©2017 Richard L. Halterman Draft date: January 18, 2018 4.3. THE SIMPLE IF STATEMENT 72 if must be indented more spaces than the line that begins the if statement. The block technically is part of the if statement. This part of the if statement is sometimes called the body of the if. Python requires the block to be indented. If the block contains just one statement, some programmers will place it on the same line as the if; for example, the following if statement that optionally assigns y: if x < 10: y = x could be written if x < 10: y = x but may not be written as if x < 10: y = x because the lack of indentation hides the fact that the assignment statement optionally is executed. Inden- tation is how Python determines which statements make up a block. How many spaces should you indent? Python requires at least one, some programmers consistently use two, four is the most popular number, but some prefer a more dramatic display and use eight. A four space indentation for a block is the recommended Python style. This text uses the recommended four spaces to set off each enclosed block. In most programming editors you can set the Tab key to insert spaces automatically so you need not count the spaces as you type. Whichever indent distance you choose, you must use this same distance consistently throughout a Python program. ©2017 Richard L. Halterman Draft date: January 18, 2018 4.3. THE SIMPLE IF STATEMENT 73 It is important not to mix spaces and tabs when indenting statements within a block. Python 3 does not allow tabs and spaces to be mixed when indenting state- ments. In many editors you cannot visually distinguish between a tab and a se- quence of spaces. The number of spaces equivalent to the spacing of a tab differs from one editor to another. Generally speaking, a tab stop represents a fixed dis- tance from the left side of the editing window. Most editors support multiple tab stops; for example, the first tab stop might be eight characters from the start of the line, followed by a series of tab stops, each one at a distance of eight characters from the previous tab stop (at columns 8, 16, 24, 32, etc. within the line of text). Furthermore, most editors allow the user to reconfigure in some way the locations of the tab stops. Pressing the Tab key in the editor causes the cursor within the editing window to jump to the next tab stop within the line. The space bar, on the other hand, always moves the cursor exactly one character to the right. Why is indentation that mixes tabs and spaces a problem and thus forbidden in Python 3? Consider creating a Python source file in one editor and then viewing it in a different editor with tab stops set differently. Lines that appear perfectly indented in the original editor would be misaligned in the new editor. Instead, code indented with four spaces within one editor would appear exactly the same in any other editor. Python 3 does allow the use of tabs for indentation—you just cannot mix them with spaces within the same source file. Most programming editors have a setting to substitute automatically a specified number of spaces when the user presses the Tab key. For Python development you should use this feature. Python best practice prefers using spaces over tabs for indentation within Python source. The if block may contain multiple statements to be optionally executed. Listing 4.3 (alternatedivision.py) optionally executes two statements depending on the input values provided by the user. Listing 4.3: alternatedivision.py # Get two integers from the user dividend = int(input('Please enter the number to divide: ')) divisor = int(input('Please enter dividend: ')) # If possible, divide them and report the result if divisor != 0: quotient = dividend/divisor print(dividend, '/', divisor, "=", quotient) print('Program finished') The assignment statement and first printing statement are both a part of the block of the if. Given the truth value of the Boolean expression divisor != 0 during a particular program run, either both statements will be executed or neither statement will be executed. The last statement is not indented, so it is not part of the if block. The program always prints Program finished, regardless of the user’s input. Remember when checking for equality, as in if x == 10: print('ten') ©2017 Richard L. Halterman Draft date: January 18, 2018 4.3. THE SIMPLE IF STATEMENT 74 to use the relational equality operator (==), not the assignment operator (=). As a convenience to programmers, Python’s notion of true and false extends beyond what we ordinarily would consider Boolean expressions. The statement if 1: print('one') always prints one, while the statement if 0: print('zero') never prints anything. Python considers the integer value zero to be false and treats every other integer value, positive and negative, to be true. Similarly, the floating-point value 0.0 is false, but any other floating-point value is true. The empty string ('' or "") is considered false, and any nonempty string is interpreted as true. Any Python expression can serve as the condition for an if statement. In later chapters we will explore additional kinds of expressions and see how they relate to Boolean conditions. Listing 4.4 (leadingzeros.py) requests an integer value from the user. The program then displays the number using exactly four digits. The program prepends leading zeros where necessary to ensure all four digits are occupied. The program treats numbers less than zero as zero and numbers greater than 9,999 as 9999. Listing 4.4: leadingzeros.py # Request input from the user num = int(input("Please enter an integer in the range 0...9999: ")) # Attenuate the number if necessary if num < 0: # Make sure number is not too small num = 0 if num > 9999: # Make sure number is not too big

num = 9999

print(end=”[“) # Print left brace

# Extract and print thousands-place digit
digit = num//1000 # Determine the thousands-place digit
print(digit, end=””) # Print the thousands-place digit
num %= 1000 # Discard thousands-place digit

# Extract and print hundreds-place digit
digit = num//100 # Determine the hundreds-place digit
print(digit, end=””) # Print the hundreds-place digit
num %= 100 # Discard hundreds-place digit

# Extract and print tens-place digit
digit = num//10 # Determine the tens-place digit
print(digit, end=””) # Print the tens-place digit
num %= 10 # Discard tens-place digit

# Remainder is the one-place digit
print(num, end=””) # Print the ones-place digit

print(“]”) # Print right brace

4.4. THE IF/ELSE STATEMENT 75

A sample run of Listing 4.4 (leadingzeros.py) produces

Please enter an integer in the range 0…9999: 38
[0038]

Another run demonstrates the effects of a user entering a negative number:

Please enter an integer in the range 0…9999: -450
[0000]

The program attenuates numbers that are too large:

Please enter an integer in the range 0…9999: 3256670
[9999]

In Listing 4.4 (leadingzeros.py), the two if statements at the beginning force the number to be in range.
The remaining arithmetic statements carve out pieces of the number to display. Recall that the statement

num %= 10

is short for

num = num % 10

4.4 The if/else Statement

One undesirable aspect of Listing 4.2 (betterdivision.py) is if the user enters a zero divisor, the program
prints nothing. It may be better to provide some feedback to the user to indicate that the divisor provided
cannot be used. The if statement has an optional else block that is executed only if the Boolean condition
is false. Listing 4.5 (betterfeedback.py) uses the if/else statement to provide the desired effect.

Listing 4.5: betterfeedback.py

# Get two integers from the user
dividend = int(input(‘Please enter the number to divide: ‘))
divisor = int(input(‘Please enter dividend: ‘))
# If possible, divide them and report the result
if divisor != 0:

print(dividend, ‘/’, divisor, “=”, dividend/divisor)
else:

print(‘Division by zero is not allowed’)

A given run of Listing 4.5 (betterfeedback.py) will execute exactly one of either the if block or the
else block. Unlike Listing 4.2 (betterdivision.py), this program always displays a message:

Please enter the number to divide: 32
Please enter dividend: 0
Division by zero is not allowed

The else block contains an alternate block of code that the program executes when the condition is false.
Figure 4.2 illustrates the program’s flow of execution.

4.4. THE IF/ELSE STATEMENT 76

Figure 4.2 if/else flowchart

do the division
and print result

Is
divisor ≠ 0?

yes no

castigate user

4.5. COMPOUND BOOLEAN EXPRESSIONS 77

Listing 4.5 (betterfeedback.py) avoids the division by zero run-time error that causes the program to
terminate prematurely, but it still alerts the user that there is a problem. Another application may handle the
situation in a different way; for example, it may substitute some default value for divisor instead of zero.

The general form of an if/else statement is

condition

if-block

if :

else:

else-block

• The reserved word if begins the if/else statement.

• The condition is a Boolean expression that determines whether or not the if block or the else block
will be executed. A colon (:) must follow the condition.

• The if-block is a block of one or more statements to be executed if the condition is true. As with
all blocks, it must be indented one level deeper than the if line. This part of the if statement is
sometimes called the body of the if.

• The reserved word else begins the second part of the if/else statement. A colon (:) must follow
the else.

• The else-block is a block of one or more statements to be executed if the condition is false. It must
be indented one level deeper than the line with the else. This part of the if/else statement is
sometimes called the body of the else.

The else block, like the if block, consists of one or more statements indented to the same level.

4.5 Compound Boolean Expressions

We can combine simple Boolean expressions, each involving one relational operator, into more complex
Boolean expressions using the logical operators and, or, and not. A combination of two or more Boolean
expressions using logical operators is called a compound Boolean expression.

To introduce compound Boolean expressions, consider a computer science degree that requires, among
other computing courses, Operating Systems and Programming Languages. If we isolate those two courses,
we can say a student must successfully complete both Operating Systems and Programming Languages to
qualify for the degree. A student that passes Operating Systems but not Programming Languages will not
have met the requirements. Similarly, Programming Languages without Operating Systems is insufficient,
and a student completing neither Operating Systems nor Programming Languages surely does not qualify.

4.5. COMPOUND BOOLEAN EXPRESSIONS 78

Table 4.3 Logical operators—e1 and e2 are Boolean expressions
e1 e2 e1 and e2 e1 or e2 not e1

False False False False True
False True False True True
True False False True False
True True True True False

The Python logical and operator works in exactly the same way. Suppose e1 and e2 are two Boolean
expressions. e1 and e2 is true only if e1 and e2 are both true; if either one is false or both are false, the
compound expression is false.

Related to the logical and operator is the logical or operator. To illustrate the logical or operator,
consider two mathematics courses, Differential Equations and Linear Algebra. A computer science degree
requires at least one of those two courses. A student who successfully completes Differential Equations but
does not take Linear Algebra meets the requirement. Similarly, a student may take Linear Algebra but not
Differential Equations. A student that takes neither Differential Equations nor Linear Algebra certainly has
not met the requirement. It is important to note the a student may elect to take both Differential Equations
and Linear Algebra (perhaps on the way to a mathematics minor), but the requirement is no less fulfilled.

Logical or works in a similar fashion. Given our Boolean expressions e1 and e2, the compound expres-
sion e1 or e2 is false only if e1 and e2 are both false; if either one is true or both are true, the compound
expression is true. Note that the or operator is an inclusive or, not an exclusive or. In informal conversion
we often imply exclusive or in a statement like ”Would you like cake or ice cream for dessert?” The impli-
cation is one or the other, not both. In computer programming the or is inclusive; if both subexpressions in
an or expression are true, the or expression is true.

Logical logical not operator reverses the truth value of the expression to which it is applied. If e is a
true Boolean expression, not e is false; if e is false, not e is true. In mathematics, if the expression x = y
is false, it must be true that x 6= y. In Python, the expression not (x == y) is equivalent to the expression
x != y. If also is the case that the Python expresion not (x != y) is just a more complicated way of
expressing x == y. In mathematics, if the expression x < y is false, it must be the case that x ≥ y. In Python, not (x < y) has the same truth value as x >= y. The expression not (x >= y) is equivalent to
x < y. You may be able to see from these examples that if e is a Boolean expression, it always is true that not not e is equivalent to e (this is known as the double negative property of mathematical logic). Table 4.3 is called a truth table. It shows all the combinations of truth values for two Boolean expres- sions and the values of compound Boolean expressions built from applying the and, or, and not Python logical operators. Both and and or are binary operators; that is, they require two operands. The not operator is a unary operator (see Section 3.1); it requires a single truth expression immediately to its right. Table 4.4 lists the Python operators we have seen so far. Table 4.4 shows that operator not has higher precedence than both and and or. The and operator has higher precedence than or. Both the and and or operators are left associative; not is right associative. The and and or operators have lower precedence than any other binary operator except assignment. This means the expression x <= y and x <= z is evaluated as (x <= y) and (x <= z) ©2017 Richard L. Halterman Draft date: January 18, 2018 4.5. COMPOUND BOOLEAN EXPRESSIONS 79 Table 4.4 Precedence of Some Python Operators. Higher precedence operators appear above lower prece- dence operators. Arity Operators Associativity binary ** unary +, - binary *, /, //, % left binary +, - left binary >, <, >=, <=, ==, != left unary not binary and left binary or left Some programmers prefer to use the parentheses as shown here even though they are not required. The parentheses improve the readability of complex expressions, and the interpreted code is no less efficient. Python allows an expression like x <= y and y <= z which means x≤ y≤ z to be expressed more naturally: x <= y <= z Similarly, Python allows a programmer to test the equivalence of three variables as if x == y == z: print('They are all the same') The following section of code assigns the indicated values to a bool: x = 10 y = 20 b = (x == 10) # assigns True to b b = (x != 10) # assigns False to b b = (x == 10 and y == 20) # assigns True to b b = (x != 10 and y == 20) # assigns False to b b = (x == 10 and y != 20) # assigns False to b b = (x != 10 and y != 20) # assigns False to b b = (x == 10 or y == 20) # assigns True to b b = (x != 10 or y == 20) # assigns True to b b = (x == 10 or y != 20) # assigns True to b b = (x != 10 or y != 20) # assigns False to b Convince yourself that the following expressions are equivalent: x != y and not (x == y) and x < y or x > y

4.6. THE PASS STATEMENT 80

In the expression e1 and e2 both subexpressions e1 and e2 must be true for the overall expression to be
true. Since the and operator evaluates left to right, this means that if e1 is false, there is no need to evaluate
e2. If e1 is false, no value of e2 can make the expression e1 and e2 true. The and operator first tests the
expression to its left. If it finds the expression to be false, it does not bother to check the right expression.
This approach is called short-circuit evaluation. In a similar fashion, in the expression e1 or e2, if e1 is true,
then e2’s value is irrelevant—an or expression is true unless both subexpressions are false. The or operator
uses short-circuit evaluation also.

Why is short-circuit evaluation important? Two situations show why it is important to consider:

• The order of the subexpressions can affect performance. When a program is running, complex ex-
pressions require more time for the computer to evaluate than simpler expressions. We classify an
expression that takes a relatively long time to evaluate as an expensive expression. If a compound
Boolean expression is made up of an expensive Boolean subexpression and an less expensive Boolean
subexpression, and the order of evaluation of the two expressions does not effect the behavior of the
program, then place the more expensive Boolean expression second. In the context of the and oper-
ator, if its left operand is False, the more more expensive right operand need not be evaluated. In
the context of the or operator, if the left operand is True, the more expensive right operand may be
ignored.

As a simple example, consider the following Python code snippet that could be part of a larger
program:

if x < 10 and input("Print value (y/n)?") == 'y': print(x) If x is a numeric value less than 10, this statement will query the user to print or not print the value of x. If x ≥ 10, the program need not stop and wait for the user’s input. If x ≥ 10, the user’s input is superfluous anyway. Now consider the statement with the Boolean expressions ordered the other way: if input("Print value (y/n)?") == 'y' and x < 10: print(x) In this case as well, both subconditions must be true to print the value of x. The difference here is that the program always pauses its execution to accept the user’s input regardless of x’s value. This statement bothers the user for input even when the second subcondition ensures the user’s answer will make no difference. • Subexpressions may be ordered to prevent run-time errors. This is especially true when one of the subexpressions depends on the other in some way. Consider the following expression: (x != 0) and (z/x > 1)

Here, if x is zero, the division by zero is avoided. If the subexpressions were switched, a run-time
error would result if x is zero.

4.6 The pass Statement

Some beginning programmers attempt to use an if/else statement when a simple if statement is more
appropriate; for example, in the following code fragment the programmer wishes to do nothing if the value
of the variable x is less than zero; otherwise, the programmer wishes to print x’s value:

4.6. THE PASS STATEMENT 81

if x < 0: # Do nothing (This will not work!) else: print(x) If the value of x is less than zero, this section of code should print nothing. Unfortunately, the code fragment above is not legal Python. The if/else statement contains an else block, but it does not contain an if block. The comment does not count as a Python statement. Both if and if/else statements require an if block that contains at least one statement. Additionally, an if/else statement requires an else block that contains at least one statement. Python has a special statement, pass, that means do nothing. We may use the pass statement in our code in places where the language requires a statement to appear but we wish the program to take no action whatsoever. We can make the above code fragment legal by adding a pass statement: if x < 0: pass # Do nothing else: print(x) While the pass statement makes the code legal, we can express its logic better by using a simple if state- ment. In mathematics, if the expression x < y is false, it must be the case that x ≥ y. If we invert the truth value of the relation within the condition, we can express the above code more succinctly as if x >= 0:
print(x)

So, if you ever feel the need to write an if/else statement with an empty if body, do the following instead:

1. invert the truth value of the condition

2. make the proposed else body the if body

3. eliminate the else

In situations where you may be tempted to use a non-functional else block, as in the following:

if x == 2:
print(x)

else:
pass # Do nothing if x is not equal to 2

do not alter the condition but simply eliminate the else and the else block altogether:

if x == 2:
print(x) # Print only if x is equal to 2

The pass statement in Python is useful for holding the place for code to appear in the future; for
example, consider the following code fragment:

if x < 0: pass # TODO: print an appropriate warning message to be determined else: print(x) ©2017 Richard L. Halterman Draft date: January 18, 2018 4.7. FLOATING-POINT EQUALITY 82 In this code fragment the programmer intends to provide an if block, but the exact nature of the code in the if block is yet to be determined. The pass statement serves as a suitable placeholder for the future code. The included comment documents what is expected to appear eventually in place of the pass statement. We will see other uses of the pass statement as we explore Python more deeply. 4.7 Floating-point Equality The equality operator (==) checks for exact equality. This can be a problem with floating-point numbers, since floating-point numbers inherently are imprecise. Listing 4.6 (samedifferent.py) demonstrates the perils of using the equality operator with floating-point numbers. Listing 4.6: samedifferent.py d1 = 1.11 - 1.10 d2 = 2.11 - 2.10 print('d1 =', d1, ' d2 =', d2) if d1 == d2: print('Same') else: print('Different') In mathematics, we expect the following equality to hold: 1.11−1.10 = 0.01 = 2.11−2.10 The output of the first print statement in Listing 4.6 (samedifferent.py) reminds us of the imprecision of floating-point numbers: d1 = 0.010000000000000009 d2 = 0.009999999999999787 Since the expression d1 == d2 checks for exact equality, the program reports that d1 and d2 are different. The solution is not to check floating-point numbers for exact equality, but rather see if the values “close enough” to each other to be considered the same. If d1 and d2 are two floating-point numbers, we need to check if the absolute value of the d1 - d2 is a very small number. Listing 4.7 (floatequals.py) adapts Listing 4.6 (samedifferent.py) using this approximately equal concept. Listing 4.7: floatequals.py d1 = 1.11 - 1.10 d2 = 2.11 - 2.10 print('d1 =', d1, ' d2 =', d2) diff = d1 - d2 # Compute difference if diff < 0: # Compute absolute value diff = -diff if diff < 0.0000001: # Are the values close enough? print('Same') else: print('Different') ©2017 Richard L. Halterman Draft date: January 18, 2018 4.8. NESTED CONDITIONALS 83 Listing 4.8 (floatequals2.py) is a variation of Listing 4.7 (floatequals.py) that does not compute the absolute value but instead checks to see if the difference is between two numbers that are very close to zero: one negative and the other positive. Listing 4.8: floatequals2.py d1 = 1.11 - 1.10 d2 = 2.11 - 2.10 print('d1 =', d1, ' d2 =', d2) if -0.0000001 < d1 - d2 < 0.0000001: print('Same') else: print('Different') In Section 7.4.6 we will see how to encapsulate this floating-point equality code within a function to make it more convenient for general use. 4.8 Nested Conditionals The statements in the block of the if or the else may be any Python statements, including other if/else statements. We can use these nested if statements to develop arbitrarily complex program logic. Consider Listing 4.9 (checkrange.py) that determines if a number is between 0 and 10, inclusive. Listing 4.9: checkrange.py value = int(input("Please enter an integer value in the range 0...10: ") if value >= 0: # First check

if value <= 10: # Second check print("In range") print("Done") Listing 4.9 (checkrange.py) behaves as follows: • The executing program checks first condition. If value is less than zero, the program does not evaluate the second condition and it continues its execution with the statement following the outer if. The statement after the outer if simply prints Done. • If the executing program finds the value variable to be greater than or equal to zero, it executes the statement within the if-block. This statement is itself an if statement. The program thus checks the second (inner) condition. If the second condition is satisfied, the program displays the In range message; otherwise, it does not. Regardless, the program eventually prints the Done message. We say that the second if (with the comment Second check) is nested within the first if (First check). We call the first if the outer if and the second if the inner if. Notice the entire inner if statement is in- dented one level relative to the outer if statement. This means the inner if’s block, the print("In range") statement, is indented two levels deeper than the outer if statement. Remember that if you use four spaces as the distance for a indentation level, you must consistently use this four space distance for each indentation level throughout the program. Both conditions of this nested if construct must be met for the In range message to be printed. Said another way, the first condition and the second condition must be met for the program to print the In range ©2017 Richard L. Halterman Draft date: January 18, 2018 4.8. NESTED CONDITIONALS 84 message. From this perspective, the program can be rewritten to behave the same way with only one if statement, as Listing 4.10 (newcheckrange.py) shows. Listing 4.10: newcheckrange.py value = int(input("Please enter an integer value in the range 0...10: ") if value >= 0 and value <= 10: # Only one, slightly more complicated check print("In range") print("Done") Listing 4.10 (newcheckrange.py) uses the and operator to check both conditions at the same time. Its logic is simpler, using only one if statement, at the expense of a slightly more complex Boolean expression in its condition. The second version is preferable here because simpler logic is usually a desirable goal. We may express the condition the if within Listing 4.10 (newcheckrange.py): value >= 0 and value <= 10 more compactly as 0 <= value <= 10 Sometimes we cannot simplify a program’s logic as readily as in Listing 4.10 (newcheckrange.py). Listing 4.11 (enhancedcheckrange.py) would be impossible to rewrite with only one if statement. Listing 4.11: enhancedcheckrange.py value = int(input("Please enter an integer value in the range 0...10: ") if value >= 0: # First check

if value <= 10: # Second check print(value, "is in range") else: print(value, "is too large") else: print(value, "is too small") print("Done") Listing 4.11 (enhancedcheckrange.py) provides a more specific message instead of a simple notification of acceptance. Exactly one of three messages is printed based on the value of the variable. A single if or if/else statement cannot choose from among more than two different execution paths. Computers store all data internally in binary form. The binary (base 2) number system is much simpler than the familiar decimal (base 10) number system because it uses only two digits: 0 and 1. The decimal system uses 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Despite the lack of digits, every decimal integer has an equivalent binary representation. Binary numbers use a place value system not unlike the decimal system. Figure 4.3 shows how the familiar base 10 place value system works. With 10 digits to work with, the decimal number system distinguishes place values with powers of 10. Compare the base 10 system to the base 2 place value system shown in Figure 4.4. With only two digits to work with, the binary number system distinguishes place values by powers of two. Since both binary and decimal numbers share the digits 0 and 1, we will use the subscript 2 to indicate a binary number; therefore, 100 represents the decimal value one hundred, while 1002 is the binary number four. Sometimes to be very clear we will attach a subscript of 10 to a decimal number, as in 10010. ©2017 Richard L. Halterman Draft date: January 18, 2018 4.8. NESTED CONDITIONALS 85 Figure 4.3 The base 10 place value system · · · 4 7 3 4 0 6 · · · 105 104 103 102 101 100 · · · 100,000 10,000 1,000 100 10 1 473,406 = 4×105 +7×104 +3×103 +4×102 +0×101 +6×100 = 400,000+70,000+3,000+400+0+6 = 473,406 Figure 4.4 The base 2 place value system · · · 1 0 0 1 1 1 · · · 25 24 23 22 21 20 · · · 32 16 8 4 2 1 1001112 = 1×25 +0×24 +0×23 +1×22 +1×21 +1×20 = 32+0+0+4+2+1 = 39 Listing 4.12 (binaryconversion.py) uses an if statement containing a series of nested if statements to print a 10-bit binary string representing the binary equivalent of a decimal integer supplied by the user. We use if/else statements to print the individual digits left to right, essentially assembling the sequence of bits that represents the binary number. Listing 4.12: binaryconversion.py # Get number from the user value = int(input("Please enter an integer value in the range 0...1023: ")) # Create an empty binary string to build upon binary_string = '' # Integer must be less than 1024 if 0 <= value < 1024: if value >= 512:
binary_string += ‘1’
value %= 512

else:
binary_string += ‘0’

if value >= 256:
binary_string += ‘1’
value %= 256

else:
binary_string += ‘0’

if value >= 128:

4.8. NESTED CONDITIONALS 86

binary_string += ‘1’
value %= 128

else:
binary_string += ‘0’

if value >= 64:
binary_string += ‘1’
value %= 64

else:
binary_string += ‘0’

if value >= 32:
binary_string += ‘1’
value %= 32

else:
binary_string += ‘0’

if value >= 16:
binary_string += ‘1’
value %= 16

else:
binary_string += ‘0’

if value >= 8:
binary_string += ‘1’
value %= 8

else:
binary_string += ‘0’

if value >= 4:
binary_string += ‘1’
value %= 4

else:
binary_string += ‘0’

if value >= 2:
binary_string += ‘1’
value %= 2

else:
binary_string += ‘0’

binary_string += str(value)

# Display the results
if binary_string != ”:

print(binary_string)
else:

print(‘Cannot convert’)

In Listing 4.12 (binaryconversion.py):

• The outer if checks to see if the value the user provides is in the proper range. The program works
only for numbers in the range 0 ≤ value < 1,024. • Each inner if compares the user-supplied entered integer against decreasing powers of two. If the number is large enough, the program: – prints appends the digit (actually character) 1 to the binary string under construction, and – removes via the remainder operator that power of two’s contribution to the value. If the number is not at least as big as the given power of two, the program concatenates a 0 instead and moves on without modifying the input value. ©2017 Richard L. Halterman Draft date: January 18, 2018 4.8. NESTED CONDITIONALS 87 Figure 4.5 The process of the binary number conversion program when the user supplies 805 as the input value. Print prompt Get value 0 ≤ 805 ≤ 1023? 805 ≥ 512? → Please enter ... ← 805 Yes Remainder 805÷512 → 293 293 ≥ 256? Yes, → 1 Remainder 293÷256 → 37 37 ≥ 128? Yes, → 1 37 ≥ 64? No, → 0 Remainder 37÷32 → 5 5 ≥ 16? No, → 0 No, → 0 5 ≥ 8? Remainder 5÷4 → 1 1 ≥ 2? No, → 0 Print remaining value → 1 37 ≥ 32? Yes, → 1 No, → 0 5 ≥ 4? Yes, → 1 • For the ones place at the end no check is necessary—the remaining value will be 0 or 1 and so the program appends the string version of 0 or 1. The following shows a sample run of Listing 4.12 (binaryconversion.py): Please enter an integer value in the range 0...1023: 805 1100100101 Figure 4.5 illustrates the execution of Listing 4.12 (binaryconversion.py) when the user enters 805. Listing 4.13 (simplerbinaryconversion.py) simplifies the logic of Listing 4.12 (binaryconversion.py) at the expense of some additional arithmetic. It uses only one if statement. Listing 4.13: simplerbinaryconversion.py # Get number from the user value = int(input("Please enter an integer value in the range 0...1023: ")) # Initial binary string is empty binary_string = '' # Integer must be less than 1024 if 0 <= value < 1024: binary_string += str(value//512) value %= 512 binary_string += str(value//256) ©2017 Richard L. Halterman Draft date: January 18, 2018 4.8. NESTED CONDITIONALS 88 value %= 256 binary_string += str(value//128) value %= 128 binary_string += str(value//64) value %= 64 binary_string += str(value//32) value %= 32 binary_string += str(value//16) value %= 16 binary_string += str(value//8) value %= 8 binary_string += str(value//4) value %= 4 binary_string += str(value//2) value %= 2 binary_string += str(value) # Report results if binary_string != '': print(binary_string) else: print('Unable to convert') The sole if statement in Listing 4.13 (simplerbinaryconversion.py) ensures that the user provides an integer in the proper range. The other if statements that originally appeared in Listing 4.12 (binaryconversion.py) are gone. A clever sequence of integer arithmetic operations replace the original conditional logic. The two programs—binaryconversion.py and simplerbinaryconversion.py—behave identically but simplerbinarycon- version.py’s logic is simpler. Listing 4.14 (troubleshoot.py) implements a very simple troubleshooting program that an (equally sim- ple) computer technician might use to diagnose an ailing computer. Listing 4.14: troubleshoot.py print("Help! My computer doesn't work!") print("Does the computer make any sounds (fans, etc.)") choice = input("or show any lights? (y/n):") # The troubleshooting control logic if choice == 'n': # The computer does not have power choice = input("Is it plugged in? (y/n):") if choice == 'n': # It is not plugged in, plug it in print("Plug it in. If the problem persists, ") print("please run this program again.") else: # It is plugged in choice = input("Is the switch in the \"on\" position? (y/n):") if choice == 'n': # The switch is off, turn it on! print("Turn it on. If the problem persists, ") print("please run this program again.") else: # The switch is on choice = input("Does the computer have a fuse? (y/n):") if choice == 'n': # No fuse choice = input("Is the outlet OK? (y/n):") if choice == 'n': # Fix outlet print("Check the outlet's circuit ") ©2017 Richard L. Halterman Draft date: January 18, 2018 4.8. NESTED CONDITIONALS 89 Figure 4.6 Decision tree for troubleshooting a computer system print("breaker or fuse. Move to a") print("new outlet, if necessary. ") print("If the problem persists, ") print("please run this program again.") else: # Beats me! print("Please consult a service technician.") else: # Check fuse print("Check the fuse. Replace if ") print("necessary. If the problem ") print("persists, then ") print("please run this program again.") else: # The computer has power print("Please consult a service technician.") This very simple troubleshooting program attempts to diagnose why a computer does not work. The potential for enhancement is unlimited, but this version deals only with power issues that have simple fixes. Notice that if the computer has power (fan or disk drive makes sounds or lights are visible), the program indicates that help should be sought elsewhere! The decision tree capturing the basic logic of the program is shown in Figure 4.6. The steps performed are: ©2017 Richard L. Halterman Draft date: January 18, 2018 4.8. NESTED CONDITIONALS 90 1. Is it plugged in? This simple fix is sometimes overlooked. 2. Is the switch in the on position? This is another simple fix. 3. If applicable, is the fuse blown? Some computer systems have a user-serviceable fuse that can blow out during a power surge. (Most newer computers have power supplies that can handle power surges and have no user-serviceable fuses.) 4. Is there power at the receptacle? Perhaps the outlet’s circuit breaker or fuse has a problem. This algorithm performs the easiest checks first. It adds progressively more difficult checks as the program continues. Based on your experience with troubleshooting computers that do not run properly, you may be able to think of many enhancements to this simple program. Note the various blocks of code and how the blocks are indented within Listing 4.14 (troubleshoot.py). Visually programmers quickly can determine the logical structure of the program by the arrangement and indentation of the blocks. Recall the time conversion program in Listing 3.9 (timeconv.py). If the user enters 10000, the program runs as follows: Please enter the number of seconds:10000 2 hr 46 min 40 sec Suppose we wish to improve the English presentation by not using abbreviations. If we spell out hours, minutes, and seconds, we must be careful to use the singular form hour, minute, or second when the corresponding value is one. Listing 4.15 (timeconvcond1.py) uses if/else statements to express to time units with the correct number. Listing 4.15: timeconvcond1.py # File timeconvcond1.py # Some useful conversion factors seconds_per_minute = 60 seconds_per_hour = 60*seconds_per_minute # 3600 # Get user input in seconds seconds = int(input("Please enter the number of seconds:")) # First, compute the number of hours in the given number of seconds hours = seconds // seconds_per_hour # 3600 seconds = 1 hour # Compute the remaining seconds after the hours are accounted for seconds = seconds % seconds_per_hour # Next, compute the number of minutes in the remaining number of seconds minutes = seconds // seconds_per_minute # 60 seconds = 1 minute # Compute the remaining seconds after the minutes are accounted for seconds = seconds % seconds_per_minute # Report the results print(hours, end='') # Decide between singular and plural form of hours if hours == 1: print(" hour ", end='') else: print(" hours ", end='') ©2017 Richard L. Halterman Draft date: January 18, 2018 4.8. NESTED CONDITIONALS 91 print(minutes, end='') # Decide between singular and plural form of minutes if minutes == 1: print(" minute ", end='') else: print(" minutes ", end='') print(seconds, end='') # Decide between singular and plural form of seconds if seconds == 1: print(" second") else: print(" seconds") The if/else statements within Listing 4.15 (timeconvcond1.py) are responsible for printing the correct version—singular or plural—for each time unit. One run of Listing 4.15 (timeconvcond1.py) produces Please enter the number of seconds:10000 2 hours 46 minutes 40 seconds All the words are plural since all the value are greater than one. Another run produces Please enter the number of seconds:9961 2 hours 46 minutes 1 second Note the word second is singular as it should be. Please enter the number of seconds:3601 1 hour 0 minutes 1 second Here again the printed words agree with the number of the value they represent. An improvement to Listing 4.15 (timeconvcond1.py) would not print a value and its associated time unit if the value is zero. Listing 4.16 (timeconvcond2.py) adds this feature. Listing 4.16: timeconvcond2.py # File timeconvcond2.py # Some useful conversion constants seconds_per_minute = 60 seconds_per_hour = 60*seconds_per_minute # 3600 seconds = int(input("Please enter the number of seconds:")) # First, compute the number of hours in the given number of seconds hours = seconds // seconds_per_hour # 3600 seconds = 1 hour # Compute the remaining seconds after the hours are accounted for seconds = seconds % seconds_per_hour # Next, compute the number of minutes in the remaining number of seconds minutes = seconds // seconds_per_minute # 60 seconds = 1 minute # Compute the remaining seconds after the minutes are accounted for seconds = seconds % seconds_per_minute # Report the results if hours > 0: # Print hours at all?

print(hours, end=”)
# Decide between singular and plural form of hours
if hours == 1:

4.8. NESTED CONDITIONALS 92

print(” hour “, end=”)
else:

print(” hours “, end=”)
if minutes > 0: # Print minutes at all?

print(minutes, end=”)
# Decide between singular and plural form of minutes
if minutes == 1:

print(” minute “, end=”)
else:

print(” minutes “, end=”)
# Print seconds at all?
if seconds > 0 or (hours == 0 and minutes == 0 and seconds == 0):

print(seconds, end=”)
# Decide between singular and plural form of seconds
if seconds == 1:

print(” second”, end=”)
else:

print(” seconds”, end=”)
print() # Finally print the newline

In Listing 4.16 (timeconvcond2.py) each code segment responsible for printing a time value and its English
word unit is protected by an if statement that only allows the code to execute if the time value is greater
than zero. The exception is in the processing of seconds: if all time values are zero, the program should
print 0 seconds. Note that each of the if/else statements responsible for determining the singular or plural
form is nested within the if statement that determines whether or not the value will be printed at all.

One run of Listing 4.16 (timeconvcond2.py) produces

Please enter the number of seconds:10000
2 hours 46 minutes 40 seconds

All the words are plural since all the value are greater than one. Another run produces

Please enter the number of seconds:9961
2 hours 46 minutes 1 second

Note the word second is singular as it should be.

Please enter the number of seconds:3601
1 hour 1 second

Here again the printed words agree with the number of the value they represent.

Please enter the number of seconds:7200
2 hours

Another run produces:

Please enter the number of seconds:60
1 minute

Finally, the following run shows that the program handles zero seconds properly:

Please enter the number of seconds:0
0 seconds

4.9. MULTI-WAY DECISION STATEMENTS 93

4.9 Multi-way Decision Statements

A simple if/else statement can select from between two execution paths. Listing 4.11 (enhancedcheckrange.py)
showed how to select from among three options. What if exactly one of many actions should be taken?
Nested if/else statements are required, and the form of these nested if/else statements is shown in
Listing 4.17 (digittoword.py).

Listing 4.17: digittoword.py

value = int(input(“Please enter an integer in the range 0…5: “))
if value < 0: print("Too small") else: if value == 0: print("zero") else: if value == 1: print("one") else: if value == 2: print("two") else: if value == 3: print("three") else: if value == 4: print("four") else: if value == 5: print("five") else: print("Too large") print("Done") Observe the following about Listing 4.17 (digittoword.py): • It prints exactly one of eight messages depending on the user’s input. • Notice that each if block contains a single printing statement and each else block, except the last one, contains an if statement. The control logic forces the program execution to check each condition in turn. The first condition that matches wins, and its corresponding if body will be executed. If none of the conditions are true, the program prints the last else’s Too large message. As a consequence of the required formatting of Listing 4.17 (digittoword.py), the mass of text drifts to the right as more conditions are checked. Python provides a multi-way conditional construct called if/elif/else that permits a more manageable textual structure for programs that must check many con- ditions. Listing 4.18 (restyleddigittoword.py) uses the if/elif/else statement to avoid the rightward code drift. Listing 4.18: restyleddigittoword.py value = int(input("Please enter an integer in the range 0...5: ")) if value < 0: ©2017 Richard L. Halterman Draft date: January 18, 2018 4.9. MULTI-WAY DECISION STATEMENTS 94 print("Too small") elif value == 0: print("zero") elif value == 1: print("one") elif value == 2: print("two") elif value == 3: print("three") elif value == 4: print("four") elif value == 5: print("five") else: print("Too large") print("Done") The word elif is a contraction of else and if; if you read elif as else if, you can see how we can transform the code fragment else: if value == 2: print("two") in Listing 4.17 (digittoword.py) into elif value == 2: print("two") in Listing 4.18 (restyleddigittoword.py). The if/elif/else statement is valuable for selecting exactly one block of code to execute from several different options. The if part of an if/elif/else statement is mandatory. The else part is optional. After the if part and before else part (if present) you may use as many elif blocks as necessary. The general form of an if/elif/else statement is ©2017 Richard L. Halterman Draft date: January 18, 2018 4.9. MULTI-WAY DECISION STATEMENTS 95 condition-1 block-1 if : elif : elif : elif : else: default-block block-2 block-3 block-4 condition-2 condition-3 condition-4 ... Listing 4.19 (datetransformer.py) uses an if/elif/else statement to transform a numeric date in mon- th/day format to an expanded US English form and an international Spanish form; for example, 2/14 would be converted to February 14 and 14 febrero. Listing 4.19: datetransformer.py month = int(input("Please enter the month as a number (1-12): ")) day = int(input("Please enter the day of the month: ")) # Translate month into English if month == 1: print("January ", end='') elif month == 2: print("February ", end='') elif month == 3: print("March ", end='') elif month == 4: print("April ", end='') elif month == 5: ©2017 Richard L. Halterman Draft date: January 18, 2018 4.9. MULTI-WAY DECISION STATEMENTS 96 print("May ", end='') elif month == 6: print("June ", end='') elif month == 7: print("July ", end='') elif month == 8: print("August ", end='') elif month == 9: print("September ", end='') elif month == 10: print("October ", end='') elif month == 11: print("November ", end='') else: print("December ", end='') # Add the day print(day, 'or', day, end='') # Translate month into Spanish if month == 1: print(" de enero") elif month == 2: print(" de febrero") elif month == 3: print(" de marzo") elif month == 4: print(" de abril") elif month == 5: print(" de mayo") elif month == 6: print(" de junio") elif month == 7: print(" de julio") elif month == 8: print(" de agosto") elif month == 9: print(" de septiembre") elif month == 10: print(" de octubre") elif month == 11: print(" de noviembre") else: print(" de diciembre") A sample run of Listing 4.19 (datetransformer.py) is shown here: Please enter the month as a number (1-12): 5 Please enter the day of the month: 20 May 20 or 20 de mayo An if/elif/else statement that includes the optional else will execute exactly one of its blocks. The first condition that evaluates to true selects the block to execute. An if/elif/else statement that omits the else block may fail to execute the code in any of its blocks if none of its conditions evaluate to True. ©2017 Richard L. Halterman Draft date: January 18, 2018 4.10. MULTI-WAY VERSUS SEQUENTIAL CONDITIONALS 97 4.10 Multi-way Versus Sequential Conditionals Beginning programmers sometimes confuse multi-way if/elif/else statement with a sequence of simple statements. Consider Listing 4.20 (simplerdigittoword.py). It does not print anything if the user enters an integer out of range; otherwise, it prints the equivalent English word. Listing 4.20: simplerdigittoword.py # Use a mult-way conditional statement value = int(input()) if value == 0: print("zero") elif value == 1: print("one") elif value == 2: print("two") elif value == 3: print("three") elif value == 4: print("four") elif value == 5: print("five") print("Done") Next, consider Listing 4.21 (simplerdigittoword2.py). It replaces the elifs with ifs. It behaves identically to Listing 4.20 (simplerdigittoword.py). Listing 4.21: simplerdigittoword2.py # Use sequential conditional statements value = int(input()) if value == 0: print("zero") if value == 1: print("one") if value == 2: print("two") if value == 3: print("three") if value == 4: print("four") if value == 5: print("five") print("Done") Despite their equivalent behavior, Listing 4.20 (simplerdigittoword.py) is the better program. Figure 4.7 traces the two programs’ progress when the user enters the value 1. Listing 4.20 (simplerdigittoword.py) performs only two comparisons before making its choice and then finally printing the message Done. In constrast, Listing 4.21 (simplerdigittoword2.py) must check every conditional expression in the program before it prints Done. For a program of this size and complexity, the difference is imperceptible. In some more complex situations, however, the extra computation may noticeably affect the application. The bigger issue is the impression that it can make on new programmers that the sequential ifs are equivalent to ©2017 Richard L. Halterman Draft date: January 18, 2018 4.10. MULTI-WAY VERSUS SEQUENTIAL CONDITIONALS 98 Figure 4.7 A trace of the execution of Listing 4.20 (simplerdigittoword.py) (left) and Listing 4.21 (simplerdigittoword2.py) (right) when the user enters the value 1. # Use a mult-way conditional statement value = int(input()) if value == 0: print("zero") elif value == 1: print("one") elif value == 2: print("two") elif value == 3: print("three") elif value == 4: print("four") elif value == 5: print("five") print("Done") Che ck # 1 Check #2 Text to print # Use sequential if statements value = int(input()) if value == 0: print("zero") if value == 1: print("one") if value == 2: print("two") if value == 3: print("three") if value == 4: print("four") if value == 5: print("five") print("Done") Che ck # 1 Che ck # 2 Text to printCheck #3 Check #6 Check #5 Chec k #4 Other checks skipped ©2017 Richard L. Halterman Draft date: January 18, 2018 4.11. CONDITIONAL EXPRESSIONS 99 the multi-way if/elifs. To dispell this idea, compare the behavior of Listing 4.22 (multivsseq1.py) to Listing 4.23 (multivsseq2.py). Listing 4.22: multivsseq1.py num = int(input("Enter a number: ")) if num == 1: print("You entered one") elif num == 2: print("You entered two") elif num > 5:

print(“You entered a number greater than five”)
elif num == 7:

print(“You entered seven”)
else:

print(“You entered some other number”)

In Listing 4.22 (multivsseq1.py) if the user enters 7, the program prints You entered a number greater than
five. Listing 4.23 (multivsseq2.py) merely changes all the elifs to ifs. In this case if the user enters 7, the
program will print the same message as does Listing 4.22 (multivsseq1.py), but it additionally will print the
message You entered seven.

Listing 4.23: multivsseq2.py

num = int(input(“Enter a number: “))
if num == 1:

print(“You entered one”)
if num == 2:

print(“You entered two”)
if num > 5:

print(“You entered a number greater than five”)
if num == 7:

print(“You entered seven”)
else:

print(“You entered some other number”)

These two programs clearly doemonstrate that multi-way conditional statements behave differently from
sequential ifs.

Figure 4.8 compares the structure of the conditional statements in Listing 4.22 (multivsseq1.py) to List-
ing 4.23 (multivsseq2.py).

4.11 Conditional Expressions

Consider the following code fragment:

if a != b:
c = d

else:
c = e

4.11. CONDITIONAL EXPRESSIONS 100

Figure 4.8 The structure of the conditional statements in Listing 4.22 (multivsseq1.py) (left) versus List-
ing 4.23 (multivsseq2.py) (right).

num = 1?

Print one num = 2?

Print two num > 5?

Print greater than
five

num > 5?

Print greater than
five

Print seven Print other

num = 7?

num = 2

Print two

num = 1?

Print one

Print seven Print other

num = 7?

Yes

Yes No

Yes

4.11. CONDITIONAL EXPRESSIONS 101

This code assigns to variable c one of two possible values. As purely a syntactical convenience, Python
provides an alternative to the if/else construct called a conditional expression. A conditional expression
evaluates to one of two values depending on a Boolean condition. We can rewrite the above code as

c = d if a != b else e

The general form of the conditional expression is

conditionexpression-1 if else expression-2

where

• expression-1 is the overall value of the conditional expression if condition is true.

• condition is a normal Boolean expression that might appear in an if statement.

• expression-2 is the overall value of the conditional expression if condition is false.

In the above code fragment, expression-1 is the variable d, condition is a != b, and expression-2 is e.

Listing 4.24 (safedivide.py) uses our familiar if/else statement to check for division by zero.

Listing 4.24: safedivide.py

# Get the dividend and divisor from the user
dividend = int(input(‘Enter dividend: ‘))
divisor = int(input(‘Enter divisor: ‘))
# We want to divide only if divisor is not zero; otherwise,
# we will print an error message
if divisor != 0:

print(dividend/divisor)
else:

print(‘Error, cannot divide by zero’)

Using a conditional expression, we can rewrite Listing 4.24 (safedivide.py) as Listing 4.25 (safedivideconditional.py).

Listing 4.25: safedivideconditional.py

Notice that in Listing 4.25 (safedivideconditional.py) the type of the msg variable depends which expression
is assigned; msg can be a floating-point value (dividend/divisor) or a string (‘Error, cannot divide by zero’).

4.12. ERRORS IN CONDITIONAL STATEMENTS 102

As another example, the absolute value of a number is defined in mathematics by the following formula:

|n| =
{

n, when n≥ 0
−n, when n < 0 In other words, the absolute value of a positive number or zero is the same as that number; the absolute value of a negative number is the additive inverse (negative of) of that number. The following Python expression represents the absolute value of the variable n: -n if n < 0 else n An equally valid way to express it is n if n >= 0 else -n

The expression itself is not statement. Listing 4.26 (absvalueconditional.py) is a small program that provides
an example of the conditional expression’s use in a statement.

Listing 4.26: absvalueconditional.py

# Acquire a number from the user and print its absolute value.
n = int(input(“Enter a number: “))
print(‘|’, n, ‘| = ‘, (-n if n < 0 else n), sep='') Some sample runs of Listing 4.26 (absvalueconditional.py) show Enter a number: -34 |-34| = 34 and Enter a number: 0 |0| = 0 and Enter a number: 100 |100| = 100 Some argue that the conditional expression is not as readable as a normal if/else statement. Regard- less, many Python programmers use it sparingly because of its very specific nature. Standard if/else blocks can contain multiple statements, but contents in the conditional expression are limited to single, simple expressions. 4.12 Errors in Conditional Statements Carefully consider each compound conditional used, such as value > 0 and value <= 10 found in Listing 4.10 (newcheckrange.py). Confusing logical and and logical or is a common programming error. Consider the Boolean expression ©2017 Richard L. Halterman Draft date: January 18, 2018 4.12. ERRORS IN CONDITIONAL STATEMENTS 103 x > 0 or x <= 10 What values of x make the expression true, and what values of x make the expression false? This expression is always true, no matter what value is assigned to the variable x. A Boolean expression that is always true is known as a tautology. Think about it. If x is a number, what value could the variable x assume that would make this Boolean expression false? Regardless of its value, one or both of the subexpressions will be true, so the compound or expression is always true. This particular or expression is just a complicated way of expressing the value True. Another common error is contriving compound Boolean expressions that are always false, known as contradictions. Suppose you wish to exclude values from a given range; for example, reject values in the range 0...10 and accept all other numbers. Is the Boolean expression in the following code fragment up to the task? # All but 0, 1, 2, ..., 10 if value < 0 and value > 10:

print(value)

A closer look at the condition reveals it can never be true. What number can be both less than zero and
greater than ten at the same time? None can, of course, so the expression is a contradiction and a compli-
cated way of expressing False. To correct this code fragment, replace the and operator with or.

Table 4.4 indicates that the logical operators and, or, and not have lower precedence than the compari-
son operators. Suppose you wish to print the word OK if a variable x is 1, 2, or 3. An informal translation
from English might yield:

if x == 1 or 2 or 3:
print(“OK”)

Unfortunately, x’s value is irrelevant; the code always prints the word OK regardless of the value of x. Since
the == operator has lower precedence than or, Python interprets the expression

x == 1 or 2 or 3

as if it were expressed as

(x == 1) or 2 or 3

The expression x == 1 is either true or false, but integer 2 is always interpreted as true, and integer 3 is
interpreted as true is as well.

The the most correct way express the original statement would be

if x == 1 or x == 2 or x == 3:
print(“OK”)

The revised Boolean expression is more verbose and less similar to the English rendition, but it is the correct
formulation for Python. Note that each of the subexpressions involves a Boolean expression, not an integer
value. If x is known to be an integer and not a floating-point number, the expression

1 <= x <= 3 also would be equivalent. Consider Listing 4.27 (digittoworderror.py), which is a variation of Listing 4.18 (restyleddigittoword.py). Listing 4.27 (digittoworderror.py) assigns a word to a string variable instead of printing it immediately. ©2017 Richard L. Halterman Draft date: January 18, 2018 4.12. ERRORS IN CONDITIONAL STATEMENTS 104 Listing 4.27: digittoworderror.py value = int(input("Please enter an integer in the range 0...5: ")) answer = "not in range" # Default answer if value == 0: answer = "zero" elif value == 1: answer = "one" elif value == 2: answer = "two" elif value == 3: amswer = "three" elif value == 4: answer = "four" elif value == 5: answer = "five" print("The number you entered was", answer) The following shows a sample run of Listing 4.27 (digittoworderror.py): Please enter an integer in the range 0...5: 2 The number you entered was two Another run shows Please enter an integer in the range 0...5: 7 The number you entered was not in range Of course the program will crash with an error if the user enters a noninteger value (the int function will raise an exception), but the program should accept any integer value and always do the right thing. In fact, Listing 4.27 (digittoworderror.py) always works as expected except when the user enters 3: Please enter an integer in the range 0...5: 3 The number you entered was not in range The program has a subtle spelling error; can you find it? On an English keyboard the M and N keys are next to each other. It is a common typographical error to press one in place of the other by mistake. Note the variable named amswer in the condition that checks for value equaling 3. The program reassigns the original answer variable for each option except when the user submits the value 3. When the user enters 3 the program creates a new variable which goes unreported in the final printing statement. This kind of error is not restricted to conditional statements but is due to the way Python manages variables. A programmer can create a new variable at any time using the simple assignment operator. The statement amswer = "three" cannot reassign the original answer variable but only create a brand new variable with a different name. Unfortunately the interpreter cannot understand what we mean by the code we write; it only can dutifully execute the code we provide to it. Listing 4.27 (digittoworderror.py) is small and focussed, and so the logic error introduced by the mis- spelled variable was easy to track down. As our programs grow in size and our logic becomes more complex, a misspelling error that creates a new variable sometimes can be difficult to track down without ©2017 Richard L. Halterman Draft date: January 18, 2018 4.13. LOGIC COMPLEXITY 105 assistance. Fortunately tools exist that can help. Programmers can use Pylint (http://www.pylint.org/) to analyze Python source code. Among other useful information, Pylint can detect variables defined within a program that have no later use. 4.13 Logic Complexity Python provides the tools to construct some very complicated conditional statements. It is important to resist the urge to make things overly complex. Composing Boolean expressions with and, or, and not allows us to build conditions with arbitrarily complex logic. There often are many ways to achieve the same effect; for example, the following four Boolean expressions are equivalent: not (a == b and c != d) not (a == b and not (c == d)) not (a == b) or not (c != d) a != b or c == d While the four expressions are logically equivalent, they exhibit various degrees of complication. Some situations require complicated logic to achieve the desired program behavior, but, in general, the simplest logic that works is better than more complex equivalent logic for several reasons: • Simpler logic usually is easier to understand. • Simpler logic is easier to write and get working. Longer, more complicated expressions increase the risk of typographical errors that can manifest themselves as logic errors. These errors are more difficult to find and correct in complex code. • Simpler logic is can be more efficient. Every relational comparison and Boolean operation executed by a running program requires machine cycles. The expression not (a == b and not (c == d)) performs up to five separate operations: == twice, not twice, and and once. If a does not equal b, the expression will perform only two operations (== and the outer not) due to short-circuit Boolean evaluation of the and. Compare this expression to the following equivalent expression: a != b or c == d An executing program can evaluate this expression faster, as it involves at most three operations: !=, ==, and or. If a is not equal to b, the execution short-circuits the or, and evaluates only the != operation. • Simpler logic is easier to modify and extend. Consider the task of computing the maximum value of four integers entered by the user. Listing 4.28 (max4a.py) provides one solution. Listing 4.28: max4a.py # Get input values from user print("Please enter four integer values.") num1 = int(input("Enter number 1: ")) num2 = int(input("Enter number 2: ")) ©2017 Richard L. Halterman Draft date: January 18, 2018 http://www.pylint.org/ 4.13. LOGIC COMPLEXITY 106 num3 = int(input("Enter number 3: ")) num4 = int(input("Enter number 4: ")) # Compute the maximum value if num1 >= num2 and num1 >= num3 and num1 >= num4:

max = num1
elif num2 >= num1 and num2 >= num3 and num2 >= num4:

max = num2
elif num3 >= num1 and num3 >= num2 and num3 >= num4:

max = num3
else: # The maximum must be num4 at this point

max = num4

# Report result
print(“The maximum number entered was:”, max)

Listing 4.28 (max4a.py) uses a multiway if/elif/else construct to select the correct value to assign to its
max variable.

Listing 4.28 (max4a.py) works correctly for any four integers a user may enter, but its logic is somewhat
complicated. We will consider a different strategy for our selection logic. All variables have a meaning,
and their names should reflect their meaning in some way. We’ll let our max variable mean “maximum I
have determined so far.” The following outlines our new approach to the solution:

1. Set max equal to n1. This means as far as we know at the moment, n1 is the biggest number because
max and n1 have the same value.

2. Compare max to n2. If n2 is larger than max, change max to have n2’s value to reflect the fact that
we determined n2 is larger; if n2 is not larger than max, we have no reason to change max, so do not
change it.

3. Compare max to n3. If n3 is larger than max, change max to have n3’s value to reflect the fact that
we determined n3 is larger; if n3 is not larger than max, we have no reason to change max, so do not
change it.

4. Compare max to n4. If n4 is larger than max, change max to have n4’s value to reflect the fact that
we determined n4 is larger; if n4 is not larger than max, we have no reason to change max, so do not
change it.

In the end the meaning of the max variable remains the same–“maximum I have determined so far,”
but, after comparing max to all the input variables, we now know it is the maximum value of all four input
numbers. The extra variable max is not strictly necessary, but it makes thinking about the problem and its
solution easier.

Listing 4.29 (max4b.py) uses our revised selection logic to provide an alternative to Listing 4.28 (max4a.py).

Listing 4.29: max4b.py

# Get input values from user
print(“Please enter four integer values.”)
num1 = int(input(“Enter number 1: “))
num2 = int(input(“Enter number 2: “))
num3 = int(input(“Enter number 3: “))
num4 = int(input(“Enter number 4: “))

4.14. EXERCISES 107

# Compute the maximum value
max = num1
if num2 > max:

max = num2
if num3 > max:

max = num3
if num4 > max:

max = num4

# Report result
print(“The maximum number entered was:”, max)

Listing 4.29 (max4b.py) uses simple, sequential if statements to eventually assign the correct value to its
max variable.

Listing 4.29 (max4b.py) always performs three > comparisons and at most four assignments regard-
less of the values provided by the user. The source code for Listing 4.28 (max4a.py) contains many
more Boolean operations than Listing 4.29 (max4b.py), but, due to short-circuit evaluation, Listing 4.28
(max4a.py) actually can outperform Listing 4.29 (max4b.py) in some situations. Simpler logic is no guar-
antee of better performance. Both programs are so simple, however, that users will perceive no difference
in execution speeds.

What changes would we need to make to both Listing 4.28 (max4a.py) and Listing 4.29 (max4b.py)
if we must extend them to handle five input values instead of four? Adding this capability to Listing 4.28
(max4a.py) forces us to modify every condition in the program, adding a check against a new num5 variable.
We also must provide an additional elif check since we will need to select from among five possible
assignments to the max variable. In Listing 4.29 (max4b.py), however, we need only add an extra sequential
if statement with a new simple condition to check.

Chapter 5 introduces loops, the ability to execute statements repeatedly. You easily can adapt the se-
quential if approach to allow users to type in as many numbers as they like and then have the program
report the maximum number the user entered. The multiway if/elif/else approach with the more com-
plex logic cannot be adapted in this manner. Not only is our sequential if version cleaner and simpler; we
more easily can extend its capabilities.

4.14 Exercises

1. What possible values can a Boolean expression have?

2. Where does the term Boolean originate?

3. What is an integer equivalent to True in Python?

4. What is the integer equivalent to False in Python?

5. Is the value -16 interpreted as True or False?

6. Given the following definitions:

x, y, z = 3, 5, 7

evaluate the following Boolean expressions:

4.14. EXERCISES 108

(a) x == 3

(b) x < y (c) x >= y

(d) x <= y (e) x != y - 2 (f) x < 10 (g) x >= 0 and x < 10 (h) x < 0 and x < 10 (i) x >= 0 and x < 2 (j) x < 0 or x < 10 (k) x > 0 or x < 10 (l) x < 0 or x > 10

7. Given the following definitions:

x, y = 3, 5
b1, b2, b3, b4 = True, False, x == 3, y < 3 evaluate the following Boolean expressions: (a) b3 (b) b4 (c) not b1 (d) not b2 (e) not b3 (f) not b4 (g) b1 and b2 (h) b1 or b2 (i) b1 and b3 (j) b1 or b3 (k) b1 and b4 (l) b1 or b4 (m) b2 and b3 (n) b2 or b3 (o) b1 and b2 or b3 (p) b1 or b2 and b3 (q) b1 and b2 and b3 (r) b1 or b2 or b3 (s) not b1 and b2 and b3 (t) not b1 or b2 or b3 (u) not (b1 and b2 and b3) (v) not (b1 or b2 or b3) ©2017 Richard L. Halterman Draft date: January 18, 2018 4.14. EXERCISES 109 (w) not b1 and not b2 and not b3 (x) not b1 or not b2 or not b3 (y) not (not b1 and not b2 and not b3) (z) not (not b1 or not b2 or not b3) 8. Express the following Boolean expressions in simpler form; that is, use fewer operators. x is an integer. (a) not (x == 2) (b) x < 2 or x == 2 (c) not (x < y) (d) not (x <= y) (e) x < 10 and x > 20

(f) x > 10 or x < 20 (g) x != 0 (h) x == 0 9. Express the following Boolean expressions in an equivalent form without the not operator. x and y are integers. (a) not (x == y) (b) not (x > y)

(e) not (x <= y) (f) not (x != y) (g) not (x != y) (h) not (x == y and x < 2) (i) not (x == y or x < 2) (j) not (not (x == y)) 10. What is the simplest tautology? 11. What is the simplest contradiction? 12. Write a Python program that requests an integer value from the user. If the value is between 1 and 100 inclusive, print ”OK;” otherwise, do not print anything. 13. Write a Python program that requests an integer value from the user. If the value is between 1 and 100 inclusive, print ”OK;” otherwise, print ”Out of range.” 14. Write a Python program that allows a user to type in an English day of the week (Sunday, Monday, etc.). The program should print the Spanish equivalent, if possible. 15. Consider the following Python code fragment: ©2017 Richard L. Halterman Draft date: January 18, 2018 4.14. EXERCISES 110 # i, j, and k are numbers if i < j: if j < k: i = j else: j = k else: if j > k:

j = i
else:

i = k
print(“i =”, i, ” j =”, j, ” k =”, k)

What will the code print if the variables i, j, and k have the following values?

(a) i is 3, j is 5, and k is 7

(b) i is 3, j is 7, and k is 5

(d) i is 5, j is 7, and k is 3

(e) i is 7, j is 3, and k is 5

(f) i is 7, j is 5, and k is 3

16. Consider the following Python program that prints one line of text:

val = int(input())
if val < 10: if val != 5: print("wow ", end='') else: val += 1 else: if val == 17: val += 10 else: print("whoa ", end='') print(val) What will the program print if the user provides the following input? (a) 3 (b) 21 (c) 5 (d) 17 (e) -5 17. Consider the following two Python programs that appear very similar: ©2017 Richard L. Halterman Draft date: January 18, 2018 4.14. EXERCISES 111 n = int(input()) if n < 1000: print('*', end='') if n < 100: print('*', end='') if n < 10: print('*', end='') if n < 1: print('*', end='') print() n = int(input()) if n < 1000: print('*', end='') elif n < 100: print('*', end='') elif n < 10: print('*', end='') elif n < 1: print('*', end='') print() How do the two programs react when the user provides the following inputs? (a) 0 (b) 1 (c) 5 (d) 50 (e) 500 (f) 5000 Why do the two programs behave as they do? 18. Write a Python program that requests five integer values from the user. It then prints the maximum and minimum values entered. If the user enters the values 3, 2, 5, 0, and 1, the program would indicate that 5 is the maximum and 0 is the minimum. Your program should handle ties properly; for example, if the user enters 2, 4 2, 3 and 3, the program should report 2 as the minimum and 4 as maximum. 19. Write a Python program that requests five integer values from the user. It then prints one of two things: if any of the values entered are duplicates, it prints "DUPLICATES"; otherwise, it prints "ALL UNIQUE". ©2017 Richard L. Halterman Draft date: January 18, 2018 4.14. EXERCISES 112 ©2017 Richard L. Halterman Draft date: January 18, 2018 113 Chapter 5 Iteration Iteration repeats the execution of a sequence of code. Iteration is useful for solving many programming problems. Iteration and conditional execution form the basis for algorithm construction. 5.1 The while Statement Listing 5.1 (counttofive.py) counts to five by printing a number on each output line. Listing 5.1: counttofive.py print(1) print(2) print(3) print(4) print(5) When executed, this program displays 1 2 3 4 5 How would you write the code to count to 10,000? Would you copy, paste, and modify 10,000 printing statements? You could, but that would be impractical! Counting is such a common activity, and computers routinely count up to very large values, so there must be a better way. What we really would like to do is print the value of a variable (call it count), then increment the variable (count += 1), and repeat this process until the variable is large enough (count == 5 or maybe count == 10000). This process of executing the same section of code over and over is known as iteration, or looping. Python has two different statements, while and for, that enable iteration. Listing 5.2 (iterativecounttofive.py) uses a while statement to count to five: Listing 5.2: iterativecounttofive.py ©2017 Richard L. Halterman Draft date: January 18, 2018 5.1. THE WHILE STATEMENT 114 count = 1 # Initialize counter while count <= 5: # Should we continue? print(count) # Display counter, then count += 1 # Increment counter The while statement in Listing 5.2 (iterativecounttofive.py) repeatedly displays the variable count. The program executes the following block of statements five times: print(count) count += 1 After each redisplay of the variable count, the program increments it by one. Eventually (after five itera- tions), the condition count <= 5 will no longer be true, and the block is no longer executed. Unlike the approach taken in Listing 5.1 (counttofive.py), it is trivial to modify Listing 5.2 (iterativecounttofive.py) to count up to 10,000—just change the literal value 5 to 10000. The line while count <= 5: begins the while statement. The expression following the while keyword is the condition that determines if the statement block is executed or continues to execute. As long as the condition is true, the program executes the code block over and over again. When the condition becomes false, the loop is finished. If the condition is false initially, the program will not execute the code block within the body of the loop at all. The while statement has the general form: condition block while : • The reserved word while begins the while statement. • The condition determines whether the body will be (or will continue to be) executed. A colon (:) must follow the condition. • block is a block of one or more statements to be executed as long as the condition is true. As a block, all the statements that comprise the block must be indented one level deeper than the line that begins the while statement. The block technically is part of the while statement. Except for the reserved word while instead of if, while statements look identical to if statements. Sometimes beginning programmers confuse the two or accidentally type if when they mean while or vice-versa. Usually the very different behavior of the two statements reveals the problem immediately; however, sometimes, especially in nested, complex logic, this mistake can be hard to detect. Figure 5.1 shows how program execution flows through Listing 5.2 (iterativecounttofive.py). ©2017 Richard L. Halterman Draft date: January 18, 2018 5.1. THE WHILE STATEMENT 115 Figure 5.1 while flowchart for Listing 5.2 (iterativecounttofive.py) Is count ≤ 5? Print count’s value Set count equal to 1 Start Increment count’s value End No Yes ©2017 Richard L. Halterman Draft date: January 18, 2018 5.1. THE WHILE STATEMENT 116 The executing program checks the condition before executing the while block and then checks the condition again after executing the while block. As long as the condition remains truth, the program repeatedly executes the code in the while block. If the condition initially is false, the program will not execute the code within the while block. If the condition initially is true, the program executes the block repeatedly until the condition becomes false, at which point the loop terminates. Listing 5.3 (countup.py) counts up from zero as long as the user wishes to do so. Listing 5.3: countup.py # Counts up from zero. The user continues the count by entering # 'Y'. The user discontinues the count by entering 'N'. count = 0 # The current count entry = 'Y' # Count to begin with while entry != 'N' and entry != 'n': # Print the current value of count print(count) entry = input('Please enter "Y" to continue or "N" to quit: ') if entry == 'Y' or entry == 'y': count += 1 # Keep counting # Check for "bad" entry elif entry != 'N' and entry != 'n': print('"' + entry + '" is not a valid choice') # else must be 'N' or 'n' A sample run of Listing 5.3 (countup.py) produces 0 Please enter "Y" to continue or "N" to quit: y 1 Please enter "Y" to continue or "N" to quit: y 2 Please enter "Y" to continue or "N" to quit: y 3 Please enter "Y" to continue or "N" to quit: q "q" is not a valid choice 3 Please enter "Y" to continue or "N" to quit: r "r" is not a valid choice 3 Please enter "Y" to continue or "N" to quit: W "W" is not a valid choice 3 Please enter "Y" to continue or "N" to quit: Y 4 Please enter "Y" to continue or "N" to quit: y 5 Please enter "Y" to continue or "N" to quit: n In Listing 5.3 (countup.py) the expression entry != 'N' and entry != 'n' ©2017 Richard L. Halterman Draft date: January 18, 2018 5.1. THE WHILE STATEMENT 117 is true if entry is neither N not n. Listing 5.4 (addnonnegatives.py) is a program that allows a user to enter any number of nonnegative integers. When the user enters a negative value, the program no longer accepts input, and it displays the sum of all the nonnegative values. If a negative number is the first entry, the sum is zero. Listing 5.4: addnonnegatives.py # Allow the user to enter a sequence of nonnegative # integers. The user ends the list with a negative # integer. At the end the sum of the nonnegative # numbers entered is displayed. The program prints # zero if the user provides no nonnegative numbers. entry = 0 # Ensure the loop is entered sum = 0 # Initialize sum # Request input from the user print("Enter numbers to sum, negative number ends list:") while entry >= 0: # A negative number exits the loop
entry = int(input()) # Get the value
if entry >= 0: # Is number nonnegative?

sum += entry # Only add it if it is nonnegative
print(“Sum =”, sum) # Display the sum

Listing 5.4 (addnonnegatives.py) uses two variables, entry and sum:

• entry

In the beginning we initialize entry to zero for the sole reason that we want the condition entry >= 0
of the while statement to be true initially. If we fail to initialize entry, the program will produce a
run-time error when it attempts to compare entry to zero in the while condition. The entry variable
holds the number entered by the user. Its value can change each time through the loop.

• sum

The variable sum is known as an accumulator because it accumulates each value the user enters. We
initialize sum to zero in the beginning because a value of zero indicates that it has not accumulated
anything. If we fail to initialize sum, the program will generate a run-time error when it attempts
to use the += operator to modify the (non-existent) variable. Within the loop we repeatedly add the
user’s input values to sum. When the loop finishes (because the user entered a negative number), sum
holds the sum of all the nonnegative values entered by the user.

The initialization of entry to zero coupled with the condition entry >= 0 of the while guarantees
that the program will execute the body of the while loop at least once. The if statement ensures that
the program will not add a negative entry to sum. (Could the if condition have used > instead of >= and
achieved the same results?) When the user enters a negative value, the executing program will not update
the sum variable, and the condition of the while will no longer be true. The loop then terminates and the
program executes the print statement.

Listing 5.4 (addnonnegatives.py) shows that a while loop can be used for more than simple counting.
The program does not keep track of the number of values entered. The program simply accumulates the
entered values in the variable named sum.

5.1. THE WHILE STATEMENT 118

Figure 5.2 Decision tree for troubleshooting a computer system

We can use a while statement to make Listing 4.14 (troubleshoot.py) more convenient for the user.
Recall that the computer troubleshooting program forces the user to rerun the program once a potential
program has been detected (for example, turn on the power switch, then run the program again to see what
else might be wrong). A more desirable decision logic is shown in Figure 5.2.

Listing 5.5 (troubleshootloop.py) incorporates a while statement so that the program’s execution con-
tinues until the problem is resolved or its resolution is beyond the capabilities of the program.

Listing 5.5: troubleshootloop.py

print(“Help! My computer doesn’t work!”)
done = False # Not done initially
while not done:

print(“Does the computer make any sounds (fans, etc.) “)
choice = input(“or show any lights? (y/n):”)
# The troubleshooting control logic
if choice == ‘n’: # The computer does not have power

choice = input(“Is it plugged in? (y/n):”)
if choice == ‘n’: # It is not plugged in, plug it in

print(“Plug it in.”)
else: # It is plugged in

5.1. THE WHILE STATEMENT 119

choice = input(“Is the switch in the \”on\” position? (y/n):”)
if choice == ‘n’: # The switch is off, turn it on!

print(“Turn it on.”)
else: # The switch is on

choice = input(“Does the computer have a fuse? (y/n):”)
if choice == ‘n’: # No fuse

choice = input(“Is the outlet OK? (y/n):”)
if choice == ‘n’: # Fix outlet

print(“Check the outlet’s circuit “)
print(“breaker or fuse. Move to a”)
print(“new outlet, if necessary. “)

else: # Beats me!
print(“Please consult a service technician.”)
done = True # Nothing else I can do

else: # Check fuse
print(“Check the fuse. Replace if “)
print(“necessary.”)

else: # The computer has power
print(“Please consult a service technician.”)
done = True # Nothing else I can do

A while block makes up the bulk of Listing 5.5 (troubleshootloop.py). The Boolean variable done
controls the loop; as long as done is false, the loop continues. A Boolean variable like done used in this
fashion is often called a flag. You can think of the flag being down when the value is false and raised when
it is true. In this case, when the flag is raised, it is a signal that the loop should terminate.

It is important to note that the expression

not done

of the while statement’s condition evaluates to the opposite truth value of the variable done; the expression
does not affect the value of done. In other words, the not operator applied to a variable does not modify
the variable’s value. In order to actually change the variable done, you would need to reassign it, as in

done = not done # Invert the truth value

For Listing 5.5 (troubleshootloop.py) we have no need to invert done’s value. We ensure that done’s value
is False initially and then make it True when the user has exhausted the program’s options.

In Python, sometimes it is convenient to use a simple value as conditional expression in an if or while
statement. Python interprets the integer value 0 and floating-point value 0.0 both as False. All other integer
and floating-point values, both positive and negative, are considered True. This means the following code:

x = int(input()) # Get integer from user
while x:

print(x) # Print x only if x is nonzero
x -= 1 # Decrement x

is equivalent to

x = int(input()) # Get integer from user
while x != 0:

print(x) # Print x only if x is nonzero
x -= 1 # Decrement x

5.1. THE WHILE STATEMENT 120

Speaking of floating-point values, Section 3.1 demonstrated how the limited precision of floating-point
numbers can be a problem. You should use caution when using a floating-point number to control a loop,
as Listing 5.6 (stopatone.py) shows

Listing 5.6: stopatone.py

x = 0.0
while x != 1.0:

print(x)
x += 0.1

print(“Done”)

The programmer’s intention is for Listing 5.6 (stopatone.py) to begin at 0.0 and count up to 1.0 by tenths.
In other words, the program should stop looping when the variable x becomes 1.0. With true mathematical

real numbers, if we add
1

10
to 0 ten times, the result equals 1. Unfortunately, Listing 5.6 (stopatone.py)

bypasses 1 and keeps going! The first few lines of its execution are

0.0
0.1
0.2
0.30000000000000004
0.4
0.5
0.6
0.7
0.7999999999999999
0.8999999999999999
0.9999999999999999
1.0999999999999999
1.2
1.3
1.4000000000000001
1.5000000000000002

The program never stops printing numbers. Note that
1

10
does not have an exact internal binary floating-

point representation. If you change the statement

x += 0.1

to be

x += 0.125

the program stops as expected. This is because
1
8

happens to have an exact internal binary floating-point
representation. Since such exact representations of floating-point values are rare, you should avoid using
the == and != operators with floating-point numbers to control the number of loop iterations. Listing 5.7
(stopatonefixed.py) uses <= to control the loop instead of !=, and it behaves as expected. Listing 5.7: stopatonefixed.py x = 0.0 ©2017 Richard L. Halterman Draft date: January 18, 2018 5.2. DEFINITE LOOPS VS. INDEFINITE LOOPS 121 while x != 1.0: print(x) x += 0.1 print("Done") 5.2 Definite Loops vs. Indefinite Loops In Listing 5.8 (definite1.py), code similar to Listing 5.1 (counttofive.py), prints the integers from one to 10. Listing 5.8: definite1.py n = 1 while n <= 10: print(n) n += 1 We can inspect the code and determine the exact number of iterations the loop will perform. This kind of loop is known as a definite loop, since we can predict exactly how many times the loop repeats. Consider Listing 5.9 (definite2.py). Listing 5.9: definite2.py n = 1 stop = int(input()) while n <= stop: print(n) n += 1 Looking at the source code of Listing 5.9 (definite2.py), we cannot predict how many times the loop will repeat. The number of iterations depends on the input provided by the user. However, at the program’s point of execution after obtaining the user’s input and before the start of the execution of the loop, we would be able to determine the number of iterations the while loop would perform. Because of this, the loop in Listing 5.9 (definite2.py) is considered to be a definite loop as well. Compare these programs to Listing 5.10 (indefinite.py). Listing 5.10: indefinite.py done = False # Enter the loop at least once while not done: entry = int(input()) # Get value from user if entry == 999: # Did user provide the magic number? done = True # If so, get out else: print(entry) # If not, print it and continue In Listing 5.10 (indefinite.py), we cannot predict at any point during the loop’s execution how many itera- tions the loop will perform. The value to match (999) is know before and during the loop, but the variable ©2017 Richard L. Halterman Draft date: January 18, 2018 5.3. THE FOR STATEMENT 122 entry can be anything the user enters. The user could choose to enter 0 exclusively or enter 999 immedi- ately and be done with it. The while statement in Listing 5.10 (indefinite.py) is an example of an indefinite loop. Listing 5.5 (troubleshootloop.py) is another example of an indefinite loop. The while statement is ideal for indefinite loops. Although we have used the while statement to implement definite loops, Python provides a better alternative for definite loops: the for statement. 5.3 The for Statement The while loop is ideal for indefinite loops. As Listing 5.5 (troubleshootloop.py) demonstrated, a program- mer cannot always predict how many times a while loop will execute. We have used a while loop to implement a definite loop, as in n = 1 while n <= 10: print(n) n += 1 The print statement in this code executes exactly 10 times every time this code runs. This code requires three crucial pieces to manage the loop: • initialization: n = 1 • check: n <= 10 • update: n += 1 Python provides a more convenient way to express a definite loop. The for statement iterates over a sequence of values. One way to express a sequence is via a tuple, as shown here: for n in 1, 2, 3, 4, 5, 6, 7, 8, 9, 10: print(n) This code behaves identically to the while loop above. The print statement here executes exactly 10 times. The code first prints 1, then 2, then 3, etc. The final value it prints is 10. During the iteration the variable n thus assumes, in order, all the values that make up the tuple. It usually is cumbersome to explicitly list all the elements of a tuple, and often it is impractical. Consider iterating over all the integers from 1 to 1,000—writing out all the tuple’s elements would be unwieldy. Fortunately, Python provides a convenient way to express a sequence of integers that follow a regular pattern. The following code uses a range expression to print the integers 1 through 10: for n in range(1, 11): print(n) The expression range(1, 11) creates a range object that allows the for loop to assign to the variable n the values 1, 2, . . . , 10. Conceptually, the expression range(1, 11) represents the sequence of integers 1,2,3,4,5,6,7,8,9,10. The line for n in range(1, 11): ©2017 Richard L. Halterman Draft date: January 18, 2018 5.3. THE FOR STATEMENT 123 is best read as “For each integer n in the range 1≤ n < 11.” During the first iteration of the loop, n’s value is 1 within the block. In the loop’s second iteration, n has the value of 2. Each time through the loop, n’s value increases by one. The code within the block will use the values of n up to 10. The general form of the range expression is range( begin,end,step ) where • begin is the first value in the range; if omitted, the default value is 0 • end is one past the last value in the range; the end value is always required and may not be omitted • step is the amount to increment or decrement; if the step parameter is omitted, it defaults to 1 (counts up by ones) begin, end, and step must all be integer expressions; floating-point expressions and other types are not allowed. The arguments in the range expression may be literal numbers (like 10), variables (like x, if x is bound to an integer), and arbitrarily complex integer expressions. The range expression is very flexible. Consider the following loop that counts down from 21 to 3 by threes: for n in range(21, 0, -3): print(n, end=' ') It prints 21 18 15 12 9 6 3 Thus range(21, 0, -3) represents the sequence 21,18,15,12,9,3. The expression range(1000) produces the sequence 0,1,2, . . . ,999. The following code computes and prints the sum of all the positive integers less than 100: sum = 0 # Initialize sum for i in range(1, 100): sum += i print(sum) The following examples show how to use range to produce a variety of sequences: • range(10)→ 0,1,2,3,4,5,6,7,8,9 • range(1, 10)→ 1,2,3,4,5,6,7,8,9 • range(1, 10, 2)→ 1,3,5,7,9 • range(10, 0, -1)→ 10,9,8,7,6,5,4,3,2,1 • range(10, 0, -2)→ 10,8,6,4,2 • range(2, 11, 2)→ 2,4,6,8,10 ©2017 Richard L. Halterman Draft date: January 18, 2018 5.3. THE FOR STATEMENT 124 • range(-5, 5)→−5,−4,−3,−2,−1,0,1,2,3,4 • range(1, 2)→ 1 • range(1, 1)→ (empty) • range(1, -1)→ (empty) • range(1, -1, -1)→ 1,0 • range(0)→ (empty) In a range expression with one argument, as in range(x), the x represents the end of the range, with 0 being the implied begin value, and 1 being the step value. In a range expression with two arguments, as in range(x, y), the x represents the begin value, and y represents the end of the range. The implied step value is 1. In a range expression with three arguments, as in range(x, y, z), the x represents the begin value, y represents the end of the range, and z is the step value. Loops allow us to rewrite an expanded form of Listing 2.20 (powers10right.py) more compactly. List- ing 5.11 (powers10loop.py) uses a for loop to print the first 16 powers of 10. Listing 5.11: powers10loop.py for i in range(16): print('{0:3} {1:16}'.format(i, 10**i)) Listing 5.11 (powers10loop.py) prints 0 1 1 10 2 100 3 1000 4 10000 5 100000 6 1000000 7 10000000 8 100000000 9 1000000000 10 10000000000 11 100000000000 12 1000000000000 13 10000000000000 14 100000000000000 15 1000000000000000 In a for loop the range object has complete control over determining the loop variable each time through the loop. To prove this, Listing 5.12 (abusefor.py) attempts to thwart the range’s loop variable by changing its value inside the loop. Listing 5.12: abusefor.py # Abuse the for statement ©2017 Richard L. Halterman Draft date: January 18, 2018 5.3. THE FOR STATEMENT 125 for i in range(10): print(i, end=' ') # Print i as served by the range object if i == 5: i = 20 # Change i inside the loop? print('({})'.format(i), end=' ') print() Listing 5.12 (abusefor.py) prints the following: 0 (0) 1 (1) 2 (2) 3 (3) 4 (4) 5 (20) 6 (6) 7 (7) 8 (8) 9 (9) The first number is i’s value at the beginning of the block, and the parenthesized number is i’s value at the end of the block before the next iteration. The code within the block can reassign i, but this binds i to a different integer object (20). The next time through the loop the for statement obtains the next integer served by the range object and binds i to this new integer. If you look in older Python books or at online examples of Python code, you prob- ably will encounter the xrange expression. Python 2 has both range and xrange, but Python 3 (the version we use in this text) does not have the xrange expres- son. The range expression in Python 3 is equivalent to the xrange expression in Python 2. The range expression in Python 2 creates a data structure called a list, and this process can involve considerable overhead for an executing pro- gram. The xrange expression in Python 2 avoids this overhead, making it more efficient than range, especially for a large sequence. When building loops with the for statement, Python 2 programmers usually use xrange rather than range to improve their code’s efficiency. In Python 3, we can use range without com- promising run-time performance. In Chapter 10 we will see it is easy to make a list out of a Python 3 range expression, so Python 3 does not need two different range expressions that do almost exactly the same thing. We initially emphasize the for loop’s ability to iterate over integer sequences because this is a useful and common task in software construction. The for loop, however, can iterate over any iterable object. As we have seen, a tuple is an iterable object, and a range object is an iterable object. A string also is an iterable object. We can use a for loop to iterate over the characters that comprise a string. Listing 5.13 (stringletters.py) uses a for loop to print the individual characters of a string. Listing 5.13: stringletters.py word = input('Enter a word: ') for letter in word: print(letter) In the following sample execution of Listing 5.13 (stringletters.py) shows how the program responds when the user enters the word tree: Enter a word: tree t r e e ©2017 Richard L. Halterman Draft date: January 18, 2018 5.4. NESTED LOOPS 126 At each iteration of its for loop Listing 5.13 (stringletters.py) assigns to the letter variable a string con- taining a single character. Listing 5.14 (stringliteralletters.py) uses a for loop to iterate over a literal string. Listing 5.14: stringliteralletters.py for c in 'ABCDEF': print('[', c, ']', end='', sep='') print() Listing 5.14 (stringliteralletters.py) prints [A][B][C][D][E][F] Listing 5.15 (countvowels.py) counts the number of vowels in the text provided by the user. Listing 5.15: countvowels.py word = input('Enter text: ') vowel_count = 0 for c in word: if c == 'A' or c == 'a' or c == 'E' or c == 'e' \ or c == 'I' or c == 'i' or c == 'O' or c == 'o': print(c, ', ', sep='', end='') # Print the vowel vowel_count += 1 # Count the vowel print(' (', vowel_count, ' vowels)', sep='') Listing 5.14 (stringliteralletters.py) prints vowels it finds and then reports how many it found: Enter text: Mary had a little lamb. a, a, a, i, e, a, (6 vowels) Chapter 10 and beyond use the for statement to traverse data structures such as lists and dictionaries. 5.4 Nested Loops Just like with if statements, while and for blocks can contain arbitrary Python statements, including other loops. A loop can therefore be nested within another loop. To see how nested loops work, consider a program that prints out a multiplication table. Elementary school students use multiplication tables, or times tables, as they learn the products of integers up to 10 or even 12. Figure 5.3 shows a 10 × 10 multiplication table. We want our multiplication table program to be flexible and allow the user to specify the table’s size. We will begin our development work with a simple program and add features as we go. First, we will not worry about printing the table’s row and column titles, nor will we print the lines separating the titles from the contents of the table. Initially we will print only the contents of the table. We will see we need a nested loop to print the table’s contents, but that still is too much to manage in our first attempt. In our first attempt we will print the rows of the table in a very rudimentary manner. Once we are satisfied that our simple program works we can add more features. Listing 5.16 (timestable1.py) shows our first attempt at a muliplication table. Listing 5.16: timestable1.py ©2017 Richard L. Halterman Draft date: January 18, 2018 5.4. NESTED LOOPS 127 Figure 5.3 A 10 × 10 multiplication table # Get the number of rows and columns in the table size = int(input("Please enter the table size: ")) # Print a size x size multiplication table for row in range(1, size + 1): print("Row #", row) The output of Listing 5.16 (timestable1.py) is somewhat underwhelming: Please enter the table size: 10 Row #1 Row #2 Row #3 Row #4 Row #5 Row #6 Row #7 Row #8 Row #9 Row #10 Listing 5.16 (timestable1.py) does indeed print each row in its proper place—it just does not supply the needed detail for each row. Our next step is to refine the way the program prints each row. Each row should contain size numbers. Each number within each row represents the product of the current row and current column; for example, the number in row 2, column 5 should be 2 × 5 = 10. In each row, therefore, we must vary the column number from from 1 to size. Listing 5.17 (timestable2.py) contains the needed refinement. Listing 5.17: timestable2.py # Get the number of rows and columns in the table size = int(input("Please enter the table size: ")) # Print a size x size multiplication table for row in range(1, size + 1): ©2017 Richard L. Halterman Draft date: January 18, 2018 5.4. NESTED LOOPS 128 for column in range(1, size + 1): product = row*column # Compute product print(product, end=' ') # Display product print() # Move cursor to next row We use a loop to print the contents of each row. The outer loop controls how many total rows the program prints, and the inner loop, executed in its entirety each time the program prints a row, prints the individual elements that make up a row. The result of Listing 5.17 (timestable2.py) is Please enter the table size: 10 1 2 3 4 5 6 7 8 9 10 2 4 6 8 10 12 14 16 18 20 3 6 9 12 15 18 21 24 27 30 4 8 12 16 20 24 28 32 36 40 5 10 15 20 25 30 35 40 45 50 6 12 18 24 30 36 42 48 54 60 7 14 21 28 35 42 49 56 63 70 8 16 24 32 40 48 56 64 72 80 9 18 27 36 45 54 63 72 81 90 10 20 30 40 50 60 70 80 90 100 The numbers within each column are not lined up nicely, but the numbers are in their correct positions relative to each other. We can use the string formatter introduced in Listing 2.20 (powers10right.py) to right justify the numbers within a four-digit area. Listing 5.18 (timestable3.py) contains this alignment adjustment. Listing 5.18: timestable3.py # Get the number of rows and columns in the table size = int(input("Please enter the table size: ")) # Print a size x size multiplication table for row in range(1, size + 1): for column in range(1, size + 1): product = row*column # Compute product print('{0:4}'.format(product), end='') # Display product print() # Move cursor to next row Listing 5.18 (timestable3.py) produces the table’s contents in an attractive form: Please enter the table size: 10 1 2 3 4 5 6 7 8 9 10 2 4 6 8 10 12 14 16 18 20 3 6 9 12 15 18 21 24 27 30 4 8 12 16 20 24 28 32 36 40 5 10 15 20 25 30 35 40 45 50 6 12 18 24 30 36 42 48 54 60 7 14 21 28 35 42 49 56 63 70 8 16 24 32 40 48 56 64 72 80 9 18 27 36 45 54 63 72 81 90 10 20 30 40 50 60 70 80 90 100 Notice that the table presentation adjusts to the user’s input: ©2017 Richard L. Halterman Draft date: January 18, 2018 5.4. NESTED LOOPS 129 Please enter the table size: 5 1 2 3 4 5 2 4 6 8 10 3 6 9 12 15 4 8 12 16 20 5 10 15 20 25 A multiplication table of size 15 looks like Please enter the table size: 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 8 16 24 32 40 48 56 64 72 80 88 96 104 112 120 9 18 27 36 45 54 63 72 81 90 99 108 117 126 135 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 11 22 33 44 55 66 77 88 99 110 121 132 143 154 165 12 24 36 48 60 72 84 96 108 120 132 144 156 168 180 13 26 39 52 65 78 91 104 117 130 143 156 169 182 195 14 28 42 56 70 84 98 112 126 140 154 168 182 196 210 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225 All that is left is to add the row and column titles and the lines that bound the edges of the table. Listing 5.19 (timestable4.py) adds the necessary code. Listing 5.19: timestable4.py # Get the number of rows and columns in the table size = int(input("Please enter the table size: ")) # Print a size x size multiplication table # First, print heading: 1 2 3 4 5 etc. print(" ", end='') # Print column heading for column in range(1, size + 1): print('{0:4}'.format(column), end='') # Display column number print() # Go down to the next line # Print line separator: +------------------ print(" +", end='') for column in range(1, size + 1): print('----', end='') # Display line print() # Drop down to next line # Print table contents for row in range(1, size + 1): print('{0:3} |'.format(row), end='') # Print heading for this row for column in range(1, size + 1): product = row*column # Compute product print('{0:4}'.format(product), end='') # Display product print() # Move cursor to next row ©2017 Richard L. Halterman Draft date: January 18, 2018 5.4. NESTED LOOPS 130 When the user supplies the value 10, Listing 5.19 (timestable4.py) produces Please enter the table size: 10 1 2 3 4 5 6 7 8 9 10 +---------------------------------------- 1 | 1 2 3 4 5 6 7 8 9 10 2 | 2 4 6 8 10 12 14 16 18 20 3 | 3 6 9 12 15 18 21 24 27 30 4 | 4 8 12 16 20 24 28 32 36 40 5 | 5 10 15 20 25 30 35 40 45 50 6 | 6 12 18 24 30 36 42 48 54 60 7 | 7 14 21 28 35 42 49 56 63 70 8 | 8 16 24 32 40 48 56 64 72 80 9 | 9 18 27 36 45 54 63 72 81 90 10 | 10 20 30 40 50 60 70 80 90 100 An input of 15 yields Please enter the table size: 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 +------------------------------------------------------------ 1 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 2 | 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 3 | 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 4 | 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 5 | 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 6 | 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 7 | 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 8 | 8 16 24 32 40 48 56 64 72 80 88 96 104 112 120 9 | 9 18 27 36 45 54 63 72 81 90 99 108 117 126 135 10 | 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 11 | 11 22 33 44 55 66 77 88 99 110 121 132 143 154 165 12 | 12 24 36 48 60 72 84 96 108 120 132 144 156 168 180 13 | 13 26 39 52 65 78 91 104 117 130 143 156 169 182 195 14 | 14 28 42 56 70 84 98 112 126 140 154 168 182 196 210 15 | 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225 If the user enters 7, the program prints Please enter the table size: 7 1 2 3 4 5 6 7 +---------------------------- 1 | 1 2 3 4 5 6 7 2 | 2 4 6 8 10 12 14 3 | 3 6 9 12 15 18 21 4 | 4 8 12 16 20 24 28 5 | 5 10 15 20 25 30 35 6 | 6 12 18 24 30 36 42 7 | 7 14 21 28 35 42 49 The user even can enter a 1: Please enter the table size: 1 1 +---- ©2017 Richard L. Halterman Draft date: January 18, 2018 5.4. NESTED LOOPS 131 1 | 1 As we can see, the table automatically adjusts to the size and spacing required by the user’s input. This is how Listing 5.19 (timestable4.py) works: • It is important to distinguish what is done only once (outside all loops) from that which is done repeatedly. The column heading across the top of the table is outside of all the loops; therefore, the program uses a loop to print it one time. • The work to print the heading for the rows is distributed throughout the execution of the outer loop. This is because the heading for a given row cannot be printed until all the results for the previous row have been printed. • The printing statement print('{0:4}'.format(product), end='') # Display product right justifies the value of product in field that is four characters wide. This technique properly aligns the columns within the times table. • In the nested loop, row is the control variable for the outer loop; column controls the inner loop. • The inner loop executes size times on every single iteration of the outer loop. This means the innermost statement print('{0:4}'.format(product), end='') # Display product executes size × size times, one time for every product in the table. • The program prints a newline after it displays the contents of each row; thus, all the values printed in the inner (column) loop appear on the same line. Nested loops are necessary when an iterative process itself must be repeated. In our times table example, a for loop prints the contents of each row, and an enclosing for loop prints out each row. Listing 5.20 (permuteabc.py) uses a triply-nested loop to print all the different arrangements of the letters A, B, and C. Each string printed is a permutation of ABC. A permutation, therefore, is a possible ordering of a sequence. Listing 5.20: permuteabc.py # File permuteabc.py # The first letter varies from A to C for first in 'ABC': for second in 'ABC': # The second varies from A to C if second != first: # No duplicate letters allowed for third in 'ABC': # The third varies from A to C # Don't duplicate first or second letter if third != first and third != second: print(first + second + third) Notice how the if statements prevent duplicate letters within a given string. The output of Listing 5.20 (permuteabc.py) is all six permutations of ABC: ©2017 Richard L. Halterman Draft date: January 18, 2018 5.5. ABNORMAL LOOP TERMINATION 132 ABC ACB BAC BCA CAB CBA Listing 5.21 (permuteabcd.py) uses a four-deep nested loop to print all the different arrangements of the letters A, B, C, and D. Each string printed is a permutation of ABCD. Listing 5.21: permuteabcd.py # File permuteabcd.py # The first letter varies from A to D for first in 'ABCD': for second in 'ABCD': # The second varies from A to D if second != first: # No duplicate letters allowed for third in 'ABCD': # The third varies from A to D # Don't duplicate first or second letter if third != first and third != second: for fourth in 'ABCD': # The fourth varies from A to D if fourth != first and fourth != second and fourth != third: print(first + second + third + fourth) Nested loops are powerful, and some novice programmers attempt to use nested loops where a single loop is more appropriate. Before you attempt to solve a problem with a nested loop, make sure that there is no way you can do so with a single loop. Nested loops are more difficult to write correctly and, when not necessary, they are less efficient than a simple loop. 5.5 Abnormal Loop Termination Normally, a while statement executes until its condition becomes false. A running program checks this condition first to determine if it should execute the statements in the loop’s body. It then re-checks this condition only after executing all the statements in the loop’s body. Ordinarily a while loop will not immediately exit its body if its condition becomes false before completing all the statements in its body. The while statement is designed this way because usually the programmer intends to execute all the statements within the body as an indivisible unit. Sometimes, however, it is desirable to immediately exit the body or recheck the condition from the middle of the loop instead. Said another way, a while statement checks its condition only at the “top” of the loop. It is not the case that a while loop finishes immediately whenever its condition becomes true. Listing 5.22 (whileexitattop.py) demonstrates this top-exit behavior. Listing 5.22: whileexitattop.py x = 10 while x == 10: print('First print statement in the while loop') x = 5 # Condition no longer true; do we exit immediately? print('Second print statement in the while loop') ©2017 Richard L. Halterman Draft date: January 18, 2018 5.5. ABNORMAL LOOP TERMINATION 133 Listing 5.22 (whileexitattop.py) prints First print statement in the while loop Second print statement in the while loop Even though the condition for continuing in the loop (x being equal to 10) changes in the middle of the loop’s body, the while statement does not check the condition until it completes all the statements in its body and execution returns to the top of the loop. Sometimes it is more convenient to exit a loop from the middle of its body; that is, quit the loop before all the statements in its body execute. This means if a certain condition becomes true in the loop’s body, exit right away. Similarly, a for statement typically iterates over all the values in its range or over all the characters in its string. Sometimes, however, it is desirable to exit the for loop prematurely. Python provides the break and continue statements to give programmers more flexibility designing the control logic of loops. 5.5.1 The break statement As we noted above, sometimes it is necessary to exit a loop from the middle of its body; that is, quit the loop before all the statements in its body execute. This means if a certain condition becomes true in the loop’s body, exit right away. This “middle-exiting” condition could be the same condition that controls the while loop (that is, the “top-exiting” condition), but it does not need to be. Python provides the break statement to implement middle-exiting loop control logic. The break statement causes the program’s execution to immediately exit from the body of the loop. Listing 5.23 (addmiddleexit.py) is a variation of Listing 5.4 (addnonnegatives.py) that illustrates the use of break. Listing 5.23: addmiddleexit.py # Allow the user to enter a sequence of nonnegative # numbers. The user ends the list with a negative # number. At the end the sum of the nonnegative # numbers entered is displayed. The program prints # zero if the user provides no nonnegative numbers. entry = 0 # Ensure the loop is entered sum = 0 # Initialize sum # Request input from the user print("Enter numbers to sum, negative number ends list:") while True: # Loop forever? Not really entry = int(input()) # Get the value if entry < 0: # Is number negative number? break # If so, exit the loop sum += entry # Add entry to running sum print("Sum =", sum) # Display the sum The condition of the while statement in Listing 5.23 (addmiddleexit.py) is a tautology, so when the program runs it is guaranteed to begin executing the statements in its while block at least once. Since the condition ©2017 Richard L. Halterman Draft date: January 18, 2018 5.5. ABNORMAL LOOP TERMINATION 134 of the while can never be false, the break statement is the only way to get out of the loop. Here, the break statement executes only when it determines that the number the user entered is negative. When the program encounters the break statement during its execution, it skips any statements that follow in the loop’s body and exits the loop immediately. The keyword break means “break out of the loop.” The placement of the break statement in Listing 5.23 (addmiddleexit.py) makes it impossible to add a negative number to the sum variable. Listing 5.5 (troubleshootloop.py) uses a variable named done that controls the duration of the loop. Listing 5.24 (troubleshootloop2.py) uses break statements in place of the Boolean done variable. Listing 5.24: troubleshootloop2.py print("Help! My computer doesn't work!") while True: print("Does the computer make any sounds (fans, etc.)") choice = input(" or show any lights? (y/n):") # The troubleshooting control logic if choice == 'n': # The computer does not have power choice = input("Is it plugged in? (y/n):") if choice == 'n': # It is not plugged in, plug it in print("Plug it in.") else: # It is plugged in choice = input("Is the switch in the \"on\" position? (y/n):") if choice == 'n': # The switch is off, turn it on! print("Turn it on.") else: # The switch is on choice = input("Does the computer have a fuse? (y/n):") if choice == 'n': # No fuse choice = input("Is the outlet OK? (y/n):") if choice == 'n': # Fix outlet print("Check the outlet's circuit ") print("breaker or fuse. Move to a") print("new outlet, if necessary. ") else: # Beats me! print("Please consult a service technician.") break # Nothing else I can do, exit loop else: # Check fuse print("Check the fuse. Replace if ") print("necessary.") else: # The computer has power print("Please consult a service technician.") break # Nothing else I can do, exit loop Some software designers believe that programmers should use the break statement sparingly because it deviates from the normal loop control logic. Ideally, every loop should have a single entry point and single exit point. While Listing 5.23 (addmiddleexit.py) has a single exit point (the break statement), some programmers commonly use break statements within while statements in the which the condition for the while is not a tautology. Adding a break statement to such a loop adds an extra exit point (the top of the loop where the condition is checked is one point, and the break statement is another). Most programmers find two exits point perfectly acceptable, but much above two break points within a single loop is particularly dubious and you should avoid that practice. The break statement is not absolutely required for full control over a while loop; that is, we can rewrite any Python program that contains a break statement within a while loop so that it behaves the same way but ©2017 Richard L. Halterman Draft date: January 18, 2018 5.5. ABNORMAL LOOP TERMINATION 135 Figure 5.4 The code on the left generically represents any while loop that uses a break statement. The code on the right shows how we can transform the loop into a functionally equivalent form that does not use break. Eliminate the break statement looping = True while looping and : if : looping = False else: Condition 1 Part A Condition 2 Part B Part C Condition 1 Condition 2 Part A Part B Part C while : if : break does not use a break. Figure 5.4 shows how we can transform any while loop that uses a break statement into a beak-free version. The no-break version introduces a Boolean variable (looping), and the loop control logic is a little more complicated. The no-break version uses more memory (an extra variable) and more time to execute (requires an extra check in the loop condition during every iteration of the loop). This extra memory is insignificant, and except for rare, specialized applications, the extra execution time is imperceptible. In most cases, the more important issue is that the more complicated the control logic for a given section of code, the more difficult the code is to write correctly. In some situations, even though it violates the “single entry point, single exit point” principle, a simple break statement is a desirable loop control option. We can use the break statement inside a for loop as well. Listing 5.25 (countvowelsnox.py) shows how we can use a break statement to exit a for loop prematurely. provided by the user. Listing 5.25: countvowelsnox.py word = input('Enter text (no X\'s, please): ') vowel_count = 0 for c in word: if c == 'A' or c == 'a' or c == 'E' or c == 'e' \ or c == 'I' or c == 'i' or c == 'O' or c == 'o': print(c, ', ', sep='', end='') # Print the vowel vowel_count += 1 # Count the vowel elif c == 'X' or c =='x': break print(' (', vowel_count, ' vowels)', sep='') If the program detects an X or x anywhere in the user’s input string, it immediately exits the for even though it may not have considered all the characters in the string. Consider the following sample run: ©2017 Richard L. Halterman Draft date: January 18, 2018 5.5. ABNORMAL LOOP TERMINATION 136 Enter text (no X's, please): Mary had a lixtle lamb. a, a, a, i, (4 vowels) The program breaks out of the loop when it attempts to process the x in the user’s input. The break statement is handy when a situation arises that requires immediate exit from a loop. The for loop in Python behaves differently from the while loop, in that it has no explicit condition that it checks to continue its iteration. We must use a break statement if we wish to prematurely exit a for loop before it has completed its specified iterations. The for loop is a definite loop, which means programmers can determine up front the number of iterations the loop will perform. The break statement has the potential to disrupt this predictability. For this reason, programmers use break statements in for loops less frequently, and they often serve as an escape from a bad situation that continued iteration might make worse. 5.5.2 The continue Statement When a program’s execution encounters a break statement inside a loop, it skips the rest of the body of the loop and exits the loop. The continue statement is similar to the break statement, except the continue statement does not necessarily exit the loop. The continue statement skips the rest of the body of the loop and immediately checks the loop’s condition. If the loop’s condition remains true, the loop’s execution resumes at the top of the loop. Listing 5.26 (continueexample.py) shows the continue statement in action. Listing 5.26: continueexample.py sum = 0 done = False while not done: val = int(input("Enter positive integer (999 quits):")) if val < 0: print("Negative value", val, "ignored") continue # Skip rest of body for this iteration if val != 999: print("Tallying", val) sum += val else: done = (val == 999) # 999 entry exits loop print("sum =", sum) Programmers do not use the continue statement as frequently as the break statement since it is very easy to transform the code that uses continue into an equivalent form that does not. Listing 5.27 (nocontinueexample.py) works exactly like Listing 5.26 (continueexample.py), but it avoids the continue statement. Listing 5.27: nocontinueexample.py sum = 0 done = False while not done: val = int(input("Enter positive integer (999 quits):")) if val < 0: print("Negative value", val, "ignored") else: if val != 999: ©2017 Richard L. Halterman Draft date: January 18, 2018 5.6. WHILE/ELSE AND FOR/ELSE 137 Figure 5.5 The code on the left generically represents any loop that uses a continue statement. It is possible to transform the code on the left to eliminate the continue statement, as the code on the right shows. Condition 1 Condition 2 Part A Part B Part C while : if : continue Eliminate the continue statement while : if : else: Condition 1 Part A Condition 2 Part B Part C print("Tallying", val) sum += val else: done = (val == 999) # 999 entry exits loop print("sum =", sum) Figure 5.5 shows how we can rewrite any program that uses a continue statement into an equivalent form that does not use continue. The transformation is simpler than for break elimination (see Figure 5.4) since the loop’s condition remains the same, and no additional variable is needed. The logic of the else version is no more complex than the continue version. Therefore, unlike the break statement above, there is no compelling reason to use the continue statement. Sometimes a programmer may add a continue statement at the last minute to an existing loop body to handle an exceptional condition (like ignoring negative numbers in the example above) that initially went unnoticed. If the body of the loop is lengthy, the programmer can add a conditional statement with a continue near the top of the loop body without touching the logic of the rest of the loop. The continue statement thus merely provides a convenient alternative for the programmer. The else version is preferred. 5.6 while/else and for/else Python loops support an optional else block. The else block in the context of a loop provides code to execute when the loop exits normally. Said another way, the code in a loop’s else block does not execute if the loop terminates due to a break statement. When a while loop exits due to its condition being false during its normal check, its associated else block executes. This is true even if its condition is found to be false before its body has had a chance to execute. Listing 5.28 (whileelse.py) shows how the while/else statement works. Listing 5.28: whileelse.py ©2017 Richard L. Halterman Draft date: January 18, 2018 5.6. WHILE/ELSE AND FOR/ELSE 138 # Add five nonnegative numbers supplied by the user count = sum = 0 print('Please provide five nonnegative numbers when prompted') while count < 5: # Get value from the user val = float(input('Enter number: ')) if val < 0: print('Negative numbers not acceptable! Terminating') break count += 1 sum += val else: print('Average =', sum/count) When the user behaves and supplies only nonnegative values to Listing 5.28 (whileelse.py), it computes the average of the values provided: Please provide five nonnegative numbers when prompted Enter number: 23 Enter number: 12 Enter number: 14 Enter number: 10 Enter number: 11 Average = 14.0 When the user does not comply with the instructions, the program will print a corrective message and not attempt to compute the average: Please provide five nonnegative numbers when prompted Enter number: 23 Enter number: 12 Enter number: -4 Negative numbers not acceptable! Terminating It may be more natural to read the else keyword for the while statement as “if no break,” meaning execute the code in the else block if the program’s execution of code in the while block did not encounter the break statement. The else block is not essential; Listing 5.29 (whilenoelse.py) uses if/else statement to achieve the same effect as Listing 5.28 (whileelse.py). Listing 5.29: whilenoelse.py # Add five nonnegative numbers supplied by the user count = sum = 0 print('Please provide five nonnegative numbers when prompted') while count < 5: # Get value from the user val = float(input('Enter number: ')) if val < 0: break count += 1 sum += val if count < 5: ©2017 Richard L. Halterman Draft date: January 18, 2018 5.7. INFINITE LOOPS 139 print('Negative numbers not acceptable! Terminating') else: print('Average =', sum/count) Listing 5.29 (whilenoelse.py) uses two distinct Python constructs, the while statement followed by an if/else statement, whereas Listing 5.28 (whileelse.py) uses only one, a while/else statement. List- ing 5.29 (whilenoelse.py) also must check the count < 5 condition twice, once in the while statement and again in the if/else statement. A for statement with an else block works similarly to the while/else statement. When a for/else loop exits because it has considered all the values in its range or all the characters in its string, it executes the code in its associated else block. If a for/else statement exits prematurely due to a break statement, it does not execute the code in its else block. Listing 5.30 (countvowelselse.py) shows how the else block works with a for statement. Listing 5.30: countvowelselse.py word = input('Enter text (no X\'s, please): ') vowel_count = 0 for c in word: if c == 'A' or c == 'a' or c == 'E' or c == 'e' \ or c == 'I' or c == 'i' or c == 'O' or c == 'o': print(c, ', ', sep='', end='') # Print the vowel vowel_count += 1 # Count the vowel elif c == 'X' or c =='x': print('X not allowed') break else: print(' (', vowel_count, ' vowels)', sep='') Unlike Listing 5.15 (countvowels.py), Listing 5.30 (countvowelselse.py), does not print the number of vow- els if the user supplies text containing and X or x. 5.7 Infinite Loops An infinite loop is a loop that executes its block of statements repeatedly until the user forces the program to quit. Once the program flow enters the loop’s body it cannot escape. Infinite loops sometimes are by design. For example, a long-running server application like a Web server may need to continuously check for incoming connections. The Web server can perform this checking within a loop that runs indefinitely. Beginning programmers, unfortunately, all too often create infinite loops by accident, and these infinite loops represent logic errors in their programs. Intentional infinite loops should be made obvious. For example, while True: # Do something forever. . . The Boolean literal True is always true, so it is impossible for the loop’s condition to be false. The only ways to exit the loop is via a break statement, return statement (see Chapter 7), or a sys.exit call (see Chapter 6) embedded somewhere within its body. Intentional infinite loops are easy to write correctly. Accidental infinite loops are quite common, but ©2017 Richard L. Halterman Draft date: January 18, 2018 5.7. INFINITE LOOPS 140 can be puzzling for beginning programmers to diagnose and repair. Consider Listing 5.31 (findfactors.py) that attempts to print all the integers with their associated factors from 1 to 20. Listing 5.31: findfactors.py # List the factors of the integers 1...MAX MAX = 20 # MAX is 20 n = 1 # Start with 1 while n <= MAX: # Do not go past MAX factor = 1 # 1 is a factor of any integer print(end=str(n) + ': ') # Which integer are we examining? while factor <= n: # Factors are <= the number if n % factor == 0: # Test to see if factor is a factor of n print(factor, end=' ') # If so, display it factor += 1 # Try the next number print() # Move to next line for next n n += 1 It displays 1: 1 2: 1 2 3: 1 and then ”freezes up” or ”hangs,” ignoring any user input (except the key sequence Ctrl C on most systems which interrupts and terminates the running program). This type of behavior is a frequent symptom of an unintentional infinite loop. The factors of 1 display properly, as do the factors of 2. The program displays the first factor of 3 properly and then hangs. Since the program is short, the problem may be easy to locate. In some programs, though, the error may be challenging to find. Even in Listing 5.31 (findfactors.py) the debugging task is nontrivial since the program involves nested loops. (Can you find and fix the problem in Listing 5.31 (findfactors.py) before reading further?) In order to avoid infinite loops, we must ensure that the loop exhibits certain properties: • The loop’s condition must not be a tautology (a Boolean expression that can never be false). For example, the statement while i >= 1 or i <= 10: # Block of code follows ... would produce an infinite loop since any value chosen for i will satisfy one or both of the two subconditions. Perhaps the programmer intended to use and instead of or to stay in the loop as long as i remains in the range 1...10. In Listing 5.31 (findfactors.py) the outer loop condition is n <= MAX If n is 21 and MAX is 20, then the condition is false. Since we can find values for n and MAX that make this expression false, it cannot be a tautology. Checking the inner loop condition: factor <= n we see that if factor is 3 and n is 2, then the expression is false; therefore, this expression also is not a tautology. ©2017 Richard L. Halterman Draft date: January 18, 2018 5.7. INFINITE LOOPS 141 • The condition of a while must be true initially to gain access to its body. The code within the body must modify the state of the program in some way so as to influence the outcome of the condition that is checked at each iteration. This usually means the body must be able to modify one of the variables used in the condition. Eventually the variable assumes a value that makes the condition false, and the loop terminates. In Listing 5.31 (findfactors.py) the outer loop’s condition involves the variables n and MAX. We observe that we assign 20 to MAX before the loop and never change it afterward, so to avoid an infinite loop it is essential that n be modified within the loop. Fortunately, the last statement in the body of the outer loop increments n. n is initially 1 and MAX is 20, so unless the circumstances arise to make the inner loop infinite, the outer loop eventually should terminate. The inner loop’s condition involves the variables n and factor. No statement in the inner loop modifies n, so it is imperative that factor be modified in the loop. The good news is factor is incremented in the body of the inner loop, but the bad news is the increment operation is protected within the body of the if statement. The inner loop contains one statement, the if statement. That if statement in turn has two statements in its body: while factor <= n: if n % factor == 0: print(factor, end=' ') factor += 1 If the condition of the if is ever false, the variable factor will not change. In this situation if the expression factor <= n was true, it will remain true. This effectively creates an infinite loop. The statement that modifies factor must be moved outside of the if statement’s body: while factor <= n: if n % factor == 0: print(factor, end=' ') factor += 1 This new version runs correctly: 1: 1 2: 1 2 3: 1 3 4: 1 2 4 5: 1 5 6: 1 2 3 6 7: 1 7 8: 1 2 4 8 9: 1 3 9 10: 1 2 5 10 11: 1 11 12: 1 2 3 4 6 12 13: 1 13 14: 1 2 7 14 15: 1 3 5 15 16: 1 2 4 8 16 17: 1 17 18: 1 2 3 6 9 18 19: 1 19 20: 1 2 4 5 10 20 ©2017 Richard L. Halterman Draft date: January 18, 2018 5.7. INFINITE LOOPS 142 We can use a debugger can be used to step through a program to see where and why an infinite loop arises. Another common technique is to put print statements in strategic places to examine the values of the variables involved in the loop’s control. We can augment the original inner loop in this way: while factor <= n: print('factor =', factor, ' n =', n) if n % factor == 0: print(factor, end=' ') factor += 1 # <-- Note, still has original error here It produces the following output: 1: factor = 1 n = 1 1 2: factor = 1 n = 2 1 factor = 2 n = 2 2 3: factor = 1 n = 3 1 factor = 2 n = 3 factor = 2 n = 3 factor = 2 n = 3 factor = 2 n = 3 factor = 2 n = 3 factor = 2 n = 3 . . . The program continues to print the same line until the user interrupts its execution. The output demonstrates that once factor becomes equal to 2 and n becomes equal to 3 the program’s execution becomes trapped in the inner loop. Under these conditions: 1. 2 < 3 is true, so the loop continues and 2. 3 % 2 is equal to 1, so the if statement will not increment factor. It is imperative that the program increment factor each time through the inner loop; therefore, the state- ment incrementing factor must be moved outside of the if’s guarded body. Moving it outside means removing it from the if statement’s block, which means unindenting it. Listing 5.32 (findfactorsfor.py) is a different version of our factor finder program that uses nested for loops instead of nested while loops. Not only is it slightly shorter, but it avoids the potential for the misplaced increment of the factor variable. This is because the for statement automatically handles the loop variable update. Listing 5.32: findfactorsfor.py # List the factors of the integers 1...MAX MAX = 20 # MAX is 20 for n in range(1, MAX + 1): # Consider numbers 1...MAX print(end=str(n) + ': ') # Which integer are we examining? for factor in range(1, n + 1): # Try factors 1...n if n % factor == 0: # Test to see if factor is a factor of n print(factor, end=' ') # If so, display it print() # Move to next line for next n ©2017 Richard L. Halterman Draft date: January 18, 2018 5.8. ITERATION EXAMPLES 143 As a final note on infinite loops, Section 1.4 mentioned the preference for using the Debug option under the WingIDE-101 integrated development environment when running our programs. When executing the program under the Run option, the IDE can become unresponsive if the program encounters an infinite loop. At that point, terminating the IDE is the only solution. Under the debugger, we very easily can interrupt a wayward program’s execution via WingIDE-101’s Stop action. 5.8 Iteration Examples We can implement some sophisticated algorithms in Python now that we are armed with if and while statements. This section provides several examples that show off the power of conditional execution and iteration. 5.8.1 Computing Square Root Suppose you must write a Python program that computes the square root of a number supplied by the user. We can compute the square root of a number by using the following simple strategy: 1. Guess the square root. 2. Square the guess and see how close it is to the original number; if it is close enough to the correct answer, stop. 3. Make a new guess that will produce a better result and proceed with step 2. Step 3 is a little vague, but Listing 5.33 (computesquareroot.py) implements the above strategy in Python, providing the missing details. Listing 5.33: computesquareroot.py # File computesquareroot.py # Get value from the user val = float(input('Enter number: ')) # Compute a provisional square root root = 1.0 # How far off is our provisional root? diff = root*root - val # Loop until the provisional root # is close enough to the actual root while diff > 0.00000001 or diff < -0.00000001: print(root, 'squared is', root*root) # Report how we are doing root = (root + val/root) / 2 # Compute new provisional root # How bad is our current approximation? diff = root*root - val # Report approximate square root print('Square root of', val, '=', root) ©2017 Richard L. Halterman Draft date: January 18, 2018 5.8. ITERATION EXAMPLES 144 The program is based on a simple algorithm that uses successive approximations to zero in on an answer that is within 0.00000001 of the true answer. The following shows the program’s output when the user enters the value 2: Enter number: 2 1.0 squared is 1.0 1.5 squared is 2.25 1.4166666666666665 squared is 2.006944444444444 1.4142156862745097 squared is 2.0000060073048824 Square root of 2 = 1.4142135623746899 The actual square root is approximately 1.4142135623730951 and so the result is within our accepted tolerance (0.00000001). Another run yields Enter number: 100 1.0 squared is 1.0 50.5 squared is 2550.25 26.24009900990099 squared is 688.542796049407 15.025530119986813 squared is 225.76655538663093 10.840434673026925 squared is 117.51502390016438 10.032578510960604 squared is 100.6526315785885 10.000052895642693 squared is 100.0010579156518 Square root of 100 = 10.000000000139897 The real answer, of course, is 10, but our computed result again is well within our programmed tolerance. While Listing 5.33 (computesquareroot.py) is a good example of the practical use of a loop, if we really need to compute the square root, Python has a library function that is more accurate and more efficient. We explore it and other handy mathematical functions in Chapter 6. 5.8.2 Drawing a Tree Suppose we wish to draw a triangular tree with its height provided by the user. A tree that is five levels tall would look like * *** ***** ******* ********* whereas a three-level tree would look like * *** ***** If the height of the tree is fixed, we can write the program as a simple variation of Listing 1.2 (arrow.py) which uses only printing statements and no loops. Our program, however, must vary its height and width based on input from the user. Listing 5.34 (startree.py) provides the necessary functionality. ©2017 Richard L. Halterman Draft date: January 18, 2018 5.8. ITERATION EXAMPLES 145 Listing 5.34: startree.py # Get tree height from user height = int(input('Enter height of tree: ')) # Draw one row for every unit of height row = 0 while row < height: # Print leading spaces; as row gets bigger, the number of # leading spaces gets smaller count = 0 while count < height - row: print(end=' ') count += 1 # Print out stars, twice the current row plus one: # 1. number of stars on left side of tree # = current row value # 2. exactly one star in the center of tree # 3. number of stars on right side of tree # = current row value count = 0 while count < 2*row + 1: print(end='*') count += 1 # Move cursor down to next line print() row += 1 # Consider next row The following shows a sample run of Listing 5.34 (startree.py) where the user enters 7: Enter height of tree: 7 * *** ***** ******* ********* *********** ************* Listing 5.34 (startree.py) uses two sequential while loops nested within a while loop. The outer while loop draws one row of the tree each time its body executes: • As long as the user enters a value greater than zero, the body of the outer while loop will execute; if the user enters zero or less, the program terminates and does nothing. This is the expected behavior. • The last statement in the body of the outer while: row += 1 ensures that the variable row increases by one each time through the loop; therefore, it eventually will equal height (since it initially had to be less than height to enter the loop), and the loop will terminate. There is no possibility of an infinite loop here. The two inner loops play distinct roles: ©2017 Richard L. Halterman Draft date: January 18, 2018 5.8. ITERATION EXAMPLES 146 • The first inner loop prints spaces. The number of spaces it prints is equal to the height of the tree the first time through the outer loop and decreases each iteration. This is the correct behavior since each succeeding row moving down contains fewer leading spaces but more asterisks. • The second inner loop prints the row of asterisks that make up the tree. The first time through the outer loop, row is zero, so it prints no left side asterisks, one central asterisk, and no right side asterisks. Each time through the loop the number of left-hand and right-hand stars to print both increase by one, but there remains just one central asterisk to print. This means the tree grows one wider on each side for each line moving down. Observe how the 2*row + 1 value expresses the needed number of asterisks perfectly. • While it seems asymmetrical, note that no third inner loop is required to print trailing spaces on the line after the asterisks are printed. The spaces would be invisible, so there is no reason to print them! For comparison, Listing 5.35 (startreefor.py) uses for loops instead of while loops to draw our star trees. The for loop is a better choice for this program since once the user provides the height, the program can calculate exactly the number of iterations required for each loop. This number will not change during the rest of the program’s execution, so the definite loop (for) is better a better choice than the indefinite loop (while). Listing 5.35: startreefor.py # Get tree height from user height = int(input('Enter height of tree: ')) # Draw one row for every unit of height for row in range(height): # Print leading spaces; as row gets bigger, the number of # leading spaces gets smaller for count in range(height - row): print(end=' ') # Print out stars, twice the current row plus one: # 1. number of stars on left side of tree # = current row value # 2. exactly one star in the center of tree # 3. number of stars on right side of tree # = current row value for count in range(2*row + 1): print(end='*') # Move cursor down to next line print() 5.8.3 Printing Prime Numbers A prime number is an integer greater than one whose only factors (also called divisors) are one and itself. For example, 29 is a prime number (only 1 and 29 divide into 29 with no remainder), but 28 is not (1, 2, 4, 7, and 14 are factors of 28). Prime numbers were once merely an intellectual curiosity of mathematicians, but now they play an important role in cryptography and computer security. The task is to write a program that displays all the prime numbers up to a value entered by the user. Listing 5.36 (printprimes.py) provides one solution. ©2017 Richard L. Halterman Draft date: January 18, 2018 5.8. ITERATION EXAMPLES 147 Listing 5.36: printprimes.py max_value = int(input('Display primes up to what value? ')) value = 2 # Smallest prime number while value <= max_value: # See if value is prime is_prime = True # Provisionally, value is prime # Try all possible factors from 2 to value - 1 trial_factor = 2 while trial_factor < value: if value % trial_factor == 0: is_prime = False # Found a factor break # No need to continue; it is NOT prime trial_factor += 1 # Try the next potential factor if is_prime: print(value, end= ' ') # Display the prime number value += 1 # Try the next potential prime number print() # Move cursor down to next line Listing 5.36 (printprimes.py), with an input of 90, produces: Display primes up to what value? 90 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 The logic of Listing 5.36 (printprimes.py) is a little more complex than that of Listing 5.34 (startree.py). The user provides a value for max_value. The main loop (outer while) iterates over all the values from two to max_value: • The program initializes the is_prime variable to true, meaning it assumes value is a prime number unless later tests prove otherwise. trial_factor takes on all the values from two to value - 1 in the inner loop: trial_factor = 2 while trial_factor < value: if value % trial_factor == 0: is_prime = False # Found a factor break # No need to continue; it is NOT prime trial_factor += 1 # Try the next potential factor The expression value % trial_factor is zero when trial_factor divides into value with no remainder—exactly when trial_factor is a factor of value. If the program discovers a value of trial_factor that actually is a factor of value, then it sets is_prime false and exits the loop via the break statement. If the loop continues to completion, the program will not set is_prime to false, which means it found no factors, and, so, value is indeed prime. • The if statement after the inner loop: if is_prime: print(value, end= ' ') # Display the prime number simply checks the status of is_prime. If is_prime is true, then value must be prime, so the pro- gram prints value followed by a space to separate it from other factors that it may print during the remaining iterations. ©2017 Richard L. Halterman Draft date: January 18, 2018 5.8. ITERATION EXAMPLES 148 Some important questions must be answered: 1. If the user enters a 2, what will the program print? In this case max_value = value = 2, so the condition of the outer loop value <= max_value is true, since 2≤ 2. The executing program sets is_prime to true, but the condition of the inner loop trial_factor < value is not true (2 is not less than 2). Thus, the program skips the inner loop, it does not change is_prime from true, and so it prints 2. This behavior is correct because 2 is the smallest prime number (and the only even prime). 2. If the user enters a number less than 2, what will the program print? The while condition ensures that values less than two are not considered. The program will never enter the body of the while. The program prints only the newline, and it displays no numbers. This behavior is correct, as there are no primes numbers less than 2. 3. Is the inner loop guaranteed to always terminate? In order to enter the body of the inner loop, trial_factor must be less than value. value does not change anywhere in the loop. trial_factor is not modified anywhere in the if statement within the loop, and it is incremented within the loop immediately after the if statement. trial_factor is, therefore, incremented during each iteration of the loop. Eventually, trial_factor will equal value, and the loop will terminate. 4. Is the outer loop guaranteed to always terminate? In order to enter the body of the outer loop, value must be less than or equal to max_value. max_value does not change anywhere in the loop. The last statement within the body of the outer loop increases value, and no where else does the program modify value. Since the inner loop is guaranteed to terminate as shown in the previous answer, eventually value will exceed max_value and the loop will end. We can rearrange slightly the logic of the inner while to avoid the break statement. The current version is: while trial_factor < value: if value % trial_factor == 0: is_prime = False # Found a factor break # No need to continue; it is NOT prime trial_factor += 1 # Try the next potential factor We can be rewrite it as: while is_prime and trial_factor < value: is_prime = (value % trial_factor != 0) # Update is_prime trial_factor += 1 # Try the next potential factor This version without the break introduces a slightly more complicated condition for the while but removes the if statement within its body. is_prime is initialized to true before the loop. Each time through the loop it is reassigned. trial_factor will become false if at any time value % trial_factor is zero. This is exactly when trial_factor is a factor of value. If is_prime becomes false, the loop cannot continue, and ©2017 Richard L. Halterman Draft date: January 18, 2018 5.8. ITERATION EXAMPLES 149 if is_prime never becomes false, the loop ends when trial_factor becomes equal to value. Because of operator precedence, the parentheses in is_prime = (value % trial_factor != 0) are not necessary. The parentheses do improve readability, since an expression including both = and != is awkward for humans to parse. When parentheses are placed where they are not needed, as in x = (y + 2) the interpreter simply ignores them, so there is no efficiency penalty in the executing program. We can shorten the code of Listing 5.36 (printprimes.py) a bit by using for statements instead of while statements as shown in Listing 5.37 (printprimesfor.py). Listing 5.37: printprimesfor.py max_value = int(input('Display primes up to what value? ')) # Try values from 2 (smallest prime number) to max_value for value in range(2, max_value + 1): # See if value is prime is_prime = True # Provisionally, value is prime # Try all possible factors from 2 to value - 1 for trial_factor in range(2, value): if value % trial_factor == 0: is_prime = False # Found a factor break # No need to continue; it is NOT prime if is_prime: print(value, end= ' ') # Display the prime number print() # Move cursor down to next line We can simplify Listing 5.37 (printprimesfor.py) even further by using the for/else statement as List- ing 5.38 (printprimesforelse.py) illustrates. Listing 5.38: printprimesforelse.py max_value = int(input('Display primes up to what value? ')) # Try values from 2 (smallest prime number) to max_value for value in range(2, max_value + 1): # See if value is prime: try all possible factors from 2 to value - 1 for trial_factor in range(2, value): if value % trial_factor == 0: break # Found a factor, no need to continue; it is NOT prime else: print(value, end= ' ') # Display the prime number print() # Move cursor down to next line If the inner for loop completes its iteration over all the values in its range, it will execute the print statement in its else block. The only way the inner for loop can be interrupted is if it discovers a factor of value. If it does find a factor, the premature exit of the inner for loop prevents the execution of its else block. This logic enables it to print only prime numbers—exactly the behavior we want. ©2017 Richard L. Halterman Draft date: January 18, 2018 5.9. EXERCISES 150 5.8.4 Insisting on the Proper Input Listing 5.39 (betterinputonly.py) traps the user in a loop until the user provides an acceptable integer value. Listing 5.39: betterinputonly.py # Require the user to enter an integer in the range 1-10 in_value = 0 # Ensure loop entry attempts = 0 # Count the number of tries # Loop until the user supplies a valid number while in_value < 1 or in_value > 10:

in_value = int(input(“Please enter an integer in the range 0-10: “))
attempts += 1

# Make singular or plural word as necessary
tries = “try” if attempts == 1 else “tries”
# in_value at this point is guaranteed to be within range
print(“It took you”, attempts, tries, “to enter a valid number”)

A sample run of Listing 5.39 (betterinputonly.py) produces

Please enter an integer in the range 0-10: 11
Please enter an integer in the range 0-10: 12
Please enter an integer in the range 0-10: 13
Please enter an integer in the range 0-10: 14
Please enter an integer in the range 0-10: -1
Please enter an integer in the range 0-10: 5
It took you 6 tries to enter a valid number

We initialize the variable in_value at the top of the program only to make sure the loop’s body executes at
least one time. A definite loop (for) is inappropriate for a program like Listing 5.39 (betterinputonly.py) be-
cause the program cannot determine ahead of time how many attempts the user will make before providing
a value in range.

5.9 Exercises

1. In Listing 5.4 (addnonnegatives.py) could the condition of the if statement have used > instead of
>= and achieved the same results? Why?

2. In Listing 5.4 (addnonnegatives.py) could the condition of the while statement have used > instead
of >= and achieved the same results? Why?

3. In Listing 5.4 (addnonnegatives.py) what would happen if the statement

entry = int(input()) # Get the value

were moved out of the loop? Is moving the assignment out of the loop a good or bad thing to do?
Why?

4. How many asterisks does the following code fragment print?

5.9. EXERCISES 151

a = 0
while a < 100: print('*', end='') a += 1 print() 5. How many asterisks does the following code fragment print? a = 0 while a < 100: print('*', end='') print() 6. How many asterisks does the following code fragment print? a = 0 while a > 100:

print(‘*’, end=”)
a += 1

print()

7. How many asterisks does the following code fragment print?

a = 0
while a < 100: b = 0 while b < 55: print('*', end='') b += 1 print() a += 1 8. How many asterisks does the following code fragment print? a = 0 while a < 100: if a % 5 == 0: print('*', end='') a += 1 print() 9. How many asterisks does the following code fragment print? a = 0 while a < 100: b = 0 while b < 40: if (a + b) % 2 == 0: print('*', end='') b += 1 print() a += 1 ©2017 Richard L. Halterman Draft date: January 18, 2018 5.9. EXERCISES 152 10. How many asterisks does the following code fragment print? a = 0 while a < 100: b = 0 while b < 100: c = 0 while c < 100: print('*', end='') c += 1 b += 1 a += 1 print() 11. What is minimum number of arguments acceptable to the range expression? 12. What is maximum number of arguments acceptable to the range expression? 13. Provide the exact sequence of integers specified by each of the following range expressions. (a) range(5) (b) range(5, 10) (c) range(5, 20, 3) (d) range(20, 5, -1) (e) range(20, 5, -3) (f) range(10, 5) (g) range(0) (h) range(10, 101, 10) (i) range(10, -1, -1) (j) range(-3, 4) (k) range(0, 10, 1) 14. What is a shorter way to express range(0, 5, 1)? 15. Provide an equivalent Python range expression for each of the following integer sequences. (a) 1,2,3,4,5 (b) 5,4,3,2,1 (c) 5,10,15,20,25,30 (d) 30,25,20,15,10,5 (e) −3,−2,−1,0,1,2,3 (f) 3,2,1,0,−1,−2,−3 (g) −50,−40,−30,−20,−10 (h) Empty sequence 16. If x is bound to the integer value 2, what integer sequence does range(x, 10*x, x) represent? 17. If x is bound to the integer value 2 and y is bound to the integer 5, what integer sequence does range(x, x + y) represent? ©2017 Richard L. Halterman Draft date: January 18, 2018 5.9. EXERCISES 153 18. Is it possible to represent the following sequence with a Python range expression: 1,−1,2,−2,3,−3,4,−4? 19. How many asterisks does the following code fragment print? for a in range(100): print('*', end='') print() 20. How many asterisks does the following code fragment print? for a in range(20, 100, 5): print('*', end='') print() 21. How many asterisks does the following code fragment print? for a in range(100, 0, -2): print('*', end='') print() 22. How many asterisks does the following code fragment print? for a in range(1, 1): print('*', end='') print() 23. How many asterisks does the following code fragment print? for a in range(-100, 100): print('*', end='') print() 24. How many asterisks does the following code fragment print? for a in range(-100, 100, 10): print('*', end='') print() 25. Rewrite the code in the previous question so it uses a while instead of a for. Your code should behave identically. 26. What does the following code fragment print? a = 0 while a < 100: print(a) a += 1 print() 27. Rewrite the code in the previous question so it uses a for instead of a while. Your code should behave identically. 28. What is printed by the following code fragment? ©2017 Richard L. Halterman Draft date: January 18, 2018 5.9. EXERCISES 154 a = 0 while a > 100:

print(a)
a += 1

print()

29. Rewrite the following code fragment using a break statement and eliminating the done variable.
Your code should behave identically to this code fragment.

done = False
n, m = 0, 100
while not done and n != m:

n = int(input())
if n < 0: done = True print("n =", n) 30. Rewrite the following code fragment so it eliminates the continue statement. Your new code’s logic should be simpler than the logic of this fragment. x = 5 while x > 0:

y = int(input())
if y == 25:

continue
x -= 1
print(‘x =’, x)

31. What is printed by the following code fragment?

a = 0
while a < 100: print(a, end=' ') a += 1 print() 32. Modify Listing 5.19 (timestable4.py) so that the it requests a number from the user. It should then print a multiplication table of the size entered by the user; for example, if the users enters 15, a 15×15 table should be printed. Print nothing if the user enters a value lager than 18. Be sure everything lines up correctly, and the table looks attractive. 33. Write a Python program that accepts a single integer value entered by the user. If the value entered is less than one, the program prints nothing. If the user enters a positive integer, n, the program prints an n×n box drawn with * characters. If the users enters 1, for example, the program prints * If the user enters a 2, it prints ** ** An entry of three yields ©2017 Richard L. Halterman Draft date: January 18, 2018 5.9. EXERCISES 155 *** *** *** and so forth. If the user enters 7, it prints ******* ******* ******* ******* ******* ******* ******* that is, a 7×7 box of * symbols. 34. Write a Python program that allows the user to enter exactly twenty floating-point values. The pro- gram then prints the sum, average (arithmetic mean), maximum, and minimum of the values entered. 35. Write a Python program that allows the user to enter any number of nonnegative floating-point values. The user terminates the input list with any negative value. The program then prints the sum, average (arithmetic mean), maximum, and minimum of the values entered. The terminating negative value is not used in the computations. 36. Redesign Listing 5.34 (startree.py) so that it draws a sideways tree pointing right; for example, if the user enters 7, the program would print * ** *** **** ***** ****** ******* ****** ***** **** *** ** * 37. Redesign Listing 5.34 (startree.py) so that it draws a sideways tree pointing left; for example, if the user enters 7, the program would print * ** *** **** ***** ****** ******* ****** ***** **** ©2017 Richard L. Halterman Draft date: January 18, 2018 5.9. EXERCISES 156 *** ** * ©2017 Richard L. Halterman Draft date: January 18, 2018 157 Chapter 6 Using Functions Recall the square root code we wrote in Listing 5.33 (computesquareroot.py). In it we used a loop to compute the approximate square root of a value provided by the user. While this code may be acceptable for many applications, better algorithms exist that work faster and produce more precise answers. Another problem with the code is this: What if you are working on a significant scientific or engineering application and must use different formulas in various parts of the source code, and each of these formulas involve square roots in some way? In mathematics, for example, we use square root to compute the distance between two geometric points (x1,y1) and (x2,y2) as √ (x2− x1)2 +(y2− y1)2 and, using the quadratic formula, the solution to the equation ax2 +bx+ c = 0 is −b± √ b2−4ac 2a In electrical engineering and physics, the root mean square of a set of values {a1,a2,a3, . . . ,an} is √ a21 +a 2 2 +a 2 3 + . . .+a 2 n n Suppose we are writing one big program that, among many other things, needs compute distances and solve quadratic equations. Must we copy and paste the relevant portions of our square root code found in Listing 5.33 (computesquareroot.py) to each location in our source code that requires a square root computation? Also, what if we develop another program that requires computing a root mean square? Will we need to copy the code from Listing 5.33 (computesquareroot.py) into every program that needs to compute square roots, or is there a better way to package the square root code and reuse it? One way to make code more reusable is by packaging it in functions. A function is a unit of reusable code. In Chapter 7 we will see how to write our own reusable functions, but in this chapter we examine some of the functions available in the Python standard library. Python provides a collection of standard functions stored in libraries called modules. Programmers can use the functions from these libraries within their own code to build sophisticated programs. ©2017 Richard L. Halterman Draft date: January 18, 2018 6.1. INTRODUCTION TO USING FUNCTIONS 158 Figure 6.1 Conceptual view of the square root function. The function is like a black box—callers do not need to know the details of the code inside the function in order to use it. 6.1 Introduction to Using Functions We have been using functions in Python since the first chapter. These functions include print, input, int, float, str, and type. The Python standard library includes many other functions useful for common programming tasks. In mathematics, a function computes a result from a given value; for example, from the function defi- nition f (x) = 2x+3 we can compute f (5) = 2 ·5 + 13 = 13 and f (0) = 2 ·0+3 = 3. A function in Python works like a mathematical function. To introduce the function concept, we will look at the standard Python function that implements mathematical square root. In Python, a function is a named block of code that performs a specific task. If an executing program needs to perform such a task, it calls upon the function to do the work. One example of a function is the mathematical square root function. Python has a function in its standard library named sqrt (see Sec- tion 6.4). The square root function accepts one numeric (integer or floating-point) value and produces a floating-point result; for example, √ 16 = 4, so when presented with 16.0, sqrt responds with 4.0. Fig- ure 6.1 illustrates the conceptual view of the sqrt function. The square root function is like a black box to the code that uses it. Callers do not need to know the details of the code inside the function in order to use it. Programmers are concerned more about what the function does, not how it does it. This sqrt function is exactly what we need for our square root program, Listing 5.33 (computesquareroot.py). The new version, Listing 6.1 (standardsquareroot.py), uses the library function sqrt, eliminating the com- plex logic of the original code. Listing 6.1: standardsquareroot.py from math import sqrt # Get value from the user num = float(input("Enter number: ")) # Compute the square root root = sqrt(num) # Report result print("Square root of", num, "=", root) The expression sqrt(num) ©2017 Richard L. Halterman Draft date: January 18, 2018 6.1. INTRODUCTION TO USING FUNCTIONS 159 is a function invocation, also known as a function call. A function provides a service to the code that uses it. Here, our code in Listing 6.1 (standardsquareroot.py) is the calling code, or client code. Our code is the client that uses the service provided by the sqrt function. We say our code calls, or invokes, sqrt passing it the value of num. The expression sqrt(num) evaluates to the square root of the value of the variable num. Unlike the other functions we have used earlier, the interpreter is not automatically aware of the sqrt function. The sqrt function is not part of the small collection of functions (like type, int, and str) always available to Python programs. The sqrt function is part of separate module within the standard library. A module is a collection of Python code that can used in other programs. The import keyword makes a module available to the interpreter. The first statement in Listing 6.1 (standardsquareroot.py) shows one way to use the import keyword: from math import sqrt This statement makes the sqrt function available for use in the program. The math module has many other mathematical functions. These include trigonometric, logarithmic, hyperbolic, and other mathematical functions. This import statement will make only the sqrt function available to the program. When calling a function, a pair of parentheses follow the function’s name. Information that the function requires to perform its task must appear within these parentheses. In the expression sqrt(num) num is the information the function needs to do its work. We say num is the argument, or parameter, passed to the function. We also can say “we are passing num to the sqrt function.” The function uses the variable num’s value to perform the computation. Parameters enable callers to communicate information to a function during the function’s execution. The program could call the sqrt function in many other ways, as Listing 6.2 (usingsqrt.py) illustrates. Listing 6.2: usingsqrt.py # This program shows the various ways the # sqrt function can be used. from math import sqrt x = 16 # Pass a literal value and display the result print(sqrt(16.0)) # Pass a variable and display the result print(sqrt(x)) # Pass an expression print(sqrt(2 * x - 5)) # Assign result to variable y = sqrt(x) print(y) # Use result in an expression y = 2 * sqrt(x + 16) - 4 print(y) # Use result as argument to a function call y = sqrt(sqrt(256.0)) print(y) print(sqrt(int('45'))) ©2017 Richard L. Halterman Draft date: January 18, 2018 6.1. INTRODUCTION TO USING FUNCTIONS 160 The sqrt function accepts a single numeric argument. As Listing 6.2 (usingsqrt.py) shows, the param- eter that a caller can pass to sqrt can be a literal number, a numeric variable, an arithmetic expression, or even a function invocation that produces a numeric result. Some functions, like sqrt, compute a value that it returns to the caller. The caller can use this returned value in various ways, as shown in Listing 6.2 (usingsqrt.py). The statement print(sqrt(16.0)) directly prints the result of computing the square root of 16. The statement y = sqrt(x) assigns the result of the function call to the variable y. The statement y = sqrt(sqrt(256.0)) computes √ 256 via the inner sqrt call and immediately passes the result to the outer sqrt call. This composition of function calls computes √√ 256 = √ 16 = 4, and the assignment operator binds the variable y to 4. The statement print(sqrt(int('45'))) prints the result of computing the square root of the integer created from the string '45'. If the calling code attempts to pass a parameter to a function that is incompatible with type expected by that function, the interpreter issues an error. Consider: print(sqrt("16")) # Illegal, a string is not a number In the interactive shell we get >>> from math import sqrt
>>>
>>> sqrt(16)
4.0
>>> sqrt(“16”)
Traceback (most recent call last):

File ““, line 1, in
sqrt(“16”)

TypeError: a float is required

The sqrt function can process only numbers: integers and floating-point numbers. Even though we know
we could convert the string parameter ’16’ to the integer 16 (with the int function) or to the floating-point
value 16.0 (with the float function), the sqrt function does not automatically do this for us.

Listing 6.2 (usingsqrt.py) shows that a program can call the sqrt function as many times and in as many
places as needed.

As noted in Figure 6.1, the square root function is a black box to the caller. The caller is concerned
strictly about what the function does, not how the function accomplishes its task. We safely can treat all
functions like black boxes. We can use the service that a function provides without being concerned about
its internal details. Ordinarily we can influence the function’s behavior only via the parameters that we pass,
and that nothing else we do can affect what the function does or how it does it. Furthermore, for the types
of objects we have considered so far (integers, floating-point numbers, and strings), when a caller passes
data to a function, the function cannot affect the caller’s copy of that data. The caller is, however, free to

6.1. INTRODUCTION TO USING FUNCTIONS 161

use the return value of function to modify any of its variables. The important distinction is that the caller is
modifying its own variables—the function is not modifying the caller’s variables. The following interactive
sequence demonstrates that the sqrt function does not affect the object passed to it:

>>> from math import sqrt
>>> x = 2
>>> sqrt(x)
1.4142135623730951
>>> x
2
>>> x = sqrt(x)
>>> x
1.4142135623730951

Observe that passing x to the sqrt function did not change x, it still refers to the integer object 2. We must
reassign x to the value that sqrt returns if we really wish to change x to be its square root.

Some functions take more than one parameter; for example, print can accept multiple parameters
separated by commas.

From the caller’s perspective a function has three important parts:

• Name. Every function has a name that identifies the code to be executed. Function names follow the
same rules as variable names; a function name is another example of an identifier (see Section 2.3).

• Parameters. A function must be called with a certain number of parameters, and each parameter
must be the correct type. Some functions like print permit callers to pass a variable number of
arguments, but most functions, like sqrt, specify an exact number. If a caller attempts to call a
function with too many or too few parameters, the interpreter will issue an error message and refuse
to run the program. Consider the following misuse of sqrt in the interactive shell:

>>> sqrt(10)
3.1622776601683795
>>> sqrt()
Traceback (most recent call last):

File ““, line 1, in
sqrt()

TypeError: sqrt() takes exactly one argument (0 given)
>>> sqrt(10, 20)
Traceback (most recent call last):

File ““, line 1, in
sqrt(10, 20)

TypeError: sqrt() takes exactly one argument (2 given)

Similarly, if the parameters the caller passes are not compatible with the types specified for the
function, the interpreter reports appropriate error messages:

>>> sqrt(16)
4.0
>>> sqrt(“16”)
Traceback (most recent call last):

File ““, line 1, in
sqrt(“16”)

TypeError: a float is required

6.2. FUNCTIONS AND MODULES 162

• Result type. A function returns a value to its caller. Generally a function will compute a result and
return the value of the result to the caller. The caller’s use of this result must be compatible with the
function’s specified result type. A function’s result type and its parameter types can be completely
unrelated. The sqrt function computes and returns a floating-point value; the interactive shell reports

>>> type(sqrt(16.0))

Some functions do not accept any parameters; for example, the function to generate a pseudorandom
floating-point number, random, requires no arguments:

>>> from random import random
>>> random()
0.9595266948278349

The random function is part of the random module. The random function returns a floating-point value, but
the caller does not pass the function any information to do its task. Any attempts to do so will fail:

>>> random(20)
Traceback (most recent call last):

File ““, line 1, in
TypeError: random() takes no arguments (1 given)

Like mathematical functions that must produce a result, a Python function always produces a value to
return to the caller. Some functions are not designed to produce any useful results. Clients call such a
function for the effects provided by the executing code within a function, not for any value that the function
computes. The print function is one such example. The print function displays text in the console
window; it does not compute and return a value to the caller. Since Python requires that all functions return
a value, print must return something. Functions that are not meant to return anything return the special
object None. We can show this in the Python shell:

>>> print(print(4))
4
None

The inner print call prints 4, and the outer print displays the return value of the inner print call.

We can assign the value None to any variable. It represents “nothing” or “no object.”

6.2 Functions and Modules

A Python module is simply a file that contains Python code. The name of the file dictates the name of the
module; for example, a file named math.py contains the functions available from the standard math module.
The modules of immediate interest to us are the standard modules that contain functions that our programs
can use. The Python standard library contains thousands of functions distributed throughout more than
230 modules. These modules cover a wide range of application domains. One of the modules, known as
the built-ins module (actual name __builtins__), contains all the functions we have been using in earlier
chapters: print, input, etc. These built-in functions make up only a very small fraction of all the functions
the standard library provides. Programmers must use one or more import statements within a program or
within the interactive interpreter to gain access to the remaining standard functions.

6.2. FUNCTIONS AND MODULES 163

Figure 6.2 General form of a statement that imports a subset of a module’s available functions. The function
list is a comma-separated list of function names to import.

module function listfrom import

The Python distribution for a given platform stores these standard modules somewhere on the com-
puter’s hard drive. The interpreter knows where to locate these standard modules when an executing pro-
gram needs to import them. It is not uncommon for a complex program to import a dozen separate modules
to obtain all functions it needs to do its job.

Python provides a number of ways to import functions from a module. We will concentrate on the two
most commonly used techniques. Section 6.10 briefly examines other, more specialized import statements.

Listing 6.1 (standardsquareroot.py) imported the square root function as follows:

from math import sqrt

A program that needs to compute square roots, common logarithms, and the trigonometric cosine function
could use the following import statement:

from math import sqrt, log10, cos

This statement makes only the sqrt, log10, and cos functions from the math module available to the
program. The math module offers many other mathematical functions—for example, the atan function
that computes the arctangent—but this limited import statement does not provide these other definitions
to the interpreter. Figure 6.2 shows the general form of this kind of import statement. Such an import
statement is appropriate for smaller Python programs that use a small number of functions from a module.
This kind of import statement allows callers to use an imported function’s simple name, as in

y = sqrt(x)

If a program requires many different functions from a module, listing them all individually can become
unwieldy. Python provides a way to import everything a module has to offer, as we will see in Section 6.10,
but we also will see why this practice is not desirable.

Rather than importing one or more components of a module, we can import the entire module, as shown
here:

import math

Figure 6.3 shows the general form of this kind of import statement. This import statement makes all of the
functions of the module available to the program, but in order to use a function the caller must attach the
module’s name during the call. The following code demonstrates the call notation:

y = math.sqrt(x)
print(math.log10(100))

Note the math. prefix attached to the calls of the sqrt and log10 functions. We call a composite name
(module-name.function-name) like this a qualified name. The qualified name includes the module name

6.3. THE BUILT-IN FUNCTIONS 164

Figure 6.3 General form of a statement that imports an entire module. The module list is a comma-separated
list of module names to import.

module listimport

and function name. Many programmers prefer this approach because the complete name unambiguously
identifies the function with its module. A large, complex program could import the math module and a
different, third-party module called extramath. Suppose the extramath module provided its own sqrt
function. There can be no mistaking the fact that the sqrt being called in the expression math.sqrt(16) is
the one provided by the math module. It is impossible for a program to import the sqrt functions separately
from both modules and use their simple names simultaneously within a program. Does

y = sqrt(x)

intend to use math’s sqrt or extramath’s sqrt?

Note that a statement such as

from math import sqrt

does not import the entire module; specifically, code under this import statement may use only the simple
name, sqrt, and cannot use the qualified name, math.sqrt.

As programs become larger and more complex, the import entire module approach becomes more com-
pelling. The qualified function names improve the code’s readability and avoids name clashes between
modules that provide functions with identical names. Soon we will be writing our own, custom functions.
Qualified names ensure that names we create ourselves will not clash with any names that modules may
provide.

6.3 The Built-in Functions

Section 6.1 observed that we have been using functions in Python since the first chapter. These functions
include print, input, int, float, str, and type. These functions and many others reside in a module
named __builtins__. The __builtins__ module is special because its components are automatically
available to any Python program with—no import statement is required. The full name of the print
function is __builtins__.print, although chances are you will never see its full name written in a Python
program. We can verify its fully qualified name in the interpreter:

>>> print(‘Hi’)
Hi
>>> __builtins__.print(‘Hi’)
Hi
>>> print

>>> __builtins__.print

>>> id(print)

6.3. THE BUILT-IN FUNCTIONS 165

9506056
>>> id(__builtins__.print)
9506056

This interactive sequence verifies that the names print and __builtins__.print refer to the same func-
tion object. The id function is another __builtins__ function. The expression id(x) evaluates to the
address in memory of object named x. Since id(print) and id(__builtins__.print) evaluate to the
same value, we know both names correspond to the same function object.

The dir function, which stands for directory, reveals all the components that a module has to offer.
The following interactive sequence prints the __builtins__ components:

>>> dir(__builtins__)
[‘ArithmeticError’, ‘AssertionError’, ‘AttributeError’, ‘BaseException’,
‘BlockingIOError’, ‘BrokenPipeError’, ‘BufferError’, ‘Bytes Warning’,
‘ChildProcessError’, ‘ConnectionAbortedError’, ‘ConnectionError’,
‘ConnectionRefusedError’, ‘ConnectionResetError’, ‘Depre cationWarning’,
‘EOFError’, ‘Ellipsis’, ‘EnvironmentError’, ‘Exception’, ‘False’,
‘FileExistsError’, ‘FileNotFoundError’, ‘FloatingP ointError’,
‘FutureWarning’, ‘GeneratorExit’, ‘IOError’, ‘ImportError’,
‘ImportWarning’, ‘IndentationError’, ‘IndexError’, ‘Interrup tedError’,
‘IsADirectoryError’, ‘KeyError’, ‘KeyboardInterrupt’, ‘LookupError’,
‘MemoryError’, ‘NameError’, ‘None’, ‘NotADirectoryEr ror’,
‘NotImplemented’, ‘NotImplementedError’, ‘OSError’, ‘OverflowError’,
‘PendingDeprecationWarning’, ‘PermissionError’, ‘ProcessL ookupError’,
‘ReferenceError’, ‘ResourceWarning’, ‘RuntimeError’, ‘RuntimeWarning’,
‘StopIteration’, ‘SyntaxError’, ‘SyntaxWarning’, ‘SystemError’,
‘SystemExit’, ‘TabError’, ‘TimeoutError’, ‘True’, ‘TypeError’,
‘UnboundLocalError’, ‘UnicodeDecodeError’, ‘UnicodeEn codeError’,
‘UnicodeError’, ‘UnicodeTranslateError’, ‘UnicodeWarning’, ‘UserWarning’,
‘ValueError’, ‘Warning’, ‘WindowsError’, ‘Zero DivisionError’,
‘__build_class__’, ‘__debug__’, ‘__doc__’, ‘__import__’, ‘__loader__’,
‘__name__’, ‘__package__’, ‘__spec__’, ‘abs’, ‘all’, ‘any’, ‘ascii’,
‘bin’, ‘bool’, ‘bytearray’, ‘bytes’, ‘callable’, ‘chr’, ‘classmethod’,
‘compile’, ‘complex’, ‘copyright’, ‘credits’, ‘delattr’, ‘dict’, ‘dir’,
‘divmod’, ‘enumerate’, ‘eval’, ‘exec’, ‘exit’, ‘filter’, ‘float’,
‘format’, ‘frozenset’, ‘getattr ‘, ‘globals’, ‘hasattr’, ‘hash’, ‘help’,
‘hex’, ‘id’, ‘input’, ‘int’, ‘isinstance’, ‘issubclass’, ‘iter’, ‘len’,
‘license’, ‘list’, ‘locals’, ‘map’, ‘max’, ‘memoryview’, ‘min’, ‘next’,
‘object’, ‘oct’, ‘open’, ‘ord’, ‘pow’, ‘print’, ‘property’, ‘quit’,
‘range’, ‘repr’, ‘reversed’, ’round’, ‘set’, ‘setattr’, ‘slice’,
‘sorted’, ‘staticmethod’, ‘str’, ‘sum’, ‘super’, ‘tuple’, ‘type’,
‘vars’, ‘zip’]
>>>

A module can contain other things besides functions. Most of the names in the first 18 lines or so of the
__builtins__ module’s directory listing are types the module defines, and most of the names in the last
11 lines are functions it provides. The list contains many recognizable names: dir, bool, float, id, input,
int, print, range, round, str, and type functions.

The __builtins__ module provides a common core of general functions useful to any Python program
regardless of its application area. The other standard modules that Python provides are aimed at specific
application domains, such as mathematics, text processing, file processing, system administration, graphics,
and Internet protocols, and multimedia. Programs that require more domain-specific functionality must

6.3. THE BUILT-IN FUNCTIONS 166

import the appropriate modules that provide the needed services.

The __builtins__ module includes a help function. In the interactive interpreter we can use the
help function to print human-readable information about specific functions in the current namespace. The
following interactive sequence shows how help works:

>>> help(print)
Help on built-in function print in module builtins:

print(…)
print(value, …, sep=’ ‘, end=’\n’, file=sys.stdout, flush=False)

Prints the values to a stream, or to sys.stdout by default.
Optional keyword arguments:
file: a file-like object (stream); defaults to the current sys.stdout.
sep: string inserted between values, default a space.
end: string appended after the last value, default a newline.
flush: whether to forcibly flush the stream.

>>> help(input)
Help on built-in function input in module builtins:

input(…)
input([prompt]) -> string

Read a string from standard input. The trailing newline is stripped.
If the user hits EOF (Unix: Ctl-D, Windows: Ctl-Z+Return), raise EOFError.
On Unix, GNU readline is used if enabled. The prompt string, if given,
is printed without a trailing newline before reading.

>>> help(sqrt)
Traceback (most recent call last):

File ““, line 1, in
NameError: name ‘sqrt’ is not defined
>>> help(math.sqrt)
Traceback (most recent call last):

File ““, line 1, in
NameError: name ‘math’ is not defined
>>> import math
>>> help(math.sqrt)
Help on built-in function sqrt in module math:

sqrt(…)
sqrt(x)

Return the square root of x.

Notice that help was powerless to provide information about math.sqrt function until we imported the
math module.

6.4. STANDARD MATHEMATICAL FUNCTIONS 167

6.4 Standard Mathematical Functions

The standard math module provides much of the functionality of a scientific calculator. Table 6.1 lists only
a few of the available functions.

Table 6.1 A few of the functions from the math module
math Module

sqrt
Computes the square root of a number: sqrt(x) =

√
x

exp
Computes e raised a power: exp(x) = ex

log
Computes the natural logarithm of a number: log(x) = loge x = lnx

log10
Computes the common logarithm of a number: log(x) = log10 x

cos
Computes the cosine of a value specified in radians: cos(x) = cosx; other trigonometric
functions include sine, tangent, arc cosine, arc sine, arc tangent, hyperbolic cosine, hyper-
bolic sine, and hyperbolic tangent

pow
Raises one number to a power of another: pow(x,y) = xy

degrees
Converts a value in radians to degrees: degrees(x) = π180 x

radians
Converts a value in degrees to radians: radians(x) = 180

π
x

fabs
Computes the absolute value of a number: fabs(x) = |x|

The math module also defines the values pi (π) and e (e). The following interactive sequence reveals
the math module’s full directory of components:

>>> import math
>>> dir(math)
[‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’, ‘__spec__’, ‘acos’,
‘acosh’, ‘asin’, ‘asinh’, ‘atan’, ‘atan2’, ‘atanh’, ‘ceil’, ‘copysign’,
‘cos’, ‘cosh’, ‘degrees’, ‘e’, ‘erf’, ‘erfc’, ‘exp’, ‘expm1’, ‘fabs’,
‘factorial’, ‘floor’, ‘fmod’, ‘frexp’, ‘fsum’, ‘g amma’, ‘hypot’,
‘isfinite’, ‘isinf’, ‘isnan’, ‘ldexp’, ‘lgamma’, ‘log’, ‘log10’, ‘log1p’,
‘log2’, ‘modf’, ‘pi’, ‘pow’, ‘radians’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’,
‘tanh’, ‘trunc’]
>>>

Most of the names in the directory represent functions.

The parameter passed by the caller is known as the actual parameter. The parameter specified by the
function is called the formal parameter. During a function call the first actual parameter is assigned to the
first formal parameter, the second actual parameter is assigned to the second formal parameter, etc. Callers
must be careful to put the arguments they pass in the proper order when calling a function; for example, the
call math.pow(10,2) computes 102 = 100, but the call math.pow(2,10) computes 210 = 1,024.

6.4. STANDARD MATHEMATICAL FUNCTIONS 168

Figure 6.4 Orbital distance problem. In this diagram, the satellite begins at point (x1,y1), a distance of d1
from the spacecraft. The satellite’s orbit takes it to point (x2,y2) after an angle of θ rotation. The distance
to its new location is d2.

(0,0)

(x1,y1)

(x2,y2)

(px,py)

A Python program that uses any of these mathematical functions must import the math module.

The functions in the math module are ideal for solving problems like the one shown in Figure 6.4.
Suppose a spacecraft is at a fixed location in space some distance from a planet. A satellite is orbiting
the planet in a circular orbit. We wish to compute how much farther away the satellite will be from the
spacecraft when it has progressed θ degrees along its orbital path.

We will let the origin of our coordinate system (0,0) be located at the center of the planet. This location
corresponds also to the center of the satellite’s circular orbital path. The satellite is located as some point,
(x,y) and the spacecraft is stationary at point (px, py). The spacecraft is located in the same plane as the
satellite’s orbit. We wish to compute the distances between the moving point (satellite) and the fixed point
(spacecraft) as the satellite orbits the planet.

Facts from mathematics provide solutions to the following two problems:

1. Problem: We must recompute the location of the moving point as it moves along the circle.

Solution: Given an initial position (x,y) of a point, a rotation of θ degrees around the origin will
yield a new point at (x′,y′), where

x′ = xcosθ − ysinθ
y′ = xsinθ + ycosθ

2. Problem: We must recalculate the distance between the moving point and the fixed point as the
moving point moves to a new position.

Solution: The distance d in Figure 6.4 between the two points (px, py) and (x,y) is given by the
formula

d =
√

(x− px)2 +(y− py)2

6.4. STANDARD MATHEMATICAL FUNCTIONS 169

Listing 6.3 (orbitdist.py) uses these mathematical results to compute a table of distances that span a
complete orbit of the satellite.

Listing 6.3: orbitdist.py

# Use some functions and values from the math module
from math import sqrt, sin, cos, pi, radians

# Get coordinates of the stationary spacecraft, (px, py)
px = float(input(“Enter x coordinate of spacecraft: “))
py = float(input(“Enter y coordinate of spacecraft: “))

# Get starting coordinates of satellite, (x1, y1)
x = float(input(“Enter initial satellite x coordinate: “))
y = float(input(“Enter initial satellite y coordinate: “))

# Convert 60 degrees to radians to be able to use the trigonometric functions
rads = radians(60)

# Precompute the cosine and sine of the angle
COS_theta = cos(rads)
SIN_theta = sin(rads)

# Make a complete revolution (6*60 = 360 degrees)
for increment in range(0, 7):

# Compute the distance to the satellite
dist = sqrt((px – x)*(px – x) + (py – y)*(py – y))
print(‘Distance to satellite {0:10.2f} km’.format(dist))
# Compute the satellite’s new (x, y) location after rotating by 60 degrees
x, y = x*COS_theta – y*SIN_theta, x*SIN_theta + y*COS_theta

Listing 6.3 (orbitdist.py) prints the distances from the spacecraft to the satellite in 60-degree orbit incre-
ments. A sample run of Listing 6.3 (orbitdist.py) looks like

Enter x coordinate of spacecraft: 100000
Enter y coordinate of spacecraft: 0
Enter initial satellite x coordinate: 20000
Enter initial satellite y coordinate: 0
Distance to satellite 80000.00 km
Distance to satellite 91651.51 km
Distance to satellite 111355.29 km
Distance to satellite 120000.00 km
Distance to satellite 111355.29 km
Distance to satellite 91651.51 km
Distance to satellite 80000.00 km

Here, the user first enters the point (100,000,0) and then the tuple (20,000,0). Observe that the satellite
begins 80,000 km away from the spacecraft and the distance increases to a maximum of 120,000 km when
it is at the far side of its orbit. Eventually the satellite returns to its starting place ready for the next orbit.

Listing 6.3 (orbitdist.py) uses tuple assignment to update the x and y variables:

# Uses tuple assignment
x, y = x*COS_theta – y*SIN_theta, x*SIN_theta + y*COS_theta

6.5. TIME FUNCTIONS 170

If we instead used two separate assignment statements, we must be careful—the following code does not
work the same way:

# Does not work correctly
x = x*COS_theta – y*SIN_theta
y = x*SIN_theta + y*COS_theta

This is because the value of x used in the second assignment statement is the new value of x computed by
the first assignment statement. The tuple assignment version uses the original x value in both computations.
If we really wanted to use two assignment statements rather than a single tuple assignment, we would need
to introduce an extra variable so we do not lose x’s original value:

new_x = x*COS_theta – y*SIN_theta # Compute new x value
y = x*SIN_theta + y*COS_theta # Compute new y value using original x
x = new_x # Update x

We can use the square root function to improve the efficiency of Listing 5.36 (printprimes.py). Instead
of trying all the potential factors of n up to n−1, we need only try potential factors up to

√
n. Listing 6.4

(moreefficientprimes.py) uses the sqrt function to reduce the number of potential factors the program needs
to consider.

Listing 6.4: moreefficientprimes.py

from math import sqrt

max_value = int(input(‘Display primes up to what value? ‘))
value = 2 # Smallest prime number

while value <= max_value: # See if value is prime is_prime = True # Provisionally, value is prime # Try all possible factors from 2 to value - 1 trial_factor = 2 root = sqrt(value) # Compute the square root of value while trial_factor <= root: if value % trial_factor == 0: is_prime = False # Found a factor break # No need to continue; it is NOT prime trial_factor += 1 # Try the next potential factor if is_prime: print(value, end= ' ') # Display the prime number value += 1 # Try the next potential prime number print() # Move cursor down to next line 6.5 time Functions The time module contains a number of functions that relate to time. We will consider two: clock and sleep. The time.clock function allows us measure the time of parts of a program’s execution. The time.clock function returns a floating-point value representing elapsed time in seconds. On Unix-like systems (Linux ©2017 Richard L. Halterman Draft date: January 18, 2018 6.5. TIME FUNCTIONS 171 and Mac OS X), time.clock returns the numbers of seconds elapsed since the program began executing. Under Microsoft Windows, time.clock returns the number of seconds since the first call to time.clock. In either case, with two calls to the time.clock function we can measure elapsed time. Listing 6.5 (timeit.py) measures how long it takes a user to enter a character from the keyboard. Listing 6.5: timeit.py from time import clock print("Enter your name: ", end="") start_time = clock() name = input() elapsed = clock() - start_time print(name, "it took you", elapsed, "seconds to respond") The following represents the program’s interaction with a particularly slow typist: Enter your name: Rick Rick it took you 7.246477029927183 seconds to respond Listing 6.6 (timeaddition.py) measures the time it takes for a Python program to add up all the integers from 1 to 100,000,000. Listing 6.6: timeaddition.py from time import clock sum = 0 # Initialize sum accumulator start = clock() # Start the stopwatch for n in range(1, 100000001): # Sum the numbers sum += n elapsed = clock() - start # Stop the stopwatch print("sum:", sum, "time:", elapsed) # Report results On one system Listing 6.6 (timeaddition.py) reports sum: 5000000050000000 time: 24.922694830903826 Listing 6.7 (measureprimespeed.py) measures how long it takes a program to count all the prime num- bers up to 10,000 using the same algorithm as Listing 5.37 (printprimesfor.py). Listing 6.7: measureprimespeed.py from time import clock max_value = 10000 count = 0 start_time = clock() # Start timer # Try values from 2 (smallest prime number) to max_value for value in range(2, max_value + 1): # See if value is prime is_prime = True # Provisionally, value is prime # Try all possible factors from 2 to value - 1 for trial_factor in range(2, value): ©2017 Richard L. Halterman Draft date: January 18, 2018 6.5. TIME FUNCTIONS 172 if value % trial_factor == 0: is_prime = False # Found a factor break # No need to continue; it is NOT prime if is_prime: count += 1 # Count the prime number print() # Move cursor down to next line elapsed = clock() - start_time # Stop the timer print("Count:", count, " Elapsed time:", elapsed, "sec") On one system, the program produces Count: 1229 Elapsed time: 1.6250698114336175 sec Repeated runs consistently report an execution time of approximately 1.6 seconds to count all the prime numbers up to 10,000. By comparison, Listing 6.8 (timemoreefficientprimes.py), based on the algorithm in Listing 6.4 (moreefficientprimes.py) using the square root optimization runs on average over 20 times faster. A sample run shows Count: 1229 Elapsed time: 0.07575643612557352 sec Exact times will vary depending on the speed of the computer. Listing 6.8: timemoreefficientprimes.py from math import sqrt from time import clock max_value = 10000 count = 0 value = 2 # Smallest prime number start = clock() # Start the stopwatch while value <= max_value: # See if value is prime is_prime = True # Provisionally, value is prime # Try all possible factors from 2 to value - 1 trial_factor = 2 root = sqrt(value) while trial_factor <= root: if value % trial_factor == 0: is_prime = False # Found a factor break # No need to continue; it is NOT prime trial_factor += 1 # Try the next potential factor if is_prime: count += 1 # Count the prime number value += 1 # Try the next potential prime number elapsed = clock() - start # Stop the stopwatch print("Count:", count, " Elapsed time:", elapsed, "sec") An even faster prime generator appears in Listing 10.24 (fasterprimes.py); it uses a completely different algorithm to generate prime numbers. The time.sleep function suspends the program’s execution for a specified number of seconds. List- ing 6.9 (countdown.py) counts down from 10 with one second intervals between numbers. ©2017 Richard L. Halterman Draft date: January 18, 2018 6.6. RANDOM NUMBERS 173 Figure 6.5 A pair of dice Listing 6.9: countdown.py from time import sleep for count in range(10, -1, -1): # Range 10, 9, 8, ..., 0 print(count) # Display the count sleep(1) # Suspend execution for 1 second The time.sleep function is useful for controlling the speed of graphical animations. 6.6 Random Numbers Some applications require behavior that appears random. Random numbers are particularly useful in games and simulations. For example, many board games use a die (one of a pair of dice—see Figure 6.5) to determine how many places a player is to advance. A die or pair of dice are used in other games of chance. A die is a cube containing spots on each of its six faces. The number of spots range from one to six. A player rolls a die or sometimes a pair of dice, and the side(s) that face up have meaning in the game being played. The value of a face after a roll is determined at random by the complex tumbling of the die. A software adaptation of a game that involves dice would need a way to simulate the random roll of a die. All algorithmic random number generators actually produce pseudorandom numbers, not true random numbers. A pseudorandom number generator has a particular period, based on the nature of the algorithm used. If the generator is used long enough, the pattern of numbers produced repeats itself exactly. A se- quence of true random numbers would not contain such a repeating subsequence. All practical algorithmic pseudorandom number generators have periods that are large enough for most applications. In addition to a long period, a good pseudorandom generator would be equally likely to generate any number in its range; that is, it would not be biased toward a subset of its possible values. Ideally, the numbers the generator produces will be uniformly distributed across its range of values. The good news is that the Python standard library has a very good pseudorandom number generator based the Mersenne Twister algorithm. See http://en.wikipedia.org/wiki/Mersenne twister for more information about the algorithm. The Python random module contains a number of standard functions that programmers can use for working with pseudorandom numbers. A few of these functions are shown in Table 6.2. ©2017 Richard L. Halterman Draft date: January 18, 2018 http://en.wikipedia.org/wiki/Mersenne_twister 6.6. RANDOM NUMBERS 174 Table 6.2 A few of the functions from the random module randomfunctions Module random Returns a pseudorandom floating-point number x in the range 0≤ x < 1 randrange Returns a pseudorandom integer value within a specified range. seed Sets the random number seed. choice Selects an element at random from a collection of elements. The random.seed function establishes the initial value from which the sequence of pseudorandom numbers is generated. Each call to random.random or random.randrange returns the next value in the sequence of pseudorandom values. Listing 6.10 (simplerandom.py) prints 100 pseudorandom integers in the range 1 . . .100. Listing 6.10: simplerandom.py from random import randrange, seed seed(23) # Set random number seed for i in range(0, 100): # Print 100 random numbers print(randrange(1, 1001), end=' ') # Range 1...1,000, inclusive print() # Print newine The numbers Listing 6.10 (simplerandom.py) prints appear to be random. The program begins its pseu- dorandom number generation with a seed value, 23. The seed value determines the exact sequence of numbers the program generates; identical seed values generate identical sequences. If you run the program again, it displays the same sequence. In order for the program to display different sequences, the seed value must be different for each run. If we omit the call to the random.seed function, the program derives its initial value in the sequence from the time kept by the operating system. This usually is adequate for simple pseudorandom number sequences. Being able to specify a seed value is useful during development and testing when we want program executions to exhibit reproducible results. We now have all we need to write a program that simulates the rolling of a die. Listing 6.11 (die.py) simulates rolling die. Listing 6.11: die.py from random import randrange # Roll the die three times for i in range(0, 3): # Generate random number in the range 1...7 value = randrange(1, 7) # Show the die print("+-------+") if value == 1: ©2017 Richard L. Halterman Draft date: January 18, 2018 6.6. RANDOM NUMBERS 175 print("| |") print("| * |") print("| |") elif value == 2: print("| * |") print("| |") print("| * |") elif value == 3: print("| * |") print("| * |") print("| * |") elif value == 4: print("| * * |") print("| |") print("| * * |") elif value == 5: print("| * * |") print("| * |") print("| * * |") elif value == 6: print("| * * * |") print("| |") print("| * * * |") else: print(" *** Error: illegal die value ***") print("+-------+") The output of one run of Listing 6.11 (die.py) is +-------+ | * * | | | | * * | +-------+ +-------+ | * * * | | | | * * * | +-------+ +-------+ | | | * | | | +-------+ Since the program generates the values pseudorandomly, actual output will vary from one run to the next. The random module provides a randint function that works similarly to random.randrange. The call random.randint(a, b) is equivalent to random.randrange(a, b + 1). We will find the choice function more useful after we examine Python’s more advanced data structures like lists. As a preview, Listing 6.12 (randomstring.py) shows how we can select a random element from a tuple of strings. Listing 6.12: randomstring.py ©2017 Richard L. Halterman Draft date: January 18, 2018 6.7. SYSTEM-SPECIFIC FUNCTIONS 176 from random import choice for i in range(10): print(choice(("one", "two", "three", "four", "five", "six", "seven", "eight", "nine", "ten"))) One run of Listing 6.12 (randomstring.py) produces three nine five nine three seven nine two eight ten The tuple of strings passed to the choice function must be enclosed within parentheses so it treated as one parameter (a tuple consisting of 10 strings) rather than 10 string parameters. 6.7 System-specific Functions The sys module provides a number of functions and variables that give programmers access to system- specific information. One useful function is exit that terminates an executing program. Listing 6.13 (exitprogram.py) uses the sys.exit function to end the program’s execution after it prints 10 numbers. Listing 6.13: exitprogram.py import sys sum = 0 while True: x = int(input('Enter a number (999 ends):')) if x == 999: sys.exit(0) sum += x print('Sum is', sum) The sys.exit function accepts a single integer argument, which it passed back to the operating system when the program completes. The value zero indicates that the program completed successfully; a nonzero value represents the program terminating due to an error of some kind. 6.8 The eval and exec Functions The input function produces a string from the user’s keyboard input. If we wish to treat that input as a number, we can use the int or float function to make the necessary conversion: ©2017 Richard L. Halterman Draft date: January 18, 2018 6.8. THE EVAL AND EXEC FUNCTIONS 177 x = float(input('Please enter a number: ')) Here, whether the user enters 2 or 2.0, x will be a variable with type floating point. What if we wish x to be of type integer if the user enters 2 and x to be floating point if the user enters 2.0? The __builtins__ module provides an interesting function named eval that attempts to evaluate a string in the same way that the interactive shell would evaluate it. Listing 6.14 (evalfunc.py) illustrates the use of eval. Listing 6.14: evalfunc.py x1 = eval(input('Entry x1? ')) print('x1 =', x1, ' type:', type(x1)) x2 = eval(input('Entry x2? ')) print('x2 =', x2, ' type:', type(x2)) x3 = eval(input('Entry x3? ')) print('x3 =', x3, ' type:', type(x3)) x4 = eval(input('Entry x4? ')) print('x4 =', x4, ' type:', type(x4)) x5 = eval(input('Entry x5? ')) print('x5 =', x5, ' type:', type(x5)) A sample run of Listing 6.14 (evalfunc.py) produces Entry x1? 4 x1 = 4 type:
Entry x2? 4.0
x2 = 4.0 type:
Entry x3? “x1”
x3 = x1 type:
Entry x4? x1
x4 = 4 type:
Entry x5? x6
Traceback (most recent call last):

File “evalfunc.py”, line 13, in
x5 = eval(input(‘Entry x5? ‘))

File ““, line 1, in
NameError: name ‘x6’ is not defined

Notice that when the user enters the text consisting of a single digit 4, the eval function interprets it as
integer 4 and assigns an integer to the variable x1. When the user enters the text 4.0, the assigned variable is
a floating-point variable. For x3, the user supplies the string “x3” (note the quotes), and the variable’s type
is string. The more interesting situation is x4. The user enters x1 (no quotes). The eval function evaluates
the unquoted text as a reference to the name x1 established by the first assignment statement. The program
bound the name x1 to the integer value 4 when executing the first line of the program. This statement thus
binds x4 to the same integer; that is, 4. Finally, the user enters x6 (no quotes). Since the quotes are missing,
the eval function does not interpret x6 as a literal string; instead eval treats x6 as a name and attempts to
evaluate it. Since no variable named x6 exists, the eval function prints an error message.

The eval function dynamically translates the text provided by the user into an executable form that the
program can process. This allows users to provide input in a variety of flexible ways; for example, users

6.8. THE EVAL AND EXEC FUNCTIONS 178

could enter multiple entries separated by commas, and the eval function would evaluate the text typed
by the user as Python tuple. As Listing 6.15 (addintegers4.py) shows, this makes tuple assignment (see
Section 2.2) from the input function possible.

Listing 6.15: addintegers4.py

num1, num2 = eval(input(‘Please enter number 1, number 2: ‘))
print(num1, ‘+’, num2, ‘=’, num1 + num2)

The following sample run shows how the user now must enter the two numbers at the same time separated
by a comma:

Please enter number 1, number 2: 23, 10
23 + 10 = 33

Listing 6.16 (enterarith.py) is a simple, one line Python program that behaves like Python’s interactive
shell, except that it accepts only one expression from the user.

Listing 6.16: enterarith.py

print(eval(input()))

A sample run of Listing 6.16 (enterarith.py) shows that the user may enter an arithmetic expression, and
eval handles it properly:

4 + 10
14

The users enters the text 4 + 10, and the program prints 14. Notice that the addition is not programmed
into Listing 6.16 (enterarith.py); as the program runs the eval function compiles the user-supplied text into
executable code and executes it to produce 14.

The exec function, also from the __builtins__ module, is similar to the eval function. The exec
function accepts a string parameter that consists of a Python source statement. The exec function inter-
prets the statement and executes it. Listing 6.17 (myinterpreter.py) plays the role of a rudimentary Python
interpreter.

Listing 6.17: myinterpreter.py

while True:
exec(input(“>>>”))

>>>from sys import exit
>>>x = 45
>>>print(x)
45
>>>x += 1000
>>>print(x)
1045
>>>exit(0)

While the eval and exec functions may seem to open up a number of interesting possibilities, their use
actually is very limited. The eval and exec functions demand much caution on the part of the programmer.

6.9. TURTLE GRAPHICS 179

In fact, the examples above that use the eval and exec functions are not advisable in practice. This is be-
cause they enable the user to make the program do things the programmer never intended. Python contains
functions that call on the operating system to perform tasks. This functionality includes the possibility of
erasing files or formatting entire disk drives. If the user knows the required Python code to accomplish such
devious tasks, he or she could hijack the program and cause havoc. As simple, harmless example, consider
the following example run of Listing 6.14 (evalfunc.py):

Entry x1? 100
x1 = 100 type:
Entry x2? exec(“import sys; sys.exit(0)”)

During the execution of Listing 6.14 (evalfunc.py) the user entered the text

exec(”import sys; sys.exit(0)”)

The eval function then interprets and evaluates the call to exec. The evaluation of the sys.exit function
will, of course, terminate the program. The program is written to interact with the user a while longer, the
user terminated it early.

In programs that use eval or exec, the programmer must preprocess the user input to defend against
unwanted and unwelcome program behavior.

6.9 Turtle Graphics

One of the simplest ways to draw pictures is the way we do it by hand with pen and paper. We place the
pen on the paper and move the pen, leaving behind a mark on the paper. The length and shape of the mark
depends on the movement of the pen. We then can lift the pen from the paper and place it elsewhere on the
paper to continue our graphical composition. We may have pens of various colors at our disposal.

Turtle graphics on a computer display mimics these actions of placing, moving, and turning a pen
on a sheet of paper. It is called Turtle graphics because originally the pen was represented as a turtle
moving within the display window. Seymour Papert originated the concept of Turtle graphics in his Logo
programming language in the late 1960s (see http://en.wikipedia.org/wiki/Turtle graphics for
more information about Turtle graphics). Python includes a Turtle graphics library that is relatively easy to
use.

In the simplest Turtle graphics program we need only issue commands to a pen (turtle) object. We must
import the turtle module to have access to Turtle graphics. Listing 6.18 (boxturtle.py) draws a rectangular
box.

Listing 6.18: boxturtle.py

# Draws a rectangular box in the window

import turtle

turtle.pencolor(‘red’) # Set pen color to red
turtle.forward(200) # Move pen forward 200 units (create bottom of rectangle)
turtle.left(90) # Turn pen by 90 degrees
turtle.pencolor(‘blue’) # Change pen color to blue
turtle.forward(150) # Move pen forward 150 units (create right wall)
turtle.left(90) # Turn pen by 90 degrees

http://en.wikipedia.org/wiki/Turtle_graphics

6.9. TURTLE GRAPHICS 180

Figure 6.6 A very simple drawing made with Turtle graphics

turtle.pencolor(‘green’) # Change pen color to green
turtle.forward(200) # Move pen forward 200 units (create top)
turtle.left(90) # Turn pen by 90 degrees
turtle.pencolor(‘black’) # Change pen color to black
turtle.forward(150) # Move pen forward 150 units (create left wall)
turtle.hideturtle() # Make pen invisible
turtle.exitonclick() # Wait for user input

Figure 6.6 shows the result of running Listing 6.18 (boxturtle.py). By default, the pen starts at the center of
the window facing to the right. Figure 6.7 shows the default Turtle graphics coordinate system. Listing 6.18
(boxturtle.py) reveals a few of the functions provided by the turtle module:

• setheading: sets the pen to face in a particular direction

• pencolor: sets pen’s current drawing color.

• forward: moves the pen forward a given distance at its current heading

• left: turns the pen to the left by an angle specified in degrees.

• right: turns the pen to the right by an angle specified in degrees.

• setposition: moves the pen to a given (x,y) coordinate within the graphics window. Draws a line
from the previous position unless the pen is up.

• title: sets the text to appear in the window’s title bar

• penup: disables drawing until the pen is put back down (allows turtle movements without drawing)

• pendown: enables the pen to draw when moved

• hideturtle: makes the pen object (turtle) itself invisible; this does not affect its ability to draw.

• tracer: turns off tracing (drawing animation) when its argument is zero—this speeds up rendering.

6.9. TURTLE GRAPHICS 181

Figure 6.7 The default coordinate system for a Turtle graphics picture. The x and y axes do not appear in an
actual image. As in the Cartesian coordinate system from algebra, the x values increase from left to right,
and the y values increase from bottom to top.

(0, 0) x

• update: renders all pending drawing actions (necessary when tracing is disabled).

• done: ends the drawing activity and waits on the user to close the window.

• exitonclick: directs the program to terminate when the user clicks the mouse over the window.

• mainloop: used in place of done to enable the graphics framework to handle events such as user
mouse clicks and keystrokes.

Listing 6.19 (octogon.py) draws in the display window a blue spiral within a red octogon.

Listing 6.19: octogon.py

# Draws in the window a spiral surrounded with an octagon

import turtle

# Draw a red octogon centered at (-45, 100)
turtle.pencolor(‘red’) # Set pen color
turtle.penup() # Lift pen to move it
turtle.setposition(-45, 100) # Move the pen to coordinates (-45, 100)
turtle.pendown() # Place pen to begin drawing
for i in range(8): # Draw the eight sides

turtle.forward(80) # Each side is 80 units long
turtle.right(45) # Each vertex is 45 degrees

# Draw a blue spiral centered at (0, 0)
distance = 0.2
angle = 40
turtle.pencolor(‘blue’) # Set pen color

6.9. TURTLE GRAPHICS 182

Figure 6.8 More Turtle graphics fun: a spiral within an octogon

turtle.penup() # Left pen to move it
turtle.setposition(0, 0) # Position the pen at coordinates (0, 0)
turtle.pendown() # Set pen down to begin drawing
for i in range(100):

turtle.forward(distance)
turtle.left(angle)
distance += 0.5

turtle.hideturtle() # Make pen invisible
turtle.exitonclick() # Quit program when user clicks mouse button

Listing 6.19 (octogon.py) uses the turtle.penup, turtle.setposition, and turtle.pendown functions
to move the pen to a particular location without leaving a mark within the display window. The center of the
display window is at coordinates (0, 0). Figure 6.8 shows the result of running Listing 6.19 (octogon.py).

After each drawing command such as forward or left the graphics environment updates the image,
thus showing the effect of the command. If you are annoyed that the drawing is too slow, you can speed up
the rendering process in several ways. You can add the following statement before moving the pen:

turtle.speed(0) # Fastest turtle actions

The speed function accepts an integer in the range 0. . . 10. The value 1 represents the slowest speed, and
the turtle’s speed increases as the arguments approach 10. Counterintuitively, 0 represents the fastest turtle
speed. The speed function will accept a string argument in place of an integer value; the permissible strings
correspond to the following numeric values:

• “fastest” is equivalent to 0

• “fast” is equivalent to 10

• “normal” is equivalent to 6

• “slow” is equivalent to 3

6.9. TURTLE GRAPHICS 183

• “slowest” is equivalent to 1

The delay function provides another way to affect the time it takes to render an image. Rather than
controlling the overall speed of the turtle’s individual movements and/or turns, the delay function specifies
the time delay in milliseconds between drawing incremental updates of the image to the screen. Listing 6.20
(speedvsdelay.py) demonstrates the subtle difference in the way speed and delay functions effect the time
to render an image.

Listing 6.20: speedvsdelay.py

import turtle

y = -200 # Initial y value

# Default speed and default delay
turtle.color(“red”)
for x in range(10):

turtle.penup()
turtle.setposition(-200, y)
turtle.pendown()
turtle.forward(400)
y += 10

# Slowest speed, but no delay
turtle.speed(“slowest”)
turtle.delay(0)
turtle.update()
turtle.color(“blue”)
for x in range(10):

turtle.penup()
turtle.setposition(-200, y)
turtle.pendown()
turtle.forward(400)
y += 10

# Fastest speed with a 500 millisecond delay
turtle.speed(“fastest”)
turtle.delay(500)
turtle.update()
turtle.color(“green”)
for x in range(10):

turtle.penup()
turtle.setposition(-200, y)
turtle.pendown()
turtle.forward(400)
y += 10

# Fastest speed with no delay
turtle.speed(“fastest”)
turtle.delay(0)
turtle.update()
turtle.color(“black”)
for x in range(10):

turtle.penup()

6.9. TURTLE GRAPHICS 184

Figure 6.9 Listing 6.20 (speedvsdelay.py) demonstrates the different effects of the turtle.speed versus
turtle.delay functions. The program renders the bottom 10 lines using the default speed and delay
settings. In the next 10 lines the program draws with the slowest speed but without a delay. The program
next draws 10 lines at the fastest speed with a 100 millisecond delay between screen updates. The top 10
lines represent the fastest speed with no delay. Note that the animation is still smooth at a slower speed, but
the delay function makes the animation choppy at regular time intervals.

turtle.setposition(-200, y)
turtle.pendown()
turtle.forward(400)
y += 10

turtle.done()

Figure 6.9 shows the eventual output of Listing 6.20 (speedvsdelay.py). The speed function does not
sacrifice the smoothness of the animation, while the delay function can make the animation choppy at
regular time intervals.

You can use the tracer function to achieve the fastest rendering possible. Listing 6.21 (noanimation.py)
produces the same drawing as Listing 6.20 (speedvsdelay.py), but the picture appears almost instantly.

6.10. OTHER TECHNIQUES FOR IMPORTING FUNCTIONS AND MODULES 185

Listing 6.21: noanimation.py

import turtle

y = -200 # Initial y value

# Turn off animation
turtle.tracer(0)
turtle.color(“red”)
for x in range(10):

turtle.penup()
turtle.setposition(-200, y)
turtle.pendown()
turtle.forward(400)
y += 10

turtle.color(“blue”)
for x in range(10):

turtle.penup()
turtle.setposition(-200, y)
turtle.pendown()
turtle.forward(400)
y += 10

turtle.color(“green”)
for x in range(10):

turtle.penup()
turtle.setposition(-200, y)
turtle.pendown()
turtle.forward(400)
y += 10

turtle.color(“black”)
for x in range(10):

turtle.penup()
turtle.setposition(-200, y)
turtle.pendown()
turtle.forward(400)
y += 10

turtle.update() # Ensure all of image is drawn
turtle.done()

When animation is disabled with the tracer function, you should call update at the point the complete
image should appear. When the tracer is active it explicitly draws the penstrokes to the screen as the turtle
moves. With the tracer turned off, the programmer must ensure all the image becomes visible by calling the
update function. Turning the tracer off is the ultimate way to speed up Turtle graphics rendering in Python.

6.10 Other Techniques for Importing Functions and Modules

Section 6.2 introduced the two most common ways programmers use to import functions into Python code.
For the sake of completeness, we briefly examine three other importing techniques that you may encounter

6.10. OTHER TECHNIQUES FOR IMPORTING FUNCTIONS AND MODULES 186

in published Python code.

Recall that we can use the from . . .import . . . notation to import some of the functions that a module
has to offer. This allows callers to use the base names of the functions without prepending the module
name. This technique becomes unwieldy when a programmer wishes to use a large number of functions
from a particular module.

The following statement:

from math import *

makes all the code in the math module available to the program. The * symbol is the wildcard symbol that
represents “everything.” Some programmers use an import statement like this one for programs that need
to use many different functions from a module.

As we will see below, however, best Python programming practice discourages this “import everything”
approach.

This “import all” statement is in some ways the easiest to use. The mindset is, “Import everything
because we may need some things in the module, but we are not sure exactly what we need starting out.”
The source code is shorter: * is quicker to type than a list of function names, and, within the program, short
function names are easier to type than the longer, qualified function names. While in the short term the
“import all” approach may appear to be attractive, in the long term it can lead to problems. As an example,
suppose a programmer is writing a program that simulates a chemical reaction in which the rate of the
reaction is related logarithmically to the temperature. The statement

from math import log10

may cover all that this program needs from the math module. If the programmer instead uses

from math import *

this statement imports everything from the math module, including a function named degrees which con-
verts an angle measurement in radians to degrees (from trigonometry, 360◦ = 2π radians). Given the nature
of the program, the word degrees is a good name to use for a variable that represents temperature. The
two words are the same, but their meanings are very different. Even though the import statement brings
in the degrees function, the programmer is free to redefine degrees to be a floating-point variable (recall
redefining the print function in Section 2.3). If the program does redefine degrees, the math module’s
degrees function is unavailable if the programmer later discovers its need. A name collision results if the
programmer tries to use the same name for both the angle conversion and temperature representation. The
same name cannot be used simultaneously for both purposes.

Most significant Python programs must import multiple modules to obtain all the functionality they
need. It is possible for two different modules to provide one or more functions with the same name. This is
another example of a name collision.

The names of variables and functions available to a program live in that program’s namespace. The dir
function prints a program’s namespace, and we can experiment with it in Python’s interactive interpreter:

>>> dir()
[‘__builtins__’, ‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’,
‘__spec__’]
>>> x = 2
>>> dir()
[‘__builtins__’, ‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’,
‘__spec__’, ‘x’]

6.10. OTHER TECHNIQUES FOR IMPORTING FUNCTIONS AND MODULES 187

>>> from math import sqrt
>>> dir()
[‘__builtins__’, ‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’,
‘__spec__’, ‘sqrt’, ‘x’]
>>> from math import *
>>> dir()
[‘__builtins__’, ‘__doc__’, ‘__loader__’, ‘__name__’, ‘__package__’,
‘__spec__’, ‘acos’, ‘acosh’, ‘asin’, ‘asinh’, ‘atan’, ‘atan2’,
‘atanh’, ‘ceil’, ‘copysign’, ‘cos’, ‘cosh’, ‘degrees’, ‘e’, ‘erf’,
‘erfc’, ‘exp’, ‘expm1’, ‘fabs’, ‘factorial’, ‘floor’, ‘fmod’, ‘frexp’,
‘fsum’, ‘gamma’, ‘hypot’, ‘isfinite’, ‘isinf’, ‘isnan’, ‘ldexp’,
‘lgamma’, ‘log’, ‘log10’, ‘log1p’, ‘log2’, ‘modf’, ‘pi’, ‘pow’,
‘radians’, ‘sin’, ‘sinh’, ‘sqrt’, ‘tan’, ‘tanh’, ‘trunc’, ‘x’]

Observe how assigning the variable x adds the name x to the interpreter’s namespace. Importing just
math.sqrt adds sqrt to the namespace. Finally, importing everything from the math module adds many
more names. If we attempt to use any of these names in a different way, they will lose their original purpose;
for example, the following continues the above interactive sequence:

>>> help(exp)
Help on built-in function exp in module math:

exp(…)
exp(x)

Return e raised to the power of x.

Now let us redefine exp:

>>> exp = None
>>> help(exp)
Help on NoneType object:

If we reassign the exp name to refer to None, we no longer can use it to compute ex.

We say that the “import everything” statement pollutes the program’s namespace. This kind of import
adds many names (variables, functions, and other objects) to the collection of names managed by the
program. This can cause name collisions as in the example above with the name degrees, and it makes it
more difficult to work with larger programs. When adding new functionality to such a program we must be
careful not to tread on any names that already exist in the program’s namespace.

Python best programming practices discourages the use of the “import everything” statement:

6.10. OTHER TECHNIQUES FOR IMPORTING FUNCTIONS AND MODULES 188

from math import *

since this provides more opportunities for name collisions and renders code less maintainable.

Most Python programmers agree that the best approach imports the whole module, as in

import math

and uses qualified names for the functions the module provides. In the above example, this module im-
port approach solves the name collision problem: math.degrees is a different name than plain degrees.
Also, if, for example, modules mod1 and mod2 both contain a function named process, the module import
statement forces programmers to write mod1.process and mod2.process, thus avoiding the name clash.

We have seen the compromise: import only the functions needed, as in

from math import sqrt, log10

This does not impact the program’s namespace very much, and it allows the program to use short function
names. Also, by explicitly naming the functions to import, the programmer is more aware of how the names
will impact the program. Many programmers find this approach acceptable for smaller programs where the
probablility of name clashes is low as the program evolves.

Python provides a way to import a module under a different name. The following statement imports the
standard math module as m:

import math as m

In this case, the caller would invoke the modules functions in the following way:

y = m.sqrt(x)
print(m.log10(100))

Note the m. prefix attached to the calls of the sqrt and log10 functions. Programmers sometimes use
this module renaming import to simplify typing when a module name is long. Listing 6.22 (octogon2.py)
is a rewrite of Listing 6.19 (octogon.py) that introduces a new name for the turtle module: t. We say
that turtle and t are aliases for the same module. This in effect shortens the qualified names for each of
the function calls. The fact that Listing 6.22 (octogon2.py) runs faster than Listing 6.19 (octogon.py) has
nothing to do with the module name aliasing or shorter qualified function names; Listing 6.22 (octogon2.py)
runs much faster because it calls the turtle.delay function to speed up the drawing.

Listing 6.22: octogon2.py

# Draws in the window a spiral surrounded with an octagon

import turtle as t # Use a shorter name for turtle module

t.delay(0) # Draw as quickly as possible
t.speed(0) # Turtle’s action as fast as possible
t.hideturtle() # Do not show the pen
# Draw a red octogon centered at (-45, 100)
t.pencolor(‘red’) # Set pen color
t.penup() # Lift pen to move it
t.setposition(-45, 100) # Move the pen to coordinates (-45, 100)
t.pendown() # Place pen to begin drawing
for i in range(8): # Draw the eight sides

t.forward(80) # Each side is 80 units long

6.10. OTHER TECHNIQUES FOR IMPORTING FUNCTIONS AND MODULES 189

t.right(45) # Each vertex is 45 degrees

# Draw a blue spiral centered at (0, 0)
distance = 0.2
angle = 40
t.pencolor(‘blue’) # Set pen color
t.penup() # Left pen to move it
t.setposition(0, 0) # Position the pen at coordinates (0, 0)
t.pendown() # Set pen down to begin drawing
for i in range(100):

t.forward(distance)
t.left(angle)
distance += 0.5

t.exitonclick() # Quit program when user clicks the mouse button

When a program imports a module this way the module’s original name is not automatically available.
This means the name turtle is not available to the code in Listing 6.22 (octogon2.py). Code must access
the turtle module’s functiom via t.

The practice of using an alias merely to shorten module name is questionable. It essentially hides a
recognized standard name and so renders the code less readable. Fortunately, the ability to alias module
names is convenient for other purposes besides shortening module names. Suppose a third-party software
vendor develops an alternative to Python’s standard math module. It includes all the functions provided
by the math module, with exactly the same names. The company markets it as a drop-in replacement for
the math module. The vendor names this module fastmath because the algorithms it uses to implement
the mathematical functions are more efficient than those used in the math module. As an example, when
invoked with the same arguments the fastmath.sqrt and math.sqrt functions compute identical results,
but fastmath.sqrt returns its result quicker than math.sqrt.

Suppose, too, that we have a large application that performs many mathematical calculations using
functions from the math module. We would like to try the third-party fastmath module to see if it indeed
speeds up our application. Among other possible module imports, our application includes the following
statement:

import math

This means our application is sprinkled with statements like

y = math.sqrt(max – alpha)
while value < max: value += math.log10(inc) calling math functions in hundreds of places throughout the code. Note the qualified function names. If we change the import statement to import fastmath we will have to edit the function invocations in hundreds of places within our code. Instead, we can change the import statement to read import fastmath as math ©2017 Richard L. Halterman Draft date: January 18, 2018 6.10. OTHER TECHNIQUES FOR IMPORTING FUNCTIONS AND MODULES 190 Adding just two words to the original import statement enables us to leave everything else in our code alone. Every mention of math will refer actually to the fastmath module. In addition to importing an entire module under a new name, Python allows programmers to alias individual functions. Consider the following code: from math import sqrt as sq print(sq(16)) The names of standard functions are well known to experienced Python developers, so such renaming renders a program immediately less less readable. We should not consider renaming standard functions unless we have a very good reason. Some have found this technique useful for resolving name clashes between two modules that define one or more functions with the same name. Returning to our example from above, suppose we wish to compare directly the performance of math.sqrt to fastmath.sqrt. The process of measuring the relative performance of software is known as benchmarking. We need to have both math.sqrt and fastmath.sqrt available in the same program. The following code performs the benchmark and avoids qualified function names: from time import clock from math import sqrt as std_sqrt from fastmath import sqrt as fast_sqrt start_time = clock() for n in range(100000): std_sqrt(n) print('Standard:', clock() - start_time) start_time = clock() for n in range(100000): fast_sqrt(n) print('Fast:', clock() - start_time) The renamed functions may be confusing. The better approach imports the modules themselves rather than the individual functions: import math, fastmath, time start_time = time.clock() for n in range(100000): math.sqrt(n) print(time.clock() - start_time) start_time = time.clock() for n in range(100000): fastmath.sqrt(n) print(time.clock() - start_time) This version arguably is better. Without looking elsewhere in the program’s source code, the programmer immediately can see exactly which function from which module the program is calling. The qualified names make it perfectly clear which function is which. While using module and function aliases can be convenient at times, you should use this feature only if necessary. Standard names are well known and recognizable by experienced Python programmers. Giving ©2017 Richard L. Halterman Draft date: January 18, 2018 6.11. EXERCISES 191 Figure 6.10 Right triangle Side 1 S id e 2 Hypotenuse new names to standard functions and modules unnecessarily can make programs less readable and confuse programmers attenpting to modify or extend an existing application. When in doubt, follow best practice and use the module import statement. This makes each function call more self-documenting by unambiguously indicating its module of origin. 6.11 Exercises 1. Suppose you need to compute the square root of a number in a Python program. Would it be a good idea to write the code to perform the square root calculation? Why or why not? 2. Which of the following values could be produced by the call random.randrange(0, 100) function (circle all that apply)? 4.5 34 -1 100 0 99 3. Classify each of the following expressions as legal or illegal. Each expression represents a call to a standard Python library function. (a) math.sqrt(4.5) (b) math.sqrt(4.5, 3.1) (c) random.rand(4) (d) random.seed() (e) random.seed(-1) 4. From geometry: Write a computer program that, given the lengths of the two sides of a right triangle adjacent to the right angle, computes the length of the hypotenuse of the triangle. (See Figure 6.10.) If you are unsure how to solve the problem mathematically, do a web search for the Pythagorean theorem. 5. Write a guessing game program in which the computer chooses at random an integer in the range 1 . . .100. The user’s goal is to guess the number in the least number of tries. For each incorrect guess the user provides, the computer provides feedback whether the user’s number is too high or too low. ©2017 Richard L. Halterman Draft date: January 18, 2018 6.11. EXERCISES 192 6. Extend Problem 5 by keeping track of the number of guesses the user needed to get the correct answer. Report the number of guesses at the end of the game. 7. Extend Problem 6 by measuring how much time it takes for the user to guess the correct answer. Report the time and number of guesses at the end of the game. 8. For each of the drawings below write a program that draws the shape using functions from Python’s Turtle graphics module. 9. Write a program that uses functions from Python’s Turtle graphics module to draw a grid of hexagons as shown in the picture below. ©2017 Richard L. Halterman Draft date: January 18, 2018 193 Chapter 7 Writing Functions As programs become more complex, programmers must structure their programs in such a way as to ef- fectively manage their complexity. Most humans have a difficult time keeping track of too many pieces of information at one time. It is easy to become bogged down in the details of a complex problem. The trick to managing complexity is to break down the problem into more manageable pieces. Each piece has its own details that must be addressed, but these details are hidden as much as possible within that piece. These pieces assemble to form the problem’s complete solution. So far all of the code we have written has been placed within a single block of code. That single block may have contained sub-blocks for the bodies of structured statements like if and while, but the program’s execution begins with the first statement in the block and ends when the last statement in that block is finished. Even though all of the code we have written has been limited to one, sometimes big, block, our programs all have executed code outside of that block. All the functions we have used—print, input, sqrt, randrange, etc.—represent blocks of code that some other programmers have written for us. These blocks of code have a structure that makes them reusable by any Python program. As the number of statements within our block of code increases, the code becomes more difficult to manage. A single block of code (like in all our programs to this point) that does all the work itself is called monolithic code. Monolithic code that is long and complex is undesirable for several reasons: • It is difficult to write correctly. Complicated monolithic code attempts to do everything that needs to done within the program. The indivisible nature of the code divides the programmer’s attention amongst all the tasks the block must perform. In order to write a statement within a block of mono- lithic code the programmer must be completely familiar with the details of all the code in that block. For instance, we must use care when introducing a new variable to ensure that variable’s name is not already being used within the block. • It is difficult to debug. If the sequence of code does not work correctly, it may be difficult to find the source of the error. The effects of an erroneous statement that appears earlier in a block of monolithic code may not become apparent until a possibly correct statement later uses the erroneous statement’s incorrect result. Programmers naturally focus their attention first to where they observe the program’s misbehavior. Unfortunately, when the problem actually lies elsewhere, it takes more time to locate and repair the problem. • It is difficult to extend. Much of the time software developments spend is modifying and extending existing code. As in the case of originally writing the monolithic block of code, a programmer must ©2017 Richard L. Halterman Draft date: January 18, 2018 7.1. FUNCTION BASICS 194 understand all the details in the entire sequence of code before attempting to modify it. If the code is complex, this may be a formidable task. We can write our own functions to divide our code into more manageable pieces. Using a divide and conquer strategy, we can decompose a complicated block of code into several simpler functions. The original code then can do its job by delegating the work to these functions. This process of is known as functional decomposition. Besides their code organization aspects, functions allow us to bundle functional- ity into reusable parts. In Chapter 6 we saw how library functions can dramatically increase the capabilities of our programs. While we should capitalize on library functions as much as possible, often we need a function exhibiting custom behavior unavailable in any standard function. Fortunately, we can create our own functions. Once created, we can use (call) these functions in numerous places within a program. If the function’s purpose is general enough and we write the function properly, we can reuse the function in other programs as well. 7.1 Function Basics There are two aspects to every Python function: • Function definition. The definition of a function contains the code that determines the function’s behavior. • Function invocation. A function is used within a program via a function invocation. In Chapter 6, we invoked standard functions that we did not have to define ourselves. Every function has exactly one definition but may have many invocations. An ordinary function definition consists of four parts: • def—The def keyword introduces a function definition. • Name—The name is an identifier (see Section 2.3). As with variable names, the name chosen for a function should accurately portray its intended purpose or describe its functionality. (Python provides for specialized anonymous functions called lambda expressions, but we defer their introduction until Section 8.7.) • Parameters—every function definition specifies the parameters that it accepts from callers. The parameters appear in a parenthesized comma-separated list. The list of parameters is empty if the function requires no information from code that calls the function. A colon follows the parameter list. • Body—every function definition has a block of indented statements that constitute the function’s body. The body contains the code to execute when callers invoke the function. The code within the body is responsible for producing the result, if any, to return to the caller. Figure 7.1 shows the general form of a function definition. A function usually accepts some values from its caller and returns a result back to its caller. Listing 7.1 (doublenumber.py) provides a very simple function definition to illustrate the process. Listing 7.1: doublenumber.py ©2017 Richard L. Halterman Draft date: January 18, 2018 7.1. FUNCTION BASICS 195 Figure 7.1 General form of a function definition block def ( ):name parameter list def double(n): return 2 * n # Return twice the given number # Call the function with the value 3 and print its result x = double(3) print(x) Listing 7.1 (doublenumber.py) is admittedly not very useful, but it illustates several important points: • The two lines def double(n): return 2 * n # Return twice the given number constitute the definition of the double function. • The def keyword marks the beginning of the function’s definition. • The function definition establishes the function’s name is double. • The function definition specifies that the function accepts one value from the user. This value will go by the name n within the function’s body. This variable n is the function’s only parameter. • The statement(s) that constitute the working part of the function definition (in this case just one statement) are indented relative to the line containing def. • The return keyword indicates the value the function is to communicate by to its caller. In this case, the function simply returns the product of its parameter n and 2. • The code that follows the double function’s definition: # Call the function with the value 3 and print its result x = double(3) print(x) calls (or invokes) the function sending it the value 3. The assignment statement binds the function’s computed return value to the variable x. The program can use x as it sees fit; in this case the program simply prints x’s value. The program runs as follows: ©2017 Richard L. Halterman Draft date: January 18, 2018 7.1. FUNCTION BASICS 196 Figure 7.2 Calling relationships among functions during the execution of Listing 7.1 (doublenumber.py). Time flows from top to bottom. A vertical bar represents the time in which a block of code is active. Observe that functions are active only during their call. The shaded area within in block represents the time that block is idle, waiting for a function call to complete. Right arrows (→) represent function calls. Function calls show parameters, where applicable. Left arrows (←) represent function returns. Function returns show return values, if applicable. Program block double print P ro g ra m E xe cu ti o n (T im e ) 3 6 6 1. The program’s execution begins with the first line in the “naked” block; that is, the block that is not part of the function definition. The program thus executes the assignment statement that calls the double function with the argument 3. Before the assignment can happen, the program’s execution transfers to the body of the double function. The code within double executes, which simply returns the product of 2 and the parameter passed in (in this case 3). 2. When double is finished, control is passed back to the point in the code where it was called, in this case effectively evaluating the expression double(3) to be 6. The assignment operator then assigns the value 6 to the variable x. 3. The program finally prints the value of x, calculated to be 6. Figure 7.2 contains a diagram illustrating the execution of Listing 7.1 (doublenumber.py) as control passes amongst the various functions. The interaction amongst functions can be quite elaborate, even for relatively simple programs. It is important to note that a program executes code within a function only when the function is called. If a program contains a function definition, but no code executing within that program calls that function, that function’s code will not execute. As another simple example, consider Listing 7.2 (countto10.py). Listing 7.2: countto10.py ©2017 Richard L. Halterman Draft date: January 18, 2018 7.1. FUNCTION BASICS 197 # Counts to ten for i in range(1, 11): print(i, end=' ') print() which simply counts to ten: 1 2 3 4 5 6 7 8 9 10 If counting to ten in this way is something we want to do frequently within a program, we can write a function as shown in Listing 7.3 (countto10func.py) and call it as many times as necessary. Listing 7.3: countto10func.py # Count to ten and print each number on its own line def count_to_10(): for i in range(1, 11): print(i, end=' ') print() print("Going to count to ten . . .") count_to_10() print("Going to count to ten again. . .") count_to_10() Listing 7.3 (countto10func.py) prints Going to count to ten . . . 1 2 3 4 5 6 7 8 9 10 Going to count to ten again. . . 1 2 3 4 5 6 7 8 9 10 The empty parentheses in count_to_10’s definition indicates that the function does not accept any param- eters from its caller. Also, the absence of a return statement indicates that this function communicates no information back to its caller. Such functions that get no information in and provide no results can be useful for the effects they achieve (in this case just printing the numbers 1 to 10. Our doublenumber and count_to_10 functions are a bit underwhelming. The doublenumber function could be eliminated, and each call to doublenumber could be replaced with a simple variation of the code in its body. The same could be said for the count_to_10 function, although it is convenient to have the simple one-line statement that hides the complexity of the loop. These examples serve simply to familiarize us with the mechanics of function definitions and invocations. Functions really shine when our problems become more complex. Our experience using a simple function like print shows us that we can alter the behavior of some functions by passing different parameters. The following successive calls to the print function produces different results: print('Hi') print('Bye') The two statements produce different results, of course, because we pass to the print function two different strings. Our double function from above will compute a different result if we pass it a different parameter. ©2017 Richard L. Halterman Draft date: January 18, 2018 7.1. FUNCTION BASICS 198 If a function is written to accept information from the caller, the caller must supply the information in order to use the function. The caller communicates the information via one or more parameters as required by the function. The count_to_10 function does us little good if we sometimes want to count up to a different number. Listing 7.4 (countton.py) generalizes Listing 7.3 (countto10func.py) to count as high as the caller needs. Listing 7.4: countton.py # Count to n and print each number on its own line def count_to_n(n): for i in range(1, n + 1): print(i, end=' ') print() print("Going to count to ten . . .") count_to_n(10) print("Going to count to five . . .") count_to_n(5) Listing 7.4 (countton.py) displays Going to count to ten . . . 1 2 3 4 5 6 7 8 9 10 Going to count to five . . . 1 2 3 4 5 When the caller code issues the call count_to_n(10) the argument 10 is known as the actual parameter. In the function definition, the parameter named n is called the formal parameter. During the call count_to_n(10) the actual parameter 10 is assigned to the formal parameter n before the function’s statements begin execut- ing. The actual parameter may be a literal value (such as 10 in the expression count_to_n(10)), or it may be a variable, as Listing 7.5 (countwithvariable.py) illustrates. Listing 7.5: countwithvariable.py def count_to_n(n): for i in range(1, n + 1): print(i, end=' ') print() for i in range(1, 10): count_to_n(i) 1 1 2 ©2017 Richard L. Halterman Draft date: January 18, 2018 7.1. FUNCTION BASICS 199 1 2 3 1 2 3 4 1 2 3 4 5 1 2 3 4 5 6 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 9 The actual parameter a caller sends to the count_to_n function may in fact be any expression that evaluates to an integer. A caller must pass exactly one integer parameter to count_to_n during a call. An attempt to pass no parameters or more than one integer parameter results in a syntax error: count_to_n() # Error, missing parameter during the call count_to_n(3, 5) # Error, too many parameters during the call An attempt to pass a non-integer results in a run-time exception because the count_to_n function passes its parameter on to the range expression, and range requires all of its arguments to be integers. count_to_n(3.2) # Run-time error, actual parameter not an integer To recap, in the first line of the function definition: def double(n): we refer to n as the formal parameter. A formal parameter is used like a variable within the function’s body, and it is local to the function. A formal parameter is the parameter from the perspective of the function definition. During an invocation of double, such as double(2), the caller passes actual parameter 2. The actual parameter is the parameter from the caller’s point of view. A function invocation, therefore, binds the actual parameters sent by the caller to their corresponding formal parameters. A caller can pass multiple pieces of information into a function via multiple parameters. Consider Listing 7.6 (regularpolygon.py) that uses Turtle graphics (see Section 6.9) to draw regular polygons with varying numbers of sides. In a regular polygon all sides have the same length, and all angles between the sides are the same (see https://en.wikipedia.org/wiki/Regular polygon). Listing 7.6: regularpolygon.py import turtle import random # Draws a regular polygon with the given number of sides. # The length of each side is length. # The pen begins at point(x, y). # The color of the polygon is color. def polygon(sides, length, x, y, color): turtle.penup() turtle.setposition(x, y) turtle.pendown() turtle.color(color) turtle.begin_fill() for i in range(sides): turtle.forward(length) ©2017 Richard L. Halterman Draft date: January 18, 2018 https://en.wikipedia.org/wiki/Regular_polygon 7.1. FUNCTION BASICS 200 turtle.left(360//sides) turtle.end_fill() # Disable rendering to speed up drawing turtle.hideturtle() turtle.tracer(0) # Draw 20 random polygons with 3-11 sides, each side ranging # in length from 10-50, located at random position (x, y). # Select a color at random from red, green, blue, black, or yellow. for i in range(20): polygon(random.randrange(3, 11), random.randrange(10, 51), random.randrange(-250, 251), random.randrange(-250, 251), random.choice(("red", "green", "blue", "black", "yellow"))) turtle.update() # Render image turtle.exitonclick() # Wait for user's mouse click The polygon function accepts four parameters: • sides specifies the number of sides, • length specifies the length of each side, • x specifies the x component of the polygon’s (x,y) location. • y specifies the y component of the polygon’s (x,y) location. • color specifies the polygon’s filled color. The polygon function does not have a return statement, so it does not communicate a result back to its caller. This program introduces the begin_fill and end_fill functions from the turtle module. When placed around code that draws a closed figure, these functions fill the shape with the current drawing color. Figure 7.3 shows a screenshot of a sample run of Listing 7.6 (regularpolygon.py). While a caller can pass multiple pieces of information into a function via multiple parameters, a func- tion ordinarily passes back to the caller one piece of information via a return statement. If necessary, a function may return multiple pieces of information packed up in a tuple or other data structure. Listing 7.7 (midpoint.py) uses a custom function to compute the midpoint between two mathematical points. Listing 7.7: midpoint.py def midpoint(pt1, pt2): x1, y1 = pt1 # Extract x and y components from the first point x2, y2 = pt2 # Extract x and y components from the second point return (x1 + x2)/2, (y1 + y2)/2 # Get two points from the user point1 = float(input("Enter first point's x: ")), \ float(input("Enter first point's y: ")) point2 = float(input("Enter second point's x: ")), \ float(input("Enter second point's y: ")) # Compute the midpoint ©2017 Richard L. Halterman Draft date: January 18, 2018 7.1. FUNCTION BASICS 201 Figure 7.3 A sample run of Listing 7.6 (regularpolygon.py). The number of sides, length of each side, location, and color of each polygon varies based on the arguments passed by the caller. mid = midpoint(point1, point2) # Report result to user print('Midpoint of', point1, 'and', point2, 'is', mid) Listing 7.7 (midpoint.py) accepts two parameters, each of which is a tuple containing two values: the x and y components of a point. Given two mathematical points (x1,y1) and (x2,y2), the function uses the following formula to compute (xm,ym), the midpoint of (x1,y1) and (x2,y2): (xm,ym) = ( x1 + x2 2 , y1 + y2 2 ) A sample run of Listing 7.7 (midpoint.py) looks like the following: Enter first point's x: 0 Enter first point's y: 0 Enter second point's x: 1 Enter second point's y: 1 Midpoint of (0.0, 0.0) and (1.0, 1.0) is (0.5, 0.5) The midpoint function returns only one result, but that result is a tuple containing two pieces of data. The mid variable in Listing 7.7 (midpoint.py) refers to a single tuple object. We will examine tuples in more detail in Chapter 11, but for now it is useful to note that we also can extract the components of the returned tuple into individual numeric variables as follows: mx, my = midpoint(point1, point2) # Unpack the returned tuple Here, the midpoint function still is returning just one value (a tuple), but the assignment statement “un- packs” the individual values stored in the tuple and assigns them to the variables mx and my. The process of extracting the pieces of a tuple object into separate variables is formally called tuple unpacking. ©2017 Richard L. Halterman Draft date: January 18, 2018 7.1. FUNCTION BASICS 202 Figure 7.4 Cutting plywood 18 inches 24 inches 6 6 Figure 7.5 Squares too small 18 inches 24 inches 3 3 Recall the greatest common divisor (also called greatest common factor) function from elementary mathematics. To determine the GCD of 24 and 18 we list all of their common factors and select the largest one: 24: 1, 2, 3, 4, 6 , 8, 12, 24 18: 1, 2, 3, 6 , 9, 18 The greatest common divisor function is useful for reducing fractions to lowest terms; for example, consider the fraction 18 24 . The greatest common divisor of 18 and 24 is 6, and we can compute the reduced fraction by dividing the numerator and the denominator by 6: 18÷6 24÷6 = 3 4 . The GCD function has applica- tions in other areas besides reducing fractions to lowest terms. Consider the problem of dividing a piece of plywood 24 inches long by 18 inches wide into square pieces of maximum size in integer dimensions, with- out wasting any material. Since the GCF(24, 18) = 6, we can cut the plywood into twelve 6 inch × 6 inch square pieces as shown in Figure 7.4. If we cut the plywood into squares of any other size without wasting the any of the material, the squares would have to be smaller than 6 inches × 6 inches; for example, we could make forty-eight 3 inch× 3 inch squares as shown in pieces as shown in Figure 7.5. If we cut squares larger than 6 inches × 6 inches, not all the plywood can be used to make the squares. Figure 7.6. shows ©2017 Richard L. Halterman Draft date: January 18, 2018 7.1. FUNCTION BASICS 203 Figure 7.6 Squares too large 18 inches 24 inches 9 in. 9 in. W a s te 18 inches 24 inches 8 in. 8 in. Waste how some larger squares would fare. In addition to basic arithmetic and geometry, the GCD function plays a vital role in cryptography, enabling secure communication across an insecure network. We can write a program that computes the GCD of two integers supplied by the user. Listing 7.8 (gcdprog.py) is one such program. Listing 7.8: gcdprog.py # Compute the greastest common factor of two integers # provided by the user # Prompt user for input num1 = int(input('Please enter an integer: ')) num2 = int(input('Please enter another integer: ')) # Determine the smaller of num1 and num2 min = num1 if num1 < num2 else num2 # 1 definitely is a common factor to all ints largest_factor = 1 ©2017 Richard L. Halterman Draft date: January 18, 2018 7.1. FUNCTION BASICS 204 for i in range(1, min + 1): if num1 % i == 0 and num2 % i == 0: largest_factor = i # Found larger factor # Print the GCD print(largest_factor) Listing 7.8 (gcdprog.py) implements a straight-forward but naive algorithm that seeks potential factors by considering every integer less than the smaller of the two values provided by the user. This algorithm is not very efficient, especially for larger numbers. Its logic is easy to follow, with no deep mathematical insight required. Soon we will see a better algorithm for computing GCD. If we need to compute the GCD from several different places within our program, we should package the code in a function rather than copying it to multiple places. The following code fragment defines a Python function that that computes the greatest common divisor of two integers. It determines the largest factor (divisor) common to its parameters: def gcd(num1, num2): # Determine the smaller of num1 and num2 min = num1 if num1 < num2 else num2 # 1 definitely is a common factor to all ints largest_factor = 1 for i in range(1, min + 1): if num1 % i == 0 and num2 % i == 0: largest_factor = i # Found larger factor return largest_factor This function is named gcd and expects two integer arguments. Its formal parameters are named num1 and num2. It returns an integer result. The function uses three local variables: min, largest_factor, and i. Local variables have meaning only within their scope. The scope of a local variable is the point within the function’s block after its first assignment until the end of that block. This means that when you write a function you can name a local variable without concern that its name may be used already in another part of the program. Two different functions can use local variables named x, and these are two different variables that have no influence on each other. Anything local to a function definition is hidden to all code outside that function definition. Since a formal parameter also is local to its function, you can reuse the names of formal parameters in different functions without a problem. Listing 7.9 (localplay.py) illustrates how function definitions provide protection for local variables. Listing 7.9: localplay.py x = 2 print("1. x =", x) # Print variable x's current value def fun1(): x = 10 print("2. x =", x) # Print this variable x's current value print("3. x =", x) # Print variable x's current value def fun2(): x = 20 print("4. x =", x) # Print this variable x's current value print("5. x =", x) # Print variable x's current value ©2017 Richard L. Halterman Draft date: January 18, 2018 7.1. FUNCTION BASICS 205 fun1() # Invoke function fun1 fun2() # Invoke function fun2 print("6. x =", x) # Print variable x's current value Notice that Listing 7.9 (localplay.py) numbers each print statement in the order of its appearance in the program’s source code. When executing the program the interpreter will executes the source code line by line, top to bottom. It executes each statement in turn, but function definitions are special—a function definition packages code into an executable unit to be executed later. The code within a function definition executes only when invoked by a caller. Listing 7.9 (localplay.py), therefore, will not execute the print statements in the order listed in the source code. Listing 7.9 (localplay.py) prints 1. x = 2 3. x = 2 5. x = 2 2. x = 10 4. x = 20 6. x = 2 The printing statements 1, 2, 5, and 6 all refer to the variable x defined outside of functions fun1 and fun2. When fun1 and fun2 assign to a variable named x, this x is local to its respective function. The assignments within fun1 and fun2 do not affect the variable involved in printing statements 1, 2, 5, or 6. Note that the printing statements within fun1 and fun2 do not execute until the program actually calls the functions. That is why printing statements 2 and 4 appear out of numerical order in the program’s execution. In the end, the last printing statement, number 6, prints the value of the original x variable that the program assigned in its first line. The code within fun1 and fun2, as they currently are written, cannot disturb the value of this external variable. (In Section 8.1 we shall see how a function can gain access to a variable defined outside the function’s definition.) In the code we have considered in earlier chapters, the name of a variable uniquely identified it and distinguished that variable from another variable. It may seem strange that now we can use the same name in two different functions within the same program to refer to two distinct variables. The block of statements that makes up a function definition constitutes a context for local variables. A simple analogy may help. In the United States, many cities have a street named Main Street; for example, there is a thoroughfare named Main Street in San Francisco, California. Dallas, Texas also has a street named Main Street. Each city and town provides its own context for the use of the term Main Street. A person in San Francisco asking “How do I get to Main Street?” will receive the directions to San Francisco’s Main Street, while someone in Dallas asking the same question will receive Dallas-specific instructions. In a similar manner, assigning a variable within a function block localizes its identity to that function. We can think of a program’s execution as a person traveling around the U.S. When in San Francisco, all references to Main Street mean San Francisco’s Main Street, but when the traveler arrives in Dallas, the term Main Street means Dallas’ Main Street. A program’s thread of execution cannot execute more than one statement at a time, which means it uses its current context to interpret any names it encounters within a statement. Similarly, at the risk of overextending the analogy, a person cannot be physically located in more than one city at a time. Furthermore, Main Street may be a bustling, multi-lane boulevard in one large city, but a street by the same name in a remote, rural township may be a narrow dirt road! Similarly, two like-named variables may mean two completely different things. A variable named x is one function may represent an integer, while a different function may use a string variable named x. Another advantage of local variables is that they occupy space in the computer’s memory only when the function is executing. The run-time environment allocates space in the computer’s memory for local ©2017 Richard L. Halterman Draft date: January 18, 2018 7.1. FUNCTION BASICS 206 variables and parameters when the function begins executing. When a function invocation is complete and control returns to the caller, the function’s variables and parameters go out of scope, and the run-time environment ensures that the memory used by the local variables is freed up for other purposes within the running program. This process of local variable allocation and deallocation happens each time a caller invokes the function. Once we have written a complete function definition we can use the function within our program. We invoke a programmer-defined function in exactly the same way as a standard library function like sqrt (6.4) or randrange (6.6). If the function returns a value, then its invocation can be used anywhere an expression of that type can be used. The function gcd can be called as part of an assignment statement: factor = gcd(val, 24) This call uses the variable val as its first actual parameter and the literal value 24 as its second actual parameter. As with the standard Python functions, we can pass variables, expressions, and literals as actual parameters. The function then computes and returns its result. Here, this result is assigned to the variable factor. How does the function call and parameter mechanism work? It’s actually quite simple. The executing program binds the actual parameters, in order, to each of the formal parameters in the function definition and then passes control to the body of the function. When the function’s body is finished executing, control passes back to the point in the program where the function was called. The value returned by the function, if any, replaces the function call expression. The statement factor = gcd(val, 24) assigns an integer value to factor. The expression on the right is a function call, so the executing program invokes the function to determine what to assign. The value of the variable val is assigned to the formal parameter num1, and the literal value 24 is assigned to the formal parameter num2. The body of the gcd function then executes. When the return statement in the body of gcd executes, program control returns back to where the function was called. The argument of the return statement becomes the value assigned to factor. Note that we can call gcd from many different places within the same program, and, since we can pass different parameter values at each of these different invocations, gcd could compute a different result at each invocation. Other invocation examples include: • print(gcd(36, 24)) This example simply prints the result of the invocation. The value 36 is bound to num1 and 24 is bound to num2 for the purpose of the function call. The statement prints 12, since 12 is the greatest common divisor of 36 and 24. • x = gcd(x - 2, 24) The execution of this statement would evaluate x - 2 and bind its value to num1. num2 would be assigned 24. The result of the call is then assigned to x. Since the right side of the assignment statement is evaluated before being assigned to the left side, the original value of x is used when calculating x - 2, and the function return value then updates x. ©2017 Richard L. Halterman Draft date: January 18, 2018 7.1. FUNCTION BASICS 207 • x = gcd(x - 2, gcd(10, 8)) This example shows two invocations in one statement. Since the function returns an inte- ger value, its result can itself be used as an actual parameter in a function call. Passing the result of one function call as an actual parameter to another function call is called function composition. Function composition is nothing new to us, consider the following statement which prints the square root of 16: print(sqrt(16)) The actual parameter passed to the print function is the result of the sqrt function call. Listing 7.10 (gcdfunc.py) is a complete Python program that uses the gcd function. Listing 7.10: gcdfunc.py # Compute the greatest common factor of two integers # provided by the user def gcd(n1, n2): # Determine the smaller of n1 and n2 min = n1 if n1 < n2 else n2 # 1 definitely is a common factor to all ints largest_factor = 1 for i in range(1, min + 1): if n1 % i == 0 and n2 % i == 0: largest_factor = i # Found larger factor return largest_factor # Exercise the gcd function # Prompt user for input num1 = int(input('Please enter an integer: ')) num2 = int(input('Please enter another integer: ')) # Determine the smaller of num1 and num2 min = num1 if num1 < num2 else num2 # Print the GCD print(gcd(num1, num2)) The following shows a sample run of Listing 7.10 (gcdfunc.py): Please enter an integer: 24 Please enter another integer: 18 6 Note that the program first defines the gcd function and then uses (calls) it in the program’s last line. As usual, we can tell where the function definition ends and the rest of the program begins since the function’s block of statements is indented relative to the rest of the program. ©2017 Richard L. Halterman Draft date: January 18, 2018 7.1. FUNCTION BASICS 208 Within a program, a function’s definition must appear before its use. Consider Listing 7.11 (gcdfuncbad.py), which moves the gcd’s definition to the end of the source code. Listing 7.11: gcdfuncbad.py # NOTE: This program will not run to completion because it # calls the gcd function before defining it! # [Attempt to] Compute the greatest common factor of two integers # provided by the user # Exercise the gcd function # Prompt user for input num1 = int(input('Please enter an integer: ')) num2 = int(input('Please enter another integer: ')) # Print the GCD print(gcd(num1, num2)) def gcd(n1, n2): # Determine the smaller of n1 and n2 min = n1 if n1 < n2 else n2 # 1 definitely is a common factor to all ints largest_factor = 1 for i in range(1, min + 1): if n1 % i == 0 and n2 % i == 0: largest_factor = i # Found larger factor return largest_factor The execution of Listing 7.11 (gcdfuncbad.py) produces an error: Please enter an integer: 2 Please enter another integer: 3 Traceback (most recent call last): File "gcdfuncbad.py", line 14, in
print(gcd(num1, num2))

NameError: name ‘gcd’ is not defined

The Python interpreter executes the code, line by line, until it encounters the call to gcd. If it has not yet
seen gcd’s definition, it will terminate the program with an error

Functions help us organize our code. It is not uncommon for programmers to write a main controlling
function that calls other functions to accomplish the work of the application. Listing 7.12 (gcdwithmain.py)
illustrates this organization.

Listing 7.12: gcdwithmain.py

# Computes the greatest common divisor of m and n
def gcd(m, n):

# Determine the smaller of m and n
min = m if m < n else n # 1 is definitely a common factor to all ints largest_factor = 1 ©2017 Richard L. Halterman Draft date: January 18, 2018 7.2. PARAMETER PASSING 209 for i in range(1, min + 1): if m % i == 0 and n % i == 0: largest_factor = i # Found larger factor return largest_factor # Get an integer from the user def get_int(): return int(input("Please enter an integer: ")) # Main code to execute def main(): n1 = get_int() n2 = get_int() print("gcd(", n1, ",", n2, ") = ", gcd(n1, n2), sep="") # Run the program main() The single free statement at the end: main() calls the main function which in turn directly calls several other functions (get_int, print, and gcd). The get_int function itself directly calls int and input. In the course of its execution the gcd function calls range. Figure 7.7 contains a diagram that shows the calling relationships among the function executions during a run of Listing 7.12 (gcdwithmain.py). The name main for the controlling function is arbitrary but traditional; several other popular program- ming languages (C, C++, Java, C#, Objective-C) require such a function and require it to be named main. 7.2 Parameter Passing When a caller invokes a function that expects a parameter, the caller must pass a parameter to the function. The process behind parameter passing in Python is simple: the function call binds to the formal parameter the object referenced by the actual parameter. The kinds of objects we have considered so far—integers, floating-point numbers, and strings—are classified as immutable objects. This means a programmer cannot change the value of the object. For example, the assignment x = 4 binds the variable named x to the integer 4. We may change x by reassigning it, but we cannot change the integer 4. Four is always four. Similarly, we may assign a string literal to a variable, as in word = 'great' but we cannot change the string object to which word refers. If the caller’s actual parameter references an immutable object, the function’s activity cannot affect the value of the actual parameter. Listing 7.13 (parampassing.py) illustrates the consequences of passing an immutable type to an function. ©2017 Richard L. Halterman Draft date: January 18, 2018 7.2. PARAMETER PASSING 210 Figure 7.7 Calling relationships among functions during the execution of Listing 7.12 (gcdwithmain.py) main get_int input int gcd range print P ro g ra m E xe cu ti o n (T im e ) "36" "36" "24" "24" 24 24 36 36 36, 24 12 "GCD(36, 24) = 12" "Please enter..." "Please enter..." 1, min-1 1,2,3,... ©2017 Richard L. Halterman Draft date: January 18, 2018 7.3. DOCUMENTING FUNCTIONS 211 Listing 7.13: parampassing.py def increment(x): print("Beginning execution of increment, x =", x) x += 1 # Increment x print("Ending execution of increment, x =", x) def main(): x = 5 print("Before increment, x =", x) increment(x) print("After increment, x =", x) main() For additional drama we chose to name the actual parameter the same as the formal parameter, but, of course, the names do not matter; the variables live in two completely different contexts. Listing 7.13 (parampassing.py) produces Before increment, x = 5 Beginning execution of increment, x = 5 Ending execution of increment, x = 6 After increment, x = 5 The variable x in main is unaffected by increment because x references an integer, and all integers are immutable. Inside the increment function the statement x += 1 is short for x = x + 1 The expression x + 1 refers to 5 + 1 = 6, a different object from 5. The assignment statement re-binds increment’s x variable to 6. At this point increment’s x variable and main’s x variable refer to two different integer objects. 7.3 Documenting Functions It is good practice to document a function’s definition with information that aids programmers who may need to use or extend the function. The essential information includes: • The purpose of the function. The function’s purpose is not always evident merely from its name. This is especially true for functions that perform complex tasks. A few sentences explaining what the function does can be helpful. • The role of each parameter. A parameter’s name is obvious in the definition, but the expected type and the purpose of a parameter may not be apparent merely from its name. ©2017 Richard L. Halterman Draft date: January 18, 2018 7.3. DOCUMENTING FUNCTIONS 212 • The nature of the return value. While the function may do a number of interesting things as indicated in the function’s purpose, what exactly does it return to the caller? It is helpful to clarify exactly what value the function produces, if any. We can use comments to document our functions, but Python provides a way that allows developers and tools to extract more easily the needed information. Recall Python’s multi-line strings, introduced in Section 2.9. When such a string appears as the first line in the block of a function definition, the string is known as a documentation string, or docstring for short. We can document our gcd function as shown in Listing 7.14 (docgcd.py). Listing 7.14: docgcd.py def gcd(n1, n2): """ Computes the greatest common divisor of integers n1 and n2. """ # Determine the smaller of n1 and n2 min = n1 if n1 < n2 else n2 # 1 definitely is a common factor to all ints largest_factor = 1 for i in range(1, min + 1): if n1 % i == 0 and n2 % i == 0: largest_factor = i # Found larger factor return largest_factor Note that Listing 7.14 (docgcd.py) is not executable Python program; it provides only the definition of the gcd function. We can start a Python interactive shell and import the gcd code: Python 3.4.3 (v3.4.3:9b73f1c3e601, Feb 24 2015, 22:44:40) [MSC v.1600 64 bit (AMD64)] on win32 Type "help", "copyright", "credits" or "license" for more information. >>> from docgcd import gcd
>>> gcd(18, 24)
6
>>>

With the docgcd code loaded into the interactive shell as so, we can type:

>>> help(gcd)
Help on function gcd in module docgcd:

gcd(n1, n2)
Computes the greatest common divisor of integers n1 and n2.

>>>

The normal # comments serve as internal documentation for developers of the gcd function, while the
function’s docstring serves as external documentation for callers of the function.

Other information often is required in a commercial environment:

• Author of the function. Specify exactly who wrote the function. An email address can be included.
If questions about the function arise, this contact information can be invaluable.

• Date that the function’s implementation was last modified. An additional comment can be added
each time the function is updated. Each update should specify the exact changes that were made and
the person responsible for the update.

7.4. FUNCTION EXAMPLES 213

• References. If the code was adapted from another source, list the source. The reference may consist
of a Web URL.

Some or all of this additional information may appear as internal documentation rather than appear in a
docstring.

The official Python style guide recommends using “”” for docstrings rather than ”’—see https:
//www.python.org/dev/peps/pep-0008/. In fact, since the docstring for our gcd function above is only
one line of text, the normal ‘ and ” quotation marks are adequate to specify its docstring. We will follow
the convention of using “”” to delimit our docstrings, even when expressing a single-line documentation.

The following fragment shows the beginning of a well-commented function definition:

# Author: Joe Algori (joe@eng-sys.net)
# Last modified: 2010-01-06
# Adapted from a formula published at
# http://en.wikipedia.org/wiki/Distance
def distance(x1, y1, x2, y2):

“””
Computes the distance between two geometric points
x1 is the x coordinate of the first point
y1 is the y coordinate of the first point
x2 is the x coordinate of the second point
y2 is the y coordinate of the second point

Returns the distance between (x1,y1) and (x2,y2)
“””
…

From the information provided

• callers know what the function can do for them (via the docstring),

• callers know how to use the function (via the docstring),

• subsequent programmers that must maintain the function can contact the original author (via the
comment) if questions arise about its use or implementation,

• subsequent programmers that must maintain the function can check the Wikipedia reference (via the
comment) if questions arise about its implementation, and

• subsequent programmers can evaluate the quality of the algorithm based upon the quality of its source
of inspiration (Wikipedia, via the comment).

7.4 Function Examples

This section contains a number of examples of code organization with functions.

7.4.1 Better Organized Prime Generator

Listing 7.15 (primefunc.py) is a simple enhancement of Listing 6.4 (moreefficientprimes.py). It uses the
square root optimization and adds a separate is_prime function.

https://www.python.org/dev/peps/pep-0008/
https://www.python.org/dev/peps/pep-0008/

7.4. FUNCTION EXAMPLES 214

Listing 7.15: primefunc.py

from math import sqrt

def is_prime(n):
“””
Determines the primality of a given value.
n an integer to test for primality.
Returns true if n is prime; otherwise, returns false.
“””
root = round(sqrt(n)) + 1
# Try all potential factors from 2 to the square root of n
for trial_factor in range(2, root):

if n % trial_factor == 0: # Is it a factor?
return False # Found a factor

return True # No factors found

def main():
“””
Tests for primality each integer from 2 up to a value provided by the user.
If an integer is prime, it prints it; otherwise, the number is not printed.
“””
max_value = int(input(“Display primes up to what value? “))
for value in range(2, max_value + 1):

if is_prime(value): # See if value is prime
print(value, end=” “) # Display the prime number

print() # Move cursor down to next line

main() # Run the program

Listing 7.15 (primefunc.py) illustrates several important points about well-organized programs:

• The complete work of the program is no longer limited to one block of code. The main function is
responsible for generating prime candidates and printing the numbers that are prime. main delegates
the task of testing for primality to the is_prime function. Both main and is_prime individually are
simpler than the original monolithic code. Also, each function is more logically coherent. A function
is coherent when it is focused on a single task. Coherence is a desirable property of functions. If a
function becomes too complex by trying to do too many different things, it can be more difficult to
write correctly and debug when problems are detected. A complex function usually can be decom-
posed into several, smaller, more coherent functions. The original function would then call these new
simpler functions to accomplish its task. Here, main is not concerned about how to determine if a
given number is prime; main simply delegates the work to is_prime and makes use of the is_prime
function’s findings. For is_prime to do its job it does not need to know anything about the history
of the number passed to it, nor does it need to know the caller’s intentions with the result it returns.

• A thorough comment describing the nature of the function precedes each function. The comment
explains the meaning of each parameter, and it indicates what the function should return.

• While the exterior comment indicates what the function is to do, comments within each function
explain in more detail how the function accomplishes its task.

7.4. FUNCTION EXAMPLES 215

A call to is_prime returns True or False depending on the value passed to it. The means a condition
like

if is_prime(value) == True:

can be expressed more compactly as

if is_prime(value):

because if is_prime(value) is True, True == True is True, and if is_prime(value) is False, False == True
is False. The expression is_prime(value) all by itself suffices.

Observe that the return statement in the is_prime function immediately exits the function. In the for
loop the return statement acts like a break statement because it immediately exits the loop on the way to
immediately exiting the function.

Some purists contend that just as it is better for a loop to have exactly one exit point, it is better for a
function to have a single return statement. The following code rewrites the is_prime function so that uses
only one return statement:

def is_prime(n):
result = True # Provisionally, n is prime
root = round(sqrt(n)) + 1
# Try all potential factors from 2 to the square root of n
trial_factor = 2
while result and trial_factor <= root: result = (n % trial_factor != 0 ) # Is it a factor? trial_factor += 1 # Try next candidate return result This version adds a local variable (result) and complicates the logic a little, so we can make a strong case for the original, two-return version. The two return statements in the original is_prime function are close enough textually in the code that the logic is easy to follow. 7.4.2 Command Interpreter Some functions are useful even if they accept no information from the caller and return no result. List- ing 7.16 (calculator.py) uses such a function. Listing 7.16: calculator.py def help_screen(): """ Displays information about how the program works. Accepts no parameters. Returns nothing. """ print("Add: Adds two numbers") print("Subtract: Subtracts two numbers") print("Print: Displays the result of the latest operation") print("Help: Displays this help screen") print("Quit: Exits the program") ©2017 Richard L. Halterman Draft date: January 18, 2018 7.4. FUNCTION EXAMPLES 216 def menu(): """ Displays a menu Accepts no parameters Returns the string entered by the user. """ return input("=== A)dd S)ubtract P)rint H)elp Q)uit ===") def main(): """ Runs a command loop that allows users to perform simple arithmetic. """ result = 0.0 done = False # Initially not done while not done: choice = menu() # Get user's choice if choice == "A" or choice == "a": # Addition arg1 = float(input("Enter arg 1: ")) arg2 = float(input("Enter arg 2: ")) result = arg1 + arg2 print(result) elif choice == "S" or choice == "s": # Subtraction arg1 = float(input("Enter arg 1: ")) arg2 = float(input("Enter arg 2: ")) result = arg1 - arg2 print(result) elif choice == "P" or choice == "p": # Print print(result) elif choice == "H" or choice == "h": # Help help_screen() elif choice == "Q" or choice == "q": # Quit done = True main() The help_screen function needs no information from main, nor does it return a result. It behaves exactly the same way each time it is called. 7.4.3 Restricted Input Listing 5.39 (betterinputonly.py) forces the user to enter a value within a specified range. We now can easily adapt that concept to a function. Listing 7.17 (betterinputfunc.py) uses a function named get_int_in_range that does not return until the user supplies a proper value. Listing 7.17: betterinputfunc.py def get_int_in_range(first, last): """ Forces the user to enter an integer within a specified range. first is either a minimum or maximum acceptable value. last is the corresponding other end of the range, either a maximum or minimum value. Returns an acceptable value from the user. ©2017 Richard L. Halterman Draft date: January 18, 2018 7.4. FUNCTION EXAMPLES 217 """ # If the larger number is provided first, # switch the parameters if first > last:

first, last = last, first
# Insist on values in the range first…last
in_value = int(input(“Please enter values in the range ” \

+ str(first) + “…” + str(last) + “: “))
while in_value < first or in_value > last:

print(in_value, “is not in the range”, first, “…”, last)
in_value = int(input(“Please try again: “))

# in_value at this point is guaranteed to be within range
return in_value

def main():
“”” Tests the get_int_in_range function “””
print(get_int_in_range(10, 20))
print(get_int_in_range(20, 10))
print(get_int_in_range(5, 5))
print(get_int_in_range(-100, 100))

main() # Run the program

Listing 7.17 (betterinputfunc.py) forces the user to enter a value within a specified range, as shown in this
sample run:

Please enter values in the range 10…20: 4
4 is not in the range 10 … 20
Please try again: 21
21 is not in the range 10 … 20
Please try again: 16
16
Please enter values in the range 10…20: 10
10
Please enter values in the range 5…5: 4
4 is not in the range 5 … 5
Please try again: 6
6 is not in the range 5 … 5
Please try again: 5
5
Please enter values in the range -100…100: -101
-101 is not in the range -100 … 100
Please try again: 101
101 is not in the range -100 … 100
Please try again: 0
0

This functionality could be useful in many programs. In Listing 7.17 (betterinputfunc.py)

• Parameters delimit the high and low values. This makes the function more flexible since it could be
used elsewhere in the program with a completely different range specified and still work correctly.

• The function is supposed to be called with the lower number passed as the first parameter and the

7.4. FUNCTION EXAMPLES 218

higher number passed as the second parameter. The function also will accept the parameters out of
order and automatically swap them to work as expected; thus,

num = get_int_in_range(20, 50)

will work exactly like

num = get_int_in_range(50, 20)

7.4.4 Better Die Rolling Simulator

Listing 7.18 (betterdie.py) reorganizes Listing 6.11 (die.py) into functions.

Listing 7.18: betterdie.py

from random import randrange

def show_die(spots):
“””
Draws a picture of a die with number of spots indicated.
spots is the number of spots on the top face.
“””
print(“+——-+”)
if spots == 1:

elif spots == 2:
print(“| * |”)
print(“| |”)
print(“| * |”)

elif spots == 3:
print(“| * |”)
print(“| * |”)
print(“| * |”)

elif spots == 4:
print(“| * * |”)
print(“| |”)
print(“| * * |”)

elif spots == 5:
print(“| * * |”)
print(“| * |”)
print(“| * * |”)

elif spots == 6:
print(“| * * * |”)
print(“| |”)
print(“| * * * |”)

else:
print(” *** Error: illegal die value ***”)

print(“+——-+”)

def roll():
“”” Returns a pseudorandom number in the range 1…6, inclusive “””

7.4. FUNCTION EXAMPLES 219

return randrange(1, 7)

def main():
“”” Simulates the roll of a die three times “””
# Roll the die three times
for i in range(0, 3):

show_die(roll())

main() # Run the program

In Listing 7.18 (betterdie.py), the main function is oblivious to the details of pseudorandom number
generation. Also, main is not responsible for drawing the die. These important components of the program
are now in functions, so their details can be perfected independently from main.

Note how the result of the call to roll is passed directly as an argument to show_die:

show_die(roll())

This is another example of function composition function composition. Function composition is not new to
us; we have been using with the standard functions input and int in statements like: statements like

x = int(input())

7.4.5 Tree Drawing Function

Listing 7.19 (treefunc.py) reorganizes Listing 5.34 (startree.py) into functions.

Listing 7.19: treefunc.py

def tree(height):
“””
Draws a tree of a given height.
“””
row = 0 # First row, from the top, to draw
while row < height: # Draw one row for every unit of height # Print leading spaces count = 0 while count < height - row: print(end=" ") count += 1 # Print out stars, twice the current row plus one: # 1. number of stars on left side of tree # = current row value # 2. exactly one star in the center of tree # 3. number of stars on right side of tree # = current row value count = 0 while count < 2*row + 1: print(end="*") count += 1 # Move cursor down to next line print() ©2017 Richard L. Halterman Draft date: January 18, 2018 7.4. FUNCTION EXAMPLES 220 # Change to the next row row += 1 def main(): """ Allows users to draw trees of various heights """ height = int(input("Enter height of tree: ")) tree(height) main() Observe that the name height is being used as a local variable in main and as a formal parameter name in tree. There is no conflict here, and the two height variables represent two distinct quantities. Furthermore, the fact that the statement tree(height) uses main’s height as an actual parameter and height happens to be the name as the formal parameter is simply a coincidence. The function call binds the value of main’s height variable to the formal parameter in tree also named height. The interpreter can keep track of which height is which based on the function in which it is being used. 7.4.6 Floating-point Equality Recall from Listing 3.2 (imprecise.py) that floating-point numbers are not mathematical real numbers; a floating-point number is finite, and is represented internally as a quantity with a binary mantissa and expo- nent. Just as we cannot represent 1/3 as a finite decimal in the base-10 number system, we cannot represent 1/10 exactly in the binary (base 2) number system with a fixed number of digits. Often, no problems arise from this imprecision, and in fact many software applications have been written using floating-point numbers that must perform precise calculations, such as directing a spacecraft to a distant planet. In such cases even small errors can result in complete failures. Floating-point numbers can and are used safely and effectively, but not without appropriate care. To build our confidence with floating-point numbers, consider Listing 7.20 (simplefloataddition.py), which adds two double-precision floating-point numbers and checks for a given value. Listing 7.20: simplefloataddition.py def main(): x = 0.9 x += 0.1 if x == 1.0: print("OK") else: print("NOT OK") main() Listing 7.20 (simplefloataddition.py) reports OK ©2017 Richard L. Halterman Draft date: January 18, 2018 7.4. FUNCTION EXAMPLES 221 All seems well judging from the behavior of Listing 7.20 (simplefloataddition.py). Next, consider List- ing 7.21 (badfloatcheck.py) which attempts to control a loop with a double-precision floating-point number. Listing 7.21: badfloatcheck.py def main(): # Count to ten by tenths i = 0.0 while i != 1.0: print("i =", i) i += 0.1 main() When executed, Listing 7.21 (badfloatcheck.py) begins as expected, but it does not end as expected: i = 0.0 i = 0.1 i = 0.2 i = 0.30000000000000004 i = 0.4 i = 0.5 i = 0.6 i = 0.7 i = 0.7999999999999999 i = 0.8999999999999999 i = 0.9999999999999999 i = 1.0999999999999999 i = 1.2 i = 1.3 i = 1.4000000000000001 i = 1.5000000000000002 i = 1.6000000000000003 i = 1.7000000000000004 i = 1.8000000000000005 i = 1.9000000000000006 i = 2.0000000000000004 We expect it stop when the loop variable i equals 1, but the program continues executing until the user types Ctrl C or otherwise interrupts the program’s execution. We are adding 0.1, just as in Listing 7.20 (simplefloataddition.py), but now there is a problem. Since 0.1 has no exact representation within the con- straints of the binary double-precision floating-point number systems, the repeated addition of 0.1 leads to round off errors that accumulate over time. Whereas 0.1 + 0.9 rounded off may equal 1, we see that 0.1 added to itself 10 times yields 0.9999999999999999 which is not exactly 1. Listing 7.21 (badfloatcheck.py) demonstrates that the == and != operators are of questionable worth when comparing floating-point values. The better approach is to check to see if two floating-point values are close enough, which means they differ by only a very small amount. When comparing two floating- point numbers x and y, we essentially must determine if the absolute value of their difference is small; for example, |x− y| < 0.00001. We can construct an equals function and incorporate the fabs function introduced in 6.4. Listing 7.22 (floatequalsfunction.py) provides such an equals function. Listing 7.22: floatequalsfunction.py ©2017 Richard L. Halterman Draft date: January 18, 2018 7.5. REFACTORING TO ELIMINATE CODE DUPLICATION 222 from math import fabs def equals(a, b, tolerance): """ Returns true if a = b or |a - b| < tolerance. If a and b differ by only a small amount (specified by tolerance), a and b are considered "equal." Useful to account for floating-point round-off error. The == operator is checked first since some special floating-point values such as floating-point infinity require an exact equality check. """ return a == b or fabs(a - b) < tolerance def main(): """ Try out the equals function """ i = 0.0 while not equals(i, 1.0, 0.0001): print("i =", i) i += 0.1 main() The third parameter, named tolerance, specifies how close the first two parameters must be in order to be considered equal. The == operator must be used for some special floating-point values such as the floating-point representation for infinity, so the function checks for == equality as well. Since Python uses short-circuit evaluation for Boolean expressions involving logical OR (see 4.2), if the == operator indicates equality, the more elaborate check is not performed. The output of Listing 4.7 (floatequals.py) is i = 0.0 i = 0.1 i = 0.2 i = 0.30000000000000004 i = 0.4 i = 0.5 i = 0.6 i = 0.7 i = 0.7999999999999999 i = 0.8999999999999999 You should use a function like equals when comparing two floating-point values for equality. 7.5 Refactoring to Eliminate Code Duplication Recall Listing 6.21 (noanimation.py) that uses Turtle graphics to draw a collection of lines of various colors. Consider the following code fragment, snipped from Listing 6.21 (noanimation.py): turtle.color("blue") for x in range(10): turtle.penup() ©2017 Richard L. Halterman Draft date: January 18, 2018 7.5. REFACTORING TO ELIMINATE CODE DUPLICATION 223 turtle.setposition(-200, y) turtle.pendown() turtle.forward(400) y += 10 turtle.color("green") for x in range(10): turtle.penup() turtle.setposition(-200, y) turtle.pendown() turtle.forward(400) y += 10 What is interesting to note about this code snippet is the similarities between the two sections. These two sections of code are performing exactly the same work, except for the variation of color. Listing 6.21 (noanimation.py) contains two additional sections not shown here that that exhibit the same similarities. This code represents duplication of coding effort, and this is known as code duplication. Code duplication is undesirable for several reasons: • The extra code to write requires more work on the part of the programmer. Copying and pasting with a good editor can save typing, but the code fragments are not identical in all ways, so a programmer must be sure to make all of the little changes required to produce the desired variance in behavior. • Code duplication results in code that is more difficult to maintain. Most commercial software is not static; developers constantly work on newer versions. Newer versions typically provide bug fixes and add features. Upon repairing a logic error or enhancing a section of duplicated code, a programmer must track down all the other code sections within the system that duplicate the modified section. Failure to do so can introduce inconsistency into the program’s behavior. Functions are ideal for consolidating duplicate code. Through a process known as code refactoring, a programmer can place the common code within a function definition and tune the minor variance in behavior of the duplicated code via parameters. Listing 7.23 (noduplication.py) refactors the duplicated code in Listing 6.21 (noanimation.py) into one function that accepts a color and y value as a parameter. Listing 7.23: noduplication.py import turtle def draw_lines(color, y): """ Draws 10 horizontal lines of a given color stacked on top of each other with the lowest line appearing at position y on the y axis. """ turtle.color(color) for x in range(10): turtle.penup() turtle.setposition(-200, y) turtle.pendown() turtle.forward(400) y += 10 ©2017 Richard L. Halterman Draft date: January 18, 2018 7.6. CUSTOM FUNCTIONS VS. STANDARD FUNCTIONS 224 # Turn off animation turtle.tracer(0) draw_lines("red", -200) draw_lines("blue", -100) draw_lines("green",0) draw_lines("black", 100) turtle.update() # Ensure all of image is drawn turtle.done() Now that the originally duplicated code appears in only one place in Listing 7.23 (noduplication.py), any correction or enhancement made to the code within the function automatically will be available to all the callers of that code. This removes the possibility of introducing an inconsistency into the application. 7.6 Custom Functions vs. Standard Functions Recall the custom square root code we saw in Listing 5.33 (computesquareroot.py). We can package this code in a function. Just like the standard math.sqrt function, our custom square root function will accept a single numeric value and return a numeric result. Listing 7.24 (customsquareroot.py) contains the definition of our custom square_root function. Listing 7.24: customsquareroot.py # File customsquareroot.py def square_root(val): """ Compute an approximation of the square root of x """ # Compute a provisional square root root = 1.0 # How far off is our provisional root? diff = root*root - val # Loop until the provisional root # is close enough to the actual root while diff > 0.00000001 or diff < -0.00000001: root = (root + val/root) / 2 # Compute new provisional root # How bad is our current approximation? diff = root*root - val return root # Use the standard square root function to compare with our custom function from math import sqrt d = 1.0 while d <= 10.0: print('{0:6.1f}: {1:16.8f} {2:16.8f}' \ .format(d, square_root(d), sqrt(d))) d += 0.5 # Next d ©2017 Richard L. Halterman Draft date: January 18, 2018 7.6. CUSTOM FUNCTIONS VS. STANDARD FUNCTIONS 225 The main function in Listing 7.24 (customsquareroot.py) compares the behavior of our custom square_root function to the sqrt library function. Its output: 1.0: 1.00000000 1.00000000 1.5: 1.22474487 1.22474487 2.0: 1.41421356 1.41421356 2.5: 1.58113883 1.58113883 3.0: 1.73205081 1.73205081 3.5: 1.87082869 1.87082869 4.0: 2.00000000 2.00000000 4.5: 2.12132034 2.12132034 5.0: 2.23606798 2.23606798 5.5: 2.34520788 2.34520788 6.0: 2.44948974 2.44948974 6.5: 2.54950976 2.54950976 7.0: 2.64575131 2.64575131 7.5: 2.73861279 2.73861279 8.0: 2.82842713 2.82842712 8.5: 2.91547595 2.91547595 9.0: 3.00000000 3.00000000 9.5: 3.08220700 3.08220700 10.0: 3.16227766 3.16227766 shows only a slight difference for √ 8. The fact that we found one difference in this small collection of test cases justifies using the standard math.sqrt function instead of our custom function. Generally speaking, if you have the choice of using a standard library function or writing your own custom function that provides the same functionality, choose to use the standard library routine. The advantages of using the standard library routine include: • Your effort to produce the custom code is eliminated entirely; you can devote more effort to other parts of the application’s development. • If you write your own custom code, you must thoroughly test it to ensure its correctness; standard library code, while not immune to bugs, generally has been subjected to a complete test suite. Ad- ditionally, library code is used by many developers, and thus any lurking errors are usually exposed early; your code is exercised only by the programs you write, and errors may not become apparent immediately. If your programs are not used by a wide audience, bugs may lie dormant for a long time. Standard library routines are well known and trusted; custom code, due to its limited exposure, is suspect until it gains wider exposure and adoption. • Standard routines typically are tuned to be very efficient; it takes a great deal of time and effort to make custom code efficient. • Standard routines are well-documented; extra work is required to document custom code, and writing good documentation is hard work. Listing 7.25 (squarerootcomparison.py) tests our custom square root function over a range of 10,000,000 floating point values. Listing 7.25: squarerootcomparison.py from math import fabs, sqrt def equals(a, b, tolerance): ©2017 Richard L. Halterman Draft date: January 18, 2018 7.6. CUSTOM FUNCTIONS VS. STANDARD FUNCTIONS 226 """ Consider two floating-point numbers equal when the difference between them is very small. Returns true if a = b or |a - b| < tolerance. If a and b differ by only a small amount (specified by tolerance), a and b are considered "equal." Useful to account for floating-point round-off error. The == operator is checked first since some special floating-point values such as floating-point infinity require an exact equality check. """ return a == b or fabs(a - b) < tolerance def square_root(val): """ Computes the approximate square root of val. val is a number """ # Compute a provisional square root root = 1.0 # How far off is our provisional root? diff = root*root - val # Loop until the provisional root # is close enough to the actual root while diff > 0.00000001 or diff < -0.00000001: root = (root + val/root) / 2 # Compute new provisional root # How bad is our current approximation? diff = root*root - val return root def main(): d = 0.0 while d < 100000.0: if not equals(square_root(d), sqrt(d), 0.001): print('*** Difference detected for', d) print(' Expected', sqrt(d)) print(' Computed', square_root(d)) d += 0.0001 # Consider next value main() # Run the program Listing 7.25 (squarerootcomparison.py) uses our equals function from Listing 4.7 (floatequals.py). Ob- serve that the tolerance used within the square root computation is smaller than the tolerance main uses to check the result. The main function, therefore, uses a less strict notion of equality. The output of List- ing 7.25 (squarerootcomparison.py) is 0.0 : Expected 0.0 but computed 6.103515625e-05 0.0006000000000000001 : Expected 0.024494897427831782 but computed 0.024495072155655266 shows that our custom square root function produces results outside of main’s acceptable tolerance for two values. Two wrong answers out of ten million tests represents a 0.00002% error rate. While this error rate is very small, it indicates our square_root function is not perfect. One of values that causes the function ©2017 Richard L. Halterman Draft date: January 18, 2018 7.7. EXERCISES 227 to fail may be very important to a particular application, so our function is not trustworthy. 7.7 Exercises 1. Is the following a legal Python program? def proc(x): return x + 2 def proc(n): return 2*n + 1 def main(): x = proc(5) main() 2. Is the following a legal Python program? def proc(x): return x + 2 def main(): x = proc(5) y = proc(4) main() 3. Is the following a legal Python program? def proc(x): print(x + 2) def main(): x = proc(5) main() 4. Is the following a legal Python program? def proc(x, y): return 2*x + y*y ©2017 Richard L. Halterman Draft date: January 18, 2018 7.7. EXERCISES 228 def main(): print(proc(5, 4)) main() 5. Is the following a legal Python program? def proc(x, y): return 2*x + y*y def main(): print(proc(5)) main() 6. Is the following a legal Python program? def proc(x): return 2*x def main(): print(proc(5, 4)) main() 7. Is the following a legal Python program? def proc(x): print(2*x*x) def main(): proc(5) main() 8. The programmer was expecting the following program to print 200. What does it print instead? Why does it print what it does? def proc(x): x = 2*x*x def main(): num = 10 proc(num) ©2017 Richard L. Halterman Draft date: January 18, 2018 7.7. EXERCISES 229 print(num) main() 9. Is the following program legal since the variable x is used in two different places (proc and main)? Why or why not? def proc(x): return 2*x*x def main(): x = 10 print(proc(x)) main() 10. Is the following program legal since the actual parameter has a different name from the formal pa- rameter (y vs. x)? Why or why not? def proc(x): return 2*x*x def main(): y = 10 print(proc(y)) main() 11. Complete the following distance function that computes the distance between two geometric points (x1,y1) and (x2,y2): def distance(x1, y1, x2, y2): ... Test it with several points to convince yourself that is correct. 12. What happens if a caller passes too many parameters to a function? 13. What happens if a caller passes too few parameters to a function? 14. What are the rules for naming a function in Python? 15. Consider the following function definitions: from random import randrange def fun1(n): result = 0 while n: ©2017 Richard L. Halterman Draft date: January 18, 2018 7.7. EXERCISES 230 result += n n -= 1 return result def fun2(stars): for i in range(stars + 1): print(end="*") print() def fun3(x, y): return 2*x*x + 3*y def fun4(n): return 10 <= n <= 20 def fun5(a, b, c): return a <= b if b <= c else false def fun6(): return randrange(0, 2) Examine each of the following statements. If the statement is illegal, explain why it is illegal; other- wise, indicate what the statement will print. (a) print(fun1(5)) (b) print(fun1()) (c) print(fun1(5, 2)) (d) print(fun2(5)) (e) fun2(5) (f) fun2(0) (g) fun2(-2) (h) print(fun3(5, 2)) (i) print(fun3(5.0, 2.0)) (j) print(fun3('A', 'B')) (k) print(fun3(5.0)) (l) print(fun3(5.0, 0.5, 1.2)) (m) print(fun4(15)) (n) print(fun4(5)) (o) print(fun4(5000)) (p) print(fun5(2, 4, 6)) (q) print(fun5(4, 2, 6)) ©2017 Richard L. Halterman Draft date: January 18, 2018 7.7. EXERCISES 231 (r) print(fun5(2, 2, 6)) (s) print(fun5(2, 6)) (t) if fun5(2, 2, 6): print("Yes") else: print("No") (u) print(fun6()) (v) print(fun6(4)) (w) print(fun3(fun1(3), 3)) (x) print(fun3(3, fun1(3))) (y) print(fun1(fun1(fun1(3)))) (z) print(fun6(fun6())) ©2017 Richard L. Halterman Draft date: January 18, 2018 7.7. EXERCISES 232 ©2017 Richard L. Halterman Draft date: January 18, 2018 233 Chapter 8 More on Functions This chapter covers some additional aspects of functions in Python. It introduces recursion, a key concept in computer science. 8.1 Global Variables Variables defined within functions are local variables. Local variables have some very desirable properties: • The memory required to store a local variable is used only when the variable is in scope; that is, the variable exists only during the function’s execution. When the program’s execution leaves the scope of a local variable, the memory for that variable is freed up. This memory then is reused for the local variables of other functions as needed. • The same variable name can be used in different functions without any conflict. The interpreter derives all of its information about a local variable from that variable’s definition within the function. If the interpreter attempts to execute a statement that uses a variable that has not been defined, the interpreter issues a run-time error. When executing code in one function the interpreter will not look for a variable definition in another function. Thus, there is no way a local variable in one function can interfere with a local variable defined in another function. A local variable is transitory, so it disappears in between function invocations. Sometimes it is desirable to have a variable that exists independent of any function executions. In contrast to a local variable, a global variable lives outside of all functions and is not local to any particular function. This means any function is capable of accessing and/or modifying a global variable. A variable is defined when it is assigned to an object. Any variable assigned within a function is local to that function, unless the variable is declared to be a global variable using the global reserved word. Listing 8.1 (globalcalculator.py) is a modification of Listing 7.16 (calculator.py) that uses a global variables named result, arg1, and arg2 that are shared by several functions in the program. Listing 8.1: globalcalculator.py def help_screen(): """ Displays information about how the program works. ©2017 Richard L. Halterman Draft date: January 18, 2018 8.1. GLOBAL VARIABLES 234 Accepts no parameters. Returns nothing. """ print("Add: Adds two numbers") print("Subtract: Subtracts two numbers") print("Print: Displays the result of the latest operation") print("Help: Displays this help screen") print("Quit: Exits the program") def menu(): """ Display a menu. Accepts no parameters. Returns the string entered by the user. """ # Display a menu return input("=== A)dd S)ubtract P)rint H)elp Q)uit ===") # Global variables used by several functions result = 0.0 arg1 = 0.0 arg2 = 0.0 def get_input(): """ Assigns the globals arg1 and arg2 from user keyboard input. """ global arg1, arg2 # arg1 and arg2 are globals arg1 = float(input("Enter argument #1: ")) arg2 = float(input("Enter argument #2: ")) def report(): """ Reports the value of the global result """ # Not assigning to result, global keyword not needed print(result) def add(): """ Assigns the sum of the globals arg1 and arg2 to the global variable result. """ global result # Assigning to result, global keyword needed result = arg1 + arg2 def subtract(): """ Assigns the difference of the globals arg1 and arg2 to the global variable result """ global result # Assigning to result, global keyword needed ©2017 Richard L. Halterman Draft date: January 18, 2018 8.1. GLOBAL VARIABLES 235 result = arg1 - arg2 def main(): """ Runs a command loop that allows users to perform simple arithmetic. """ done = False # Initially not done while not done: choice = menu() # Get user's choice if choice == "A" or choice == "a": # Addition get_input() add() report() elif choice == "S" or choice == "s": # Subtraction get_input() subtract() report() elif choice == "P" or choice == "p": # Print report() elif choice == "H" or choice == "h": # Help help_screen() elif choice == "Q" or choice == "q": # Quit done = True main() Listing 8.1 (globalcalculator.py) uses global variables result, arg1, and arg2. These names no longer appear in the main function. The program accesses and/or modifies these global variables in four different functions: get_input, report, add, and subtract. The global keyword within a function’s block of code identifies the variables which are global variables. Notice that if a function uses a global variable without assigning its value, the global declaration is not necessary. This is because variable assignment is variable definition, and a local variable must be defined within a function. A function may be use a global variable without declaring it with the global keyword if the function does not assign a variable of that name anywhere in its body. A function that assigns a global variable must declare that variable as global with the global keyword. If a function defines a local variable with the same name as a global variable, the global variable become inaccessible to code within the function. We say the local variable hides the like-named global variable from code in the function’s body. When it is acceptable to use global variables, and when is it better to use local variables? In general, local variables are preferable to global variables for several reasons: • When a function uses local variables exclusively and performs no other input operations (like calling the input function), only parameters passed in by the caller can influence the function’s behavior. If ©2017 Richard L. Halterman Draft date: January 18, 2018 8.1. GLOBAL VARIABLES 236 a global variable appears in a function, the function’s behavior potentially is affected by every other function that can modify that global variable. As a simple example, consider the following trivial function that appears in a program: def increment(n): return n + 1 Can you predict what the following statement within that program will print? print(increment(12)) If your guess is 13, you are correct. The increment function simply returns the result of adding one to its argument. The increment function behaves the same way each time it is called with the same argument. Next, consider the following three functions that appear in some program: def process(n): return n + m # m is a global integer variable def assign_m(): global m m = 5 def inc_m(): global m m += 1 Can you predict what the following statement within the program will print? print(process(12)) We cannot predict what this statement in isolation will print. The following scenarios all produce different results: assign_m() print(process(12)) prints 17, m = 10 # m is the global print(process(12)) prints 22, m = 0 # m is the global inc_m() inc_m() print(process(12)) prints 14, and assign_m() inc_m() inc_m() print(process(12)) ©2017 Richard L. Halterman Draft date: January 18, 2018 8.1. GLOBAL VARIABLES 237 prints 19. The identical printing statements print different values depending on the cumulative effects of the program’s execution up to that point. It may be difficult to locate an error if a function that uses a global variable fails because it may be the fault of another function that assigned an incorrect value to the global variable. The situation may be more complicated than the one portrayed in the simple examples above; consider: assign_m() . . # 30 statements in between, some of which may change a, . # b, and m . if a < 2 and b <= 10: m = a + b - 100 . . # 20 statements in between, some of which may change m . print(process(12)) • A nontrivial program that uses global variables will be more difficult for a human reader to understand than one that does not. When examining the contents of a function, a global variable requires the reader to look elsewhere (outside the function) for its meaning: # Linear function def f(x): return m*x + b What are m and b? How, where, and when are they assigned or re-assigned? • A function that uses only local variables can be tested for correctness in isolation from other func- tions, since other functions do not affect the behavior of this function. This function’s behavior is only influenced only by its parameters, if it has any. The exclusion of global variables from a function leads to functional independence. A function that depends on information outside of its scope to correctly perform its task is a dependent function. When a function operates on a global variable it depends on that global variable being in the correct state for the function to complete its task correctly. Nontrivial programs that contain many dependent functions are more difficult debug and extend. A truly independent function that use no global variables and uses no programmer-defined functions to help it out can be tested for correctness in isolation. Additionally, an independent function can be copied from one program, pasted into another program, and work without modification. Functional independence is a desirable quality. The exclusion of global variables from a function’s definition does not guarantee that the function always will produce the same results given the same parameter values; consider def compute(n): favorite = int(input("Please enter your favorite number: ")) return n + favorite The compute function avoids global variables, yet we cannot predict the value of the expression compute(12). Recall the increment function from above: def increment(n): return n + 1 ©2017 Richard L. Halterman Draft date: January 18, 2018 8.2. DEFAULT PARAMETERS 238 Its behavior is totally predictable. Furthermore, increment does not modify any global variables, meaning its code all by itself cannot in any way influence the overall program’s behavior. We say that increment is a pure function. A pure function cannot perform any input or output (for example, use the print or input statements), nor may it use global variables. While increment is pure, the compute function is impure. The following function is impure also, since it performs output: def increment_and_report(n): print("Incrementing", n) return n + 1 A pure function simply computes its return value and has no other observable side effects. A function that calls only other pure functions and otherwise would be considered pure is itself a pure function; for example: def double_increment(n): return increment(n) + 1 double_increment is a pure function since increment is pure; however, double_increment_with_report: def double_increment_with_report(n): return increment_and_report(n) + 1 is not a pure function since it calls increment_and_report which is impure. 8.2 Default Parameters We have seen how callers may invoke some Python functions with differing numbers of parameters. Com- pare a = input() to a = input("Enter your name: ") We can define our own functions that accept a varying number of parameters by using a technique known as default parameters. Consider the following function that counts down: def countdown(n=10): for count in range(n, -1, -1): # Count down from n to zero print(count) The formal parameter expressed as n=10 represents a default parameter or default argument. If the caller does not supply an actual parameter, the formal parameter n is assigned 10. The following call countdown() prints 10 9 8 7 ©2017 Richard L. Halterman Draft date: January 18, 2018 8.2. DEFAULT PARAMETERS 239 6 5 4 3 2 1 0 but the invocation countdown(5) displays 5 4 3 2 1 0 As we can see, when the caller does not supply a parameter specified by a function, and that parameter has a default value, the default value is used during the caller’s call. We may mix non-default and default parameters in the parameter lists of a function declaration, but all default parameters within the parameter list must appear after all the non-default parameters. This means the following definitions are acceptable: def sum_range(n, m=100): # OK, default follows non-default sum = 0 for val in range(n, m + 1): sum += val and def sum_range(n=0, m=100): # OK, both default sum = 0 for val in range(n, m + 1): sum += val but the following definition is illegal, since a default parameter precedes a non-default parameter in the function’s parameter list: def sum_range(n=0, m): # Illegal, non-default follows default sum = 0 for val in range(n, m + 1): sum += val Default arguments allow programmers to provide a highly tunable function that offer a simpler interface for its typical uses. Recall Listing 7.6 (regularpolygon.py) that uses Turtle graphics to draw a regular poly- gon with specified number of sides, of a given size, location, and color. Listing 8.2 (enhancedpolygon.py) enhances Listing 7.6 (regularpolygon.py) by adding the ability to optionally fill the polygon with a color. Since the number of parameters is becoming unwieldy for a caller to manage, the color and fill directives are specified as optional. ©2017 Richard L. Halterman Draft date: January 18, 2018 8.2. DEFAULT PARAMETERS 240 Listing 8.2: enhancedpolygon.py import turtle import random # Draws a regular polygon with the given number of sides. # The length of each side is length. # The pen begins at point(x, y). # The color of the polygon is color (defaults to black). # The polygon is rendered solid if fill is True (defaults to False). def polygon(sides, length, x, y, color="black", fill=False): turtle.penup() turtle.setposition(x, y) turtle.pendown() turtle.color(color) if fill: turtle.begin_fill() for i in range(sides): turtle.forward(length) turtle.left(360//sides) if fill: turtle.end_fill() # Disable rendering to speed up drawing turtle.hideturtle() turtle.tracer(0) # Draw a few polygons polygon(3, 30, 10, 10) # Back triangle outline polygon(4, 30, 50, 50, "blue") # Blue square outline polygon(5, 30, 100, 100, "red", True) # Red solid pentagon turtle.update() # Render image turtle.exitonclick() # Wait for user's mouse click Observe that the caller must pass at least four parameters and optionally can pass one or two more. The idea here is that when drawing a polygon it is important to know how many sides it has, the length of each side, and its location. Such a polygon will consist of a black outline of the shape. Callers can enhance the figure by specifying a color for the outline. Finally, a caller can indicate that the polygon should be filled. The color and fill are optional extras that are required just to draw a basic polygon. Figure 8.1 shows the shapes drawn by Listing 8.2 (enhancedpolygon.py). Note that it is not possible to produce a filled polygon without also providing a color; for example, the call polygon(5, 30, 150, 150, True) # Black solid pentagon? would attempt to assign 5 to the sides formal parameter (which is fine), 30 to length (also fine), 150 to x (so far, so good), 150 to y (again, okay), and True to color (what about this?). Inside the definition of the polygon function, the statement turtle.color(color) ©2017 Richard L. Halterman Draft date: January 18, 2018 8.3. INTRODUCTION TO RECURSION 241 Figure 8.1 The shapes drawn by Listing 8.2 (enhancedpolygon.py) with color bound to True will generate an exception because True is not one of the color strings like "red", "blue", etc. that the turtle.color function expects. The polygon function therefore will fail. Default parameters always substitute for missing parameters from back to front in a function’s parameter list. 8.3 Introduction to Recursion The factorial function is widely used in combinatorial analysis (counting theory in mathematics), probabil- ity theory, and statistics. The factorial of n usually is expressed as n!. Factorial is defined for nonnegative integers as n! = n · (n−1) · (n−2) · (n−3) · · ·3 ·2 ·1 and 0! is defined to be 1. Thus 6! = 6 ·5 ·4 ·3 ·2 ·1 = 720. Mathematicians precisely define factorial in this way: n! =   1, if n = 0 n · (n−1)!, otherwise. This definition is recursive since the ! function is being defined, but ! is used also in the definition. A Python function can be defined recursively as well. Listing 8.3 (factorialtest.py) includes a factorial function that exactly models the mathematical definition. Listing 8.3: factorialtest.py def factorial(n): """ Computes n! Returns the factorial of n. """ if n == 0: return 1 else: return n * factorial(n - 1) ©2017 Richard L. Halterman Draft date: January 18, 2018 8.3. INTRODUCTION TO RECURSION 242 def main(): """ Try out the factorial function """ print(" 0! = ", factorial(0)) print(" 1! = ", factorial(1)) print(" 6! = ", factorial(6)) print("10! = ", factorial(10)) main() Listing 8.3 (factorialtest.py) produces 0! = 1 1! = 1 6! = 720 10! = 3628800 Observe that the factorial function in Listing 8.3 (factorialtest.py) uses no loop to compute its result. The factorial function simply calls itself. The call factorial(6) is computed as follows: factorial(6) = 6 * factorial(5) = 6 * 5 * factorial(4) = 6 * 5 * 4 * factorial(3) = 6 * 5 * 4 * 3 * factorial(2) = 6 * 5 * 4 * 3 * 2 * factorial(1) = 6 * 5 * 4 * 3 * 2 * 1 * factorial(0) = 6 * 5 * 4 * 3 * 2 * 1 * 1 = 6 * 5 * 4 * 3 * 2 * 1 = 6 * 5 * 4 * 3 * 2 = 6 * 5 * 4 * 6 = 6 * 5 * 24 = 6 * 120 = 720 Note that we can optimize the factorial function slightly by changing the if’s condition from n == 0 to n < 2. This change results in a function execution trace that eliminates one function call at the end: factorial(6) = 6 * factorial(5) = 6 * 5 * factorial(4) = 6 * 5 * 4 * factorial(3) = 6 * 5 * 4 * 3 * factorial(2) = 6 * 5 * 4 * 3 * 2 * factorial(1) = 6 * 5 * 4 * 3 * 2 * 1 = 6 * 5 * 4 * 3 * 2 = 6 * 5 * 4 * 6 = 6 * 5 * 24 = 6 * 120 = 720 Figure 8.2 illustrates the chain of recursive factorial invocations when executing the statement print(factorial(6)). A correct simple recursive function definition is based on four key concepts: ©2017 Richard L. Halterman Draft date: January 18, 2018 8.3. INTRODUCTION TO RECURSION 243 Figure 8.2 A graphial representation of the chain of recursive factorial invocations when executing the statement print(factorial(6)), where the factorial function is from Listing 8.3 (factorialtest.py) with the condition optimized to n < 2. The vertical bars represent the time a function invocation is active. The shaded area within each bar represents the time that the function, while still active, is idle, waiting for a function it calls to complete. Note that during the process of recursion all earlier function invocations in the call chain remain active (but idle) until all the functions further down the call chain return. factorial factorial factorial factorial factorial factorial print P ro g ra m E xe cu ti o n (T im e ) 24 5 6 4 3 2 1 1 2 6 120 720 720 ©2017 Richard L. Halterman Draft date: January 18, 2018 8.3. INTRODUCTION TO RECURSION 244 1. The function optionally must call itself within its definition; this is the recursive case. 2. The function optionally must not call itself within its definition; this is the base case. 3. Some sort of conditional execution (such as an if/else statement) selects between the recursive case and the base case based on one or more parameters passed to the function. 4. Each invocation that does correspond to the base case must call itself with parameter(s) that move the execution closer to the base case. The function’s recursive execution must converge to the base case. Each recursive invocation must bring the function’s execution closer to its base case. The factorial function calls itself in the else block of the if/else statement. Its base case is executed if the condition of the if statement is true. Since the factorial is defined only for nonnegative integers, the initial invocation of factorial must be passed a value of zero or greater. A zero parameter (the base case) results in no recursive call. Any other positive parameter results in a recursive call with a parameter that is closer to zero than the one before. The nature of the recursive process progresses towards the base case, upon which the recursion terminates. Recursion is not our only option when computing a factorial. Listing 8.4 (nonrecursfact.py) provides a nonrecursive factorial function. Listing 8.4: nonrecursfact.py def factorial(n): """ Computes n! Returns the factorial of n. """ product = 1 while n: product *= n n -= 1 return product def main(): """ Try out the factorial function """ print(" 0! = ", factorial(0)) print(" 1! = ", factorial(1)) print(" 6! = ", factorial(6)) print("10! = ", factorial(10)) main() Which factorial function is better, the recursive or non-recursive version? Generally, if both the recur- sive and non-recursive functions implement the same basic algorithm, the non-recursive function will be more efficient. A function call is a relatively expensive operation compared to a variable assignment or comparison. The body of the non-recursive factorial function invokes no functions, but the recursive version calls a function—it calls itself—during all but the last recursive invocation. The iterative version of factorial is therefore more efficient than the recursive version. Even though the iterative version of the factorial function is technically more efficient than the recursive version, on most systems you could not tell the difference. The reason is the factorial function “grows” fast, meaning it returns fairly large results for relatively small arguments. ©2017 Richard L. Halterman Draft date: January 18, 2018 8.3. INTRODUCTION TO RECURSION 245 Recall the gcd function from Section 7.4. It computed he greatest common divisor (also known as greatest common factor) of two integer values. It works, but it is not very efficient. Listing 8.5 (gcd.py) uses a better algorithm. It is based on one of the oldest algorithms known, attributed to Euclid around 300 B.C. Listing 8.5: gcd.py def gcd(m, n): """ Uses Euclid's method to compute the greatest common divisor (also called greatest common factor) of m and n. Returns the GCD of m and n. """ if n == 0: return m else: return gcd(n, m % n) def iterative_gcd(num1, num2): """ Uses a naive algorithm to compute the greatest common divisor (also called greatest common factor) of m and n. Returns the GCD of m and n. """ # Determine the smaller of num1 and num2 min = num1 if num1 < num2 else num2 # 1 is definitely a common factor to all integers largest_factor = 1; for i in range(1, min + 1): if num1 % i == 0 and num2 % i == 0: largest_factor = i # Found larger factor return largest_factor def main(): """ Try out the gcd function """ for num1 in range(1, 101): for num2 in range(1, 101): print("gcd of", num1, "and", num2, "is", gcd(num1, num2)) main() Note that this gcd function is recursive. The algorithm it uses is much different from our original iterative version. Because of the difference in the algorithms, this recursive version is actually much more efficient than our original iterative version. A recursive function, therefore, cannot be dismissed as inefficient just because it is recursive. We will revisit recursion in Section 15.5. A recursive function may call itself within its definition multiple times. Consider the following sequence of integer values: 0,1,1,2,3,5,8,13,21,34,55,89,144, . . . This is beginning of the infinite Fibonacci sequence (see https://en.wikipedia.org/wiki/Fibonacci number). It is a sequence of integers beginning with 0 followed by 1. Subsequent elements of the sequence ©2017 Richard L. Halterman Draft date: January 18, 2018 https://en.wikipedia.org/wiki/Fibonacci_number https://en.wikipedia.org/wiki/Fibonacci_number 8.4. MAKING FUNCTIONS REUSABLE 246 are the sum of their two immediately preceding elements; thus, the third number is 0+ 1 = 1, the fourth number is 1+1 = 2, the fifth number is 1+2 = 3, etc. The numbers that comprise the Fibonacci sequence are known as Fibonacci numbers. Note that 3 is a Fibonacci number but 4 is not. The mathematical properties of Fibonacci numbers have bearing in such diverse fields as biology, eco- nomics, and art. A common problem is computing the nth Fibonacci number. Zero is the 0th, 1 is the 1st, 1 is also the 2nd, 2 is the 3rd, 3 is the 4th, 5 is the 5th, etc. A recursive Python function to compute the nth Fibonacci number follows easily from the definition of the Fibonacci sequence: def fibonacci(n): """ Returns the nth Fibonacci number. """ if n <= 0: return 0 elif n == 1: return 1 else: return fibonacci(n - 2) + fibonacci(n - 1) Figure 15.10 illstrates the recursive computation of fibonacci(5) using this fibonacci function. Note that the call fibonacci(5) invokes the fibonacci function a total of 15 times. While this factorial function computes the correct result, this tendency to call itself so many times makes it impractical for larger values. Section 15.9 introduces an algorithm design technique that greatly improves the performance of this recursive function. 8.4 Making Functions Reusable In a function definition we can package functionality that can be used in many different places within a pro- gram. We have yet to see how we can easily reuse our function definitions in other programs. For example, our is_prime function in Listing 7.15 (primefunc.py) works well within Listing 7.15 (primefunc.py), and we could put it to good use in other programs that need to test primality (encryption software, for example, makes heavy use of prime numbers). We could use the copy-and-paste feature of our favorite text editor to copy the is_prime function definition from Listing 7.15 (primefunc.py) into the new encryption program we are developing. It is possible to reuse a function in this way only if the function definition does not use any programmer-defined global variables nor any other programmer-defined functions. If a function does use any of these programmer-defined external entities, we must include these dependencies as well in the new code for the function to viable. Said another way, the code in the function definition ideally will use only local variables and parameters. Such a function truly is independent and easily transportable to other programs. The notion of copying source code from one program to another is not ideal, however. It is too easy for the copy to be incomplete or otherwise incorrect. Furthermore, such code duplication is wasteful. If 100 programs on a particular system all need to use the is_prime function, under this scheme they must all include the is_prime code. This redundancy wastes space. Finally, in perhaps the most compelling demonstration of the weakness of this copy-and-paste approach, what if a bug is discovered in the is_prime function that all 100 programs are built around? When the error is discovered and fixed in one program, the other 99 programs will still contain the bug. Their source code must be updated, and it may be difficult to determine which files need to be fixed. The problem becomes much worse if the code has been released to the general public. It may be impossible to track down and correct all the copies of the faulty function. The ©2017 Richard L. Halterman Draft date: January 18, 2018 8.4. MAKING FUNCTIONS REUSABLE 247 Figure 8.3 The recursive computation of fibonacci(5). Each rectangle represents an invocation of the fibonacci fuunction. The call at the top of the diagram represents the initial call of fibonacci(5). An arrow pointing down indicates the argument being passed into an invocation of fibonacci, and an arrow pointing up represents the value returned by that invocation. An invocation of fibonacci with no arrow pointing down away from the invocation represents a base case; observe that any invocation receiving a 0 or 1 is a base case. We see that the recursive process for fibonacci(5) invokes the function a total of 15 times. Caller 1 1 12 2 1 23 0 0 11 fibonacci(0) fibonacci(2) fibonacci(1) fibonacci(1) fibonacci(3) fibonacci(4) 3 2 34 fibonacci(5) 5 5 0 0 11 fibonacci(0) fibonacci(2) fibonacci(1) 1 1 12 0 0 11 fibonacci(0) fibonacci(2) fibonacci(1) fibonacci(1) fibonacci(3) ©2017 Richard L. Halterman Draft date: January 18, 2018 8.4. MAKING FUNCTIONS REUSABLE 248 situation would be the same if a correct is_prime function were updated to be made more efficient. The problem is this: all the programs using is_prime define their own is_prime function; while the function definitions are meant to be identical, there is no mechanism tying all these common definitions together. We really would like to reuse the function as is without copying it. Fortunately, Python makes is easy for developers to package their functions into modules. Programmers can build modules independently from the programs that use them. Software engineers did exactly that when developing Python’s standard modules. They did so without the foreknowledge of exactly how we would use the functions they provide. A Python source file constitutes a module. Consider the module Listing 8.6 (primecode.py). Listing 8.6: primecode.py """ Contains the definition of the is_prime function """ from math import sqrt def is_prime(n): """ Returns True if nonnegative integer n is prime; otherwise, returns false """ trial_factor = 2 root = sqrt(n) while trial_factor <= root: if n % trial_factor == 0: # Is trial factor a factor? return False # Yes, return right away trial_factor += 1 # Consider next potential factor return True # Tried them all, must be prime Other Python programs can use the code within the Listing 8.6 (primecode.py) file. In the simplest case, this module (file) appears in the same directory (folder) as the calling code file that uses it. Listing 8.7 (usingprimecode.py) contains a sample program that uses our packaged is_prime function. Listing 8.7: usingprimecode.py from primecode import is_prime num = int(input("Enter an integer: ")) if is_prime(num): print(num, "is prime") else: print(num, "is NOT prime") The statement from primecode import is_prime directs the interpreter to import the is_prime function from the file primecode.py, which is the primecode module. A program that imports is_prime this way can use the name without any additional qualification. Listing 8.8 (usingprimecode2.py) illustrates the alternative way of importing code from a module. Listing 8.8: usingprimecode2.py import primecode ©2017 Richard L. Halterman Draft date: January 18, 2018 8.5. FUNCTIONS AS DATA 249 num = int(input("Enter an integer: ")) if primecode.is_prime(num): print(num, "is prime") else: print(num, "is NOT prime") The statement import primecode directs the interpreter to import the entire module. Any access to names defined in the module require the module name prefix. In this example, the call to the is_prime function requires the module qualification: primecode.is_prime. If we want our Listing 8.6 (primecode.py) module to be more widely available, we can place the file in a special Python library folder. This makes it available to all users on the system. Observe the docstring at the top of the Listing 8.6 (primecode.py) module. This provides external documentation that can be used as an overview to the functions the module makes available. As we saw in Section 7.3, we can use the help function to reveal the information developers have provided in their docstrings. The following interactive sequence demonstrates how the help function accesses information in the primecode module’s docstring: >>> import primecode
>>> help(primecode)
Help on module primecode:

NAME
primecode – Contains the definition of the is_prime function

FUNCTIONS
is_prime(n)

Returns True if nonnegative integer n is prime; otherwise, returns false

sqrt(…)
sqrt(x)

Return the square root of x.

FILE
c:\users\rick\documents\books\pythonbook\src\chap8\primecode.py

Notice that our primecode module provides access to the math module’s sqrt function as well as our
is_prime function. This is because the primecode module directly imports math.sqrt.

8.5 Functions as Data

In Python, a function is special kind of object, just as integers, and strings are objects. Consider the
following sequence in the interactive shell:

>>> type(2)

8.5. FUNCTIONS AS DATA 250

>>> type(‘Rick’)

>>> from math import sqrt
>>> type(sqrt)

The sqrt function has the Python type builtin_function_or_method. The word class indicates that
builtin_function_or_method is an object type, just as int and str are object types. As such, we can
treat a function as if it were a data value; for example, we can assign a variable to a function, as shown here:

from math import sqrt

x = sqrt # Assign x to sqrt function object
print(x(16)) # Prints 4.0

We also can pass a function as a parameter to another function. Listing 8.9 (arithmeticeval.py) includes a
function that accepts a function as a parameter.

Listing 8.9: arithmeticeval.py

def add(x, y):
“””
Adds the parameters x and y and returns the result
“””
return x + y

def multiply(x, y):
“””
Multiplies the parameters x and y and returns the result
“””
return x * y

def evaluate(f, x, y):
“””
Calls the function f with parameters x and y:
f(x, y)
“””
return f(x, y)

def main():
“””
Tests the add, multiply, and evaluate functions
“””
print(add(2, 3))
print(multiply(2, 3))
print(evaluate(add, 2, 3))
print(evaluate(multiply, 2, 3))

main() # Call main

8.5. FUNCTIONS AS DATA 251

Listing 8.9 (arithmeticeval.py) prints

5
6
5
6

The first parameter of evaluate, f, is a function. Examining the code in the body of evaluate, we can see
that f must be a function that can be called with two arguments. We also see that evaluate calls f passing
it the second and third parameter it receives from its caller. The expression

evaluate(add, 2, 3)

passes the add function and the literal values 2 and 3 to evaluate. The evaluate function then invokes
the add function with arguments 2 and 3.

A closer examination of the add function reveals that it applies the + operator to its two parameters. If
its parameters are numbers, it computes the sum of its parameters. Notice, however, that the call

print(evaluate(add, ‘2’, ‘3’))

would print

since applying the + operator to strings represents string concatenation instead of arithmetic addition. The
* operator is not so flexible, as the following statement produces an error:

print(evaluate(multiply, ‘2’, ‘3’)) # Produces an exception

The * operator is not defined to operate on two string operands.

The ability to pass a function object to another function is a powerful concept. It provides one mech-
anism that enables programmers to develop code that interoperates with a larger software framework.
Python’s Turtle graphics environment is one such framework. Our Turtle graphics examples to this point
have involved drawing pictures in the graphics window with no provision for user interaction. With our
knowledge of functions as parameters we now have the tools to write graphical programs that respond to
mouse clicks and key presses.

The turtle module contains the function onscreenclick that accepts a function as a parameter. It
expects the function the caller passes to it to accept two numeric parameters. Listing 8.10 (trackmouse.py)
is a very simple program that shows how onscreenclick works.

Listing 8.10: trackmouse.py

import turtle

def report_position(x, y):
“”” Simply prints the values of x and y. “””
print(“x =”, x, ” y =”, y, flush=True)

# Establish a function the framework should call when the user clicks the mouse
turtle.onscreenclick(report_position)

# Start the graphics loop that listens for user input
turtle.mainloop()

8.5. FUNCTIONS AS DATA 252

Run Listing 8.10 (trackmouse.py), move the mouse over various locations within the graphical window, and
press the mouse button at each location. You will see no feedback in the graphical window, but the print
statement should print the mouse’s location within the non-graphical console. The statement

print(“x =”, x, ” y =”, y, flush=True)

uses the flush keyword argument of the print function. When omitted, this keyword argument defaults
to False. The Python print function uses a technique known as buffering, and this optional keyword
argument affects the print function’s buffer.

To understand the concept of buffering, consider the task of building a wall with bricks. Estimates
indicate that the wall will require about 1,350 bricks. Once we are ready to start building the wall we can
drive to the building supply store and purchase a brick. We then can drive to the job site and place the brick
in its appropriate position using mortar as required. Now we are ready to place the next brick, so we must
drive back to the store to get the next brick. We then drive back to the job site and set the brick. We repeat
this process about 1,350 times.

If this seems very inefficient, it is. It would be better to put as many bricks as possible into the vehicle
on the first trip, and then make subsequent trips to the store for more loads of bricks as needed until the wall
is complete.

In this analogy, the transport vehicle is the buffer. The print function uses a special place in memory
called a buffer. Like the vehicle used to transport our bricks, the memory buffer has a fixed capability. The
print statement writes the individual characters to display to the buffer, and when the buffer is full, the
function in one operation sends all the characters in the buffer out to the display screen. As with the bricks,
this is more efficient than sending just one character at a time to the display. This buffering process can
speed up significantly the output of programs that display a lot text.

Ordinarily, at the end of its output the print function flushes the last characters from its buffer, even if
the buffer is not full. The is analogous to the last load of bricks that may not be a full load. In some situations
it is necessary to ensure the buffer is flushed to the screen even before it is full. Some graphical IDEs
such as WingIDE manage their own console windows. The print function executed from an application
launched from the IDE sends its output to the IDE’s console. Under certain circumstances programs such as
Listing 8.10 (trackmouse.py) may not print a full line of text immediately when executed from a graphical
IDE. In the case of Listing 8.10 (trackmouse.py) the full printed output may be a mouse click behind.
The interplay between the graphical IDE and the executing graphical application under development can
interfere with the normal operation of print. If you experience the print function not displaying its full
line of text, adding the flush keyword argument with the value True often can correct print’s behavior.

As a more interesting, yet still relatively simple example, Listing 8.11 (placesquares.py) draws a square
centered at each location the user clicks the mouse.

Listing 8.11: placesquares.py

import turtle

def draw_square(x, y):
“”” Draws a 10 x 10 square centered at the point (x, y). “””
turtle.penup()
turtle.setheading(0) # Ensure the pen is pointed the proper direction
turtle.setposition(x – 5, y – 5) # Center square
turtle.pendown()
for i in range(4):

turtle.forward(10)

8.6. SEPARATING CONCERNS WITH PLUGGABLE MODULES 253

turtle.left(90)
turtle.update()

# Turn off animation
turtle.tracer(0)
turtle.hideturtle()

# Allow user to place 10 x 10 squares using the mouse
turtle.onscreenclick(draw_square)

# Start the graphics loop that listens for user input
turtle.mainloop()

The turtle.onscreenclick function allows a programmer to register a function with the graphical
framework. The registered function (for example, report_position in Listing 8.10 (trackmouse.py) or
draw_square in Listing 8.11 (placesquares.py)) is known as a callback function because the graphical
framework will call back the function when a mouse click event occurs.

It is important to note that no code within Listing 8.10 (trackmouse.py) or Listing 8.11 (placesquares.py)
actually calls the callback function. Neither does the turtle.onscreenclick function call the callback
function; the call to onscreenclick merely registers the callback function with the graphical framework.
It is the responsibility of the graphical framework to call the callback function. The graphical framework
tracks mouse events, and so it is the framework that must call the callback function with the appropriate
(x,y) location.

We will see in Section 15.3 that the ability to pass function objects around enables us to develop flexible
algorithms that we can adapt at run time.

8.6 Separating Concerns with Pluggable Modules

Consider a very simple connect-the-dots game. In such a game two players compete on a two-dimensional
rectangular grid of dots, as shown in Figure 8.4. Typically played with pen and paper, the number of rows
and columns can vary, sometimes limited only by the size of the paper. The rules of the game are simple.
Two players take turns drawing a line between adjacent dots. A player can draw a horizontal or vertical
connecting line; diagonal lines are forbidden. Turns alternate until a player’s line completes a square. At
that point the player that drew the line becomes the square’s owner and marks the square with an initial. As
a bonus for winning the square, the square owner can immediately take another turn. Figure 8.5 shows a
game in progress. The player owning the most squares at the end of the game is the winner.

We will implement a simplified version of the connect-the-dots game so that we can exercise some of
the concepts introduced in this chapter. We will limit our game to a 3×3 grid because we have yet to cover
the concepts required to maintain a large amount of data at one time. (Lists in Chapter 10 provide a way
to build connect-the-dot grids of arbitrary size.) Even in its simplified form, our program will be the most
complex we have considered so far. This is because instead of writing the application in one large source
file, we intentionally will divide our implementation into two parts:

• Game engine. The game engine controls the logic of the game. It enforces the game rules, dictates
whose turn it is, determines who wins a square, and declares a winner or draw when no more moves
are possible.

• Presentation. The presentation communicates the status of the game to the players and allows players

8.6. SEPARATING CONCERNS WITH PLUGGABLE MODULES 254

Figure 8.4 The initial playing field for a connect-the-dots game.

Figure 8.5 A connect-the-dots game in progress.

8.6. SEPARATING CONCERNS WITH PLUGGABLE MODULES 255

to make moves. The presentation could provide a graphical representation and respond to mouse
clicks, or it could print to a text-based console and accept typed information from the keyboard.

This kind of design depends on several important points:

• Developers must precisely specify the interface that connects both parts of the system. The interface
specifies how the two parts communicate with each other. The interface includes function names,
expected function parameters, and purpose of the function.

• Developers working on each part must conscientiously follow the requirements of the interface. Fail-
ure to comply with the agreed upon interface diminishes the ability of the two parts to interoperate.

• The presentation must be aware of the services the game engine provides, but the game engine will
have no knowledge of the presentation component.

If implemented properly, software engineers may develop both parts of the system independently of each
other.

Listing 8.12 (dot3x3logic.py) provides the game engine for our 3×3 connect-the-dots game.

Listing 8.12: dot3x3logic.py

“””
dot3x3_logic.py

Provides the logic for a simplified connect the dots game.
The code in this module determines and enforces the rules of the
game. Callers are responsible for the game’s presentation component,
that is, the user experience.

The playing surface consists of a 3×3 grid of dots:

@ @ @

The game allows two players, X and Y, to alternately add horizontal and
vertical lines to connect the dots. The following shows a game in
progress:

@—@ @
| |

@ @ @
|

@ @—@

When a player completes a square, that player wins the square and
retains control of the next turn. The following shows a game in
which player y has completed a square:

@—@ @
| |

@ @—@

8.6. SEPARATING CONCERNS WITH PLUGGABLE MODULES 256

| Y |
@ @—@

If a player connects two dots and does not complete a square,
control passes to the other player. A player must add a line
during his/her turn. The game ends when all dots have been
connected. The player with more squares wins the game, and the game
is a draw if both players have two squares each.

This game engine manages 12 lines. Each line is distinguished by its
name (a string) as shown here:

@—‘Northwest_North’—@—‘North_Northeast’—@
| | |
| | |
| | |

‘Northwest_West’ ‘North_Center’ ‘Northeast_East’
| | |
| | |
| | |
@—‘West_Center’——-@—–‘Center_East’—–@
| | |
| | |
| | |

‘West_Southwest’ ‘Center_South’ ‘East_Southeast’
| | |
| | |
| | |
@—‘Southwest_South’—@—‘South_Southeast’—@

The game engine manages four squares. Each square is distinguished by
its name (a string) as shown here:

@————–@—————@
| | |
| | |
| ‘LeftTop’ | ‘RightTop’ |
| | |
| | |
@————–@—————@
| | |
| | |
| ‘LeftBottom’ | ‘RightBottom’ |
| | |
| | |
@————–@—————@

The string ‘X’ represents player X, and the string ‘Y’ represents
player Y.

“””

#—————————————————————
# Global variables that maintain the state of the current game.
# These variables are meant to be used only by code within this file;

8.6. SEPARATING CONCERNS WITH PLUGGABLE MODULES 257

# the underscore prefix discourages their access outside of this
# module.
#—————————————————————

# Boolean variables that keep track of whether or not a line
# exists between two dots; for example, if
# _nw_n is true, this means the line identified as
# ‘Northwest_North’ exists.

# Initially, no lines exist anywhere
_nw_n, _n_ne = False, False
_nw_w, _n_c, _ne_e = False, False, False
_w_c, _c_e = False, False
_w_sw, _c_s, _e_se = False, False, False
_sw_s, _s_se = False, False

# The player whose turn it is currently (player X or player Y)
# The value of this variable should be either the string ‘X’ or the
# string ‘Y’
_current_player = ‘X’

# Stores the owner of the given squares.
# If _leftbottom_owner equals the string ‘X’, that means
# player X owns the left-bottom square. Initially none of the
# squares have an owner, hence their owners are each None.
_lefttop_owner, _righttop_owner = None, None
_leftbottom_owner, _rightbottom_owner = None, None

#—————————————————————
# Functions used only by functions within this file.
# Note the names begin with an underscore to discourage access
# outside of this module.
#—————————————————————

def _update_square(sq):
“”” Updates the owner of square sq, if possible.

sq must be one of the strings ‘LeftTop’, ‘RightTop’,
‘LeftBottom’, or ‘RightBottom’.
The function checks to see

1) if the square currently is not owned by a player and
2) if all the lines are in place to complete the square.

If both conditions are met, it marks the square with the
current player and returns True. If one of the players

8.6. SEPARATING CONCERNS WITH PLUGGABLE MODULES 258

already owns the square, or if not all four lines exist to
complete the square, the function simply returns False. “””

# The function may affect one of the following global variables:
global _lefttop_owner, _righttop_owner, _leftbottom_owner, \

_rightbottom_owner

if sq == ‘LeftTop’ and _lefttop_owner == None \
and _nw_n and _nw_w and _n_c and _w_c:

_lefttop_owner = _current_player
return True

elif sq == ‘RightTop’ and _righttop_owner == None \
and _n_ne and _ne_e and _c_e and _n_c:

_righttop_owner = _current_player
return True

elif sq == ‘LeftBottom’ and _leftbottom_owner == None \
and _w_c and _c_s and _sw_s and _w_sw:

_leftbottom_owner = _current_player
return True

elif sq == ‘RightBottom’ and _rightbottom_owner == None \
and _c_e and _e_se and _s_se and _c_s:

_rightbottom_owner = _current_player
return True

else:
return False # Owners unchanged

def _update_squares():
“”” Attempts to update the owners of all squares that a new line

might affect. Returns True if one or more squares receives a
new owner; otherwise, the function returns False. “””

lt = _update_square(‘LeftTop’)
rt = _update_square(‘RightTop’)
lb = _update_square(‘LeftBottom’)
rb = _update_square(‘RightBottom’)
return lt or rt or lb or rb

#—————————————————————
# Functions that reveal or control the state of the current game.
# These functions are meant to be used outside of this
# module.
#—————————————————————

def add_line(line):
“”” Attempts to add a line between the two dots.

The parameter line must be one of ‘Northwest_North’,
‘North_Northeast’, etc.; that is, a string representing
a line on the game board.
If the line if not present, the function adds the line
and returns True.
If the line already is present, the function
does not change the state of the board and returns false. “””

# The function can change one of the following global variables
# maintaining the state of the game.

8.6. SEPARATING CONCERNS WITH PLUGGABLE MODULES 259

global _nw_n, _n_ne, _nw_w, _n_c, _ne_e, _w_c, _c_e, \
_w_sw, _c_s, _e_se, _sw_s, _s_se, _current_player

line_added = False # Unsuccessful by default
if line == ‘Northwest_North’ and not _nw_n:

_nw_n = True
line_added = True

elif line == ‘North_Northeast’ and not _n_ne:
_n_ne = True
line_added = True

elif line == ‘Northwest_West’ and not _nw_w:
_nw_w = True
line_added = True

elif line == ‘North_Center’ and not _n_c:
_n_c = True
line_added = True

elif line == ‘Northeast_East’ and not _ne_e:
_ne_e = True
line_added = True

elif line == ‘West_Center’ and not _w_c:
_w_c = True
line_added = True

elif line == ‘Center_East’ and not _c_e:
_c_e = True
line_added = True

elif line == ‘West_Southwest’ and not _w_sw:
_w_sw = True
line_added = True

elif line == ‘Center_South’ and not _c_s:
_c_s = True
line_added = True

elif line == ‘East_Southeast’ and not _e_se:
_e_se = True
line_added = True

elif line == ‘Southwest_South’ and not _sw_s:
_sw_s = True
line_added = True

elif line == ‘South_Southeast’ and not _s_se:
_s_se = True
line_added = True

# If the line was added successfully,
# check to see if it completes a square
if line_added and not _update_squares():

# Turn moves to other player upon a successful move
if _current_player == ‘X’:

_current_player = ‘Y’
else:

_current_player = ‘X’
return line_added

def square_owner(sq):
“”” Returns the player who owns the given square.

sq must be one of the strings ‘LeftTop’, ‘RightTop’,
‘LeftBottom’, or ‘RightBottom’.

8.6. SEPARATING CONCERNS WITH PLUGGABLE MODULES 260

Returns None if the square has no owner. “””
if sq == ‘LeftTop’:

return _lefttop_owner
elif sq == ‘RightTop’:

return _righttop_owner
elif sq == ‘LeftBottom’:

return _leftbottom_owner
elif sq == ‘RightBottom’:

return _rightbottom_owner
else:

return None

def check_line(line):
“”” Returns True if the line exists on the game board.

The parameter line must be one of ‘Northwest_North’,
‘North_Northeast’, etc.; that is, a string representing
a line on the game board.
If the function returns False if the line does not yet
exist. “””

if line == ‘Northwest_North’:
return _nw_n

elif line == ‘North_Northeast’:
return _n_ne

elif line == ‘Northwest_West’:
return _nw_w

elif line == ‘North_Center’:
return _n_c

elif line == ‘Northeast_East’:
return _ne_e

elif line == ‘West_Center’:
return _w_c

elif line == ‘Center_East’:
return _c_e

elif line == ‘West_Southwest’:
return _w_sw

elif line == ‘Center_South’:
return _c_s

elif line == ‘East_Southeast’:
return _e_se

elif line == ‘Southwest_South’:
return _sw_s

elif line == ‘South_Southeast’:
return _s_se

else:
return False

def winner():
“”” Returns the winner, ‘X’ or ‘Y’, or ‘Draw’ if the game

board is full and X and Y both own two squares. Returns
None if open squares still exist, and so the game can
continue. “””

# Count the player squares
x_count, y_count = 0, 0

8.6. SEPARATING CONCERNS WITH PLUGGABLE MODULES 261

if _lefttop_owner == ‘X’:
x_count += 1

elif _lefttop_owner == ‘Y’:
y_count += 1

if _righttop_owner == ‘X’:
x_count += 1

elif _righttop_owner == ‘Y’:
y_count += 1

if _rightbottom_owner == ‘X’:
x_count += 1

elif _rightbottom_owner == ‘Y’:
y_count += 1

if _leftbottom_owner == ‘X’:
x_count += 1

elif _leftbottom_owner == ‘Y’:
y_count += 1

if x_count + y_count == 4: # All squares filled
if x_count > y_count:

return ‘X’ # Player X won
elif x_count < y_count: return 'Y' # Player Y won else: return 'Draw' # Tie game, no winner else: return None # No winner or draw; the game continues def initialize_board(): """ Makes the playing board ready for a new game: 1) clears all the lines from the board, 2) makes all the squares empty, and 3) sets the current player to X This function does not return a value to the caller. """ # All of the following global variables are affected: global _nw_n, _n_ne, _nw_w, _n_c, _ne_e, _w_c, _c_e, \ _w_sw, _c_s, _e_se, _sw_s, _s_se, _current_player, \ _lefttop_owner, _righttop_owner, \ _leftbottom_owner, _rightbottom_owner _nw_n = _n_ne = _nw_w = _n_c = _ne_e = _w_c = _c_e = _w_sw \ = _c_s = _e_se = _sw_s = _s_se = False # Clear all the squares (neither player owns any squares) _lefttop_owner = _righttop_owner = _leftbottom_owner \ = _rightbottom_owner = None # X always begins _current_player = 'X' def current_player(): """ Returns the player whose turn it is to move """ return _current_player The docstring at the beginning of Listing 8.12 (dot3x3logic.py) explains overall design of the game ©2017 Richard L. Halterman Draft date: January 18, 2018 8.6. SEPARATING CONCERNS WITH PLUGGABLE MODULES 262 engine. The game engine module consists of a collection of 17 global variables and eight functions: • Global variables: The comments that follow the docstring reveals the purpose of the global variables that maintain the state of the game. The game engine’s global variables fall into three categories: – The first set of global variables (_nw_n, _n_ne, etc.) store Boolean values that indicate if a line exists in a given location. If the global variable _nw_n is False, no line connects the top left and top center dots. If _nw_n is True, however, a line connects the top left and top center dots. – The global variable player keeps track of the player (indicated by the string "X" or string "Y") whose turn it is. – The final set of global variables (_lefttop_owner, _righttop_owner, etc.) store the owners of the squares. They begin with the special value None, which means no one owns any squares at the start of a game. When a player completes a square, the game engine assigns "X" or "Y" to the appropriate variable. • Functions: The presentation part of the game code is not meant to access directly the global variables of the game engine; instead, the presentation should influence the global variables only via six of the supplied functions. The functions in the dot3x3logic module fall into three categories: – The _update_square and _update_squares functions are meant to be internal to the dot3x3logic module, meaning that only the functions within this file should call these two functions. These two functions determine which, if any squares become complete by a player’s move. The only caller of the _update_square function is _update_squares. The docstrings within these two functions provide more information about their purpose and use. – The add_line and initialize_board functions are available to the presentation and can mod- ify the state of the game. The presentation calls add_line when a player attempts to draw a line. The add_line function calls the _update_squares function to check whether a new line completes a square. The initialize_board function resets all the global variables in prepara- tion of a new game. The presentation calls the add_line function when a player provides input representing a move. The presentation calls the initialize_board function to begin a new game. The docstrings within these two functions provide more information about their purpose and use. – The check_line, square_owner, winner, and current_player functions cannot change the state of the game. They serve to report the state of the game to the presentation. The presentation can call these functions to determine how to change its appearance. The docstrings within these functions provide more information about their purpose and use. Listing 8.13 (dot3x3turtle.py) provides the graphical presentation using Python’s turtle module. Listing 8.13: dot3x3turtle.py from turtle import * from tkinter import messagebox # Gain access to the game engine functions from dot3x3logic import * # Some global variables supporting the graphical interface # The first dot selected by a player when creating a line ©2017 Richard L. Halterman Draft date: January 18, 2018 8.6. SEPARATING CONCERNS WITH PLUGGABLE MODULES 263 initial_dot = None dot_radius = 10 # Can adjust for larger or smaller dots def square_to_point(sq): """ Compute the (x, y) coordinates of the center of a square. Used to properly place the square's owner when it becomes captured. """ if sq == "LeftTop": return (200, 400) elif sq == "RightTop": return (400, 400) elif sq == "LeftBottom": return (200, 200) elif sq == "RightBottom": return (400, 200) def hit(x, y): """ Returns the dot (if any) that the point (x, y) is within. Returns None if the point (x, y) does not overlap any dot. Used when a player clicks the mouse over the board to determine which dot (if any) was selected. """ dot = None # Default result if 90 < x < 110 and 490 < y < 510: dot = "Northwest" elif 290 < x < 310 and 490 < y < 510: dot = "North" elif 490 < x < 510 and 490 < y < 510: dot = "Northeast" elif 90 < x < 110 and 290 < y < 310: dot = "West" elif 290 < x < 310 and 290 < y < 310: dot = "Center" elif 490 < x < 510 and 290 < y < 310: dot = "East" elif 90 < x < 110 and 90 < y < 110: dot = "Southwest" elif 290 < x < 310 and 90 < y < 110: dot = "South" elif 490 < x < 510 and 90 < y < 110: dot = "Southeast" return dot def dot_to_point(dot): """ Maps a dot to its location on the board. Used to render a dot in its proper place. """ if dot == "Northwest": return 100, 500 elif dot == "North": return 300, 500 elif dot == "Northeast": return 500, 500 elif dot == "West": ©2017 Richard L. Halterman Draft date: January 18, 2018 8.6. SEPARATING CONCERNS WITH PLUGGABLE MODULES 264 return 100, 300 elif dot == "Center": return 300, 300 elif dot == "East": return 500, 300 elif dot == "Southwest": return 100, 100 elif dot == "South": return 300, 100 elif dot == "Southeast": return 500, 100 def draw_dot(name, col="black"): """ Draws a graphical dot within the graphical window. col specifies the dot's color (black by default). """ global dot_radius pensize(1) penup() x, y = dot_to_point(name) setposition(x, y - dot_radius) pendown() color(col) begin_fill() circle(dot_radius) end_fill() update() def draw_line(x1, y1, x2, y2): """ Draws a line segment with endpoints (x1, y1) and (x2, y2). """ penup() setposition(x1, y1) pendown() setposition(x2, y2) update() def draw_X(x, y): """ Draws player X's mark at position (x,y). """ color("blue") pensize(10) draw_line(x - 40, y - 40, x + 40, y + 40) draw_line(x - 40, y + 40, x + 40, y - 40) def draw_Y(x, y): """ Draws player Y's mark at position (x,y). """ color("blue") pensize(10) draw_line(x - 40, y + 40, x, y) draw_line(x + 40, y + 40, x, y) draw_line(x, y, x, y - 40) ©2017 Richard L. Halterman Draft date: January 18, 2018 8.6. SEPARATING CONCERNS WITH PLUGGABLE MODULES 265 def draw_square(sq, owner): """ Draws the owner of a square in the square, if the square has an owner. """ # Coordinates the square x, y = square_to_point(sq) if owner == "X": draw_X(x, y) elif owner == "Y": draw_Y(x, y) # Else do not draw anything--the square has no owner def check_squares(): """ Checks all squares to determine if any are complete. Draws the square owner's mark in a completed square. If all squares are owned, the function declares a winner or announces a draw. """ # Check the ownership of each potential square draw_square("LeftTop", square_owner("LeftTop")) draw_square("RightTop", square_owner("RightTop")) draw_square("LeftBottom", square_owner("LeftBottom")) draw_square("RightBottom", square_owner("RightBottom")) # Determine win = winner() if win == "X": messagebox.showinfo("Game Over", "X wins") elif win == "Y": messagebox.showinfo("Game Over", "Y wins") elif win == "Draw": messagebox.showinfo("Game Over", "Tie Game") def mouse_click(x, y): """ Responds to the user clicking the mouse when the cursor is over the window. Determines if the user clicked on a dot. Activates an initial dot if the initial dot is not already active. Establishes a line to a terminal dot if possible. If the move is illegal, the function produces a message box alerting the player. """ global initial_dot print("initial_dot =", initial_dot) print("clicked at x =", x, " y =", y) dot = hit(x, y) # Did the player click on a dot? if dot: print(dot) if not initial_dot: initial_dot = dot draw_dot(initial_dot, "red") elif dot != initial_dot: if add_line(line_name(initial_dot, dot)): # Draw the added line color("black") pensize(5) ©2017 Richard L. Halterman Draft date: January 18, 2018 8.6. SEPARATING CONCERNS WITH PLUGGABLE MODULES 266 x1, y1 = dot_to_point(initial_dot) x2, y2 = dot_to_point(dot) draw_line(x1, y1, x2, y2) # Adjust title bar to current player title("3x3 Connect the Dots Current Player: " + current_player()) # Check to see if the move captured a square # and/or ended the game check_squares() # Clear the initial dot and redraw both connecting dots draw_dot(initial_dot) initial_dot = None # Initial dot no longer in play draw_dot(dot) else: if initial_dot: draw_dot(initial_dot) initial_dot = None def reset_game(): """ Reinitialize the game's state for the start of a new game. """ clearscreen() initialize() def line_name(dot1, dot2): """ Returns the name of the line that connects the Dot objects dot1 and dot2. Derives the line's name from the names of the two dot objects. Displays an error message box if the two dots do not participate in a valid line. """ if (dot1 == "Northwest" and dot2 == "North") or \ (dot1 == "North" and dot2 == "Northwest"): return "Northwest_North" elif (dot1 == "North" and dot2 == "Northeast") or \ (dot1 == "Northeast" and dot2 == "North"): return "North_Northeast" elif (dot1 == "Northwest" and dot2 == "West") or \ (dot1 == "West" and dot2 == "Northwest"): return "Northwest_West" elif (dot1 == "North" and dot2 == "Center") or \ (dot1 == "Center" and dot2 == "North"): return "North_Center" elif (dot1 == "Northeast" and dot2 == "East") or \ (dot1 == "East" and dot2 == "Northeast"): return "Northeast_East" elif (dot1 == "West" and dot2 == "Center") or \ (dot1 == "Center" and dot2 == "West"): return "West_Center" elif (dot1 == "Center" and dot2 == "East") or \ (dot1 == "East" and dot2 == "Center"): return "Center_East" elif (dot1 == "West" and dot2 == "Southwest") or \ (dot1 == "Southwest" and dot2 == "West"): return "West_Southwest" ©2017 Richard L. Halterman Draft date: January 18, 2018 8.6. SEPARATING CONCERNS WITH PLUGGABLE MODULES 267 elif (dot1 == "Center" and dot2 == "South") or \ (dot1 == "South" and dot2 == "Center"): return "Center_South" elif (dot1 == "East" and dot2 == "Southeast") or \ (dot1 == "Southeast" and dot2 == "East"): return "East_Southeast" elif (dot1 == "Southwest" and dot2 == "South") or \ (dot1 == "South" and dot2 == "Southwest"): return "Southwest_South" elif (dot1 == "South" and dot2 == "Southeast") or \ (dot1 == "Southeast" and dot2 == "South"): return "South_Southeast" else: print('Not a valid dot link') messagebox.showerror("Invalid Link", "You may not connect those two dots") return None def initialize(): """ Initializes the graphical presentation and game engine. """ # Global dot objects # Initialize game engine initialize_board() # Specify the dimensions of the window screensize(600, 600) # Move origin (0, 0) to the left bottom of the window setworldcoordinates(0, 0, 599, 599) # Apply the usual tricks to speed up the image rendering tracer(0) hideturtle() # Register callback functions with the Turtle graphics framework onscreenclick(mouse_click) # What to do on a mouse click onkeyrelease(reset_game, "q") # What to do when user presses the Q key # Permit window to receive keypress events listen() # Set initial widow title title("3x3 Connect the Dots Current Player: " + current_player()) # No initial dot has been selected initial_dot = None # Draw all the dots for dot in ("Northwest", "North", "Northeast", "West", "Center", "East", "Southwest", "South", "Southeast"): draw_dot(dot) update() # Force the window to show drawing ©2017 Richard L. Halterman Draft date: January 18, 2018 8.6. SEPARATING CONCERNS WITH PLUGGABLE MODULES 268 Figure 8.6 A graphical 3×3 connect-the-dots game in progress. if __name__ == "__main__": initialize() # Set up the game mainloop() # Start game running Listing 8.13 (dot3x3turtle.py) uses its own global variables to determine which dots the user selects when making a line. Note that the presentation registers the function mouse_click for the graphical framework to call when the user clicks the mouse button. The mouse_click function must determine if the click occurred over a graphical dot. It uses the initial_dot global to keep track if this is the initial endpoint of a line or the terminal endpoint of a line. The mouse_click function than calls the line_name function to translate the information about the two graphical dots into the proper line string to send to the game engine’s add_line function. If the player attempts an illegal move, the presentation pops up a message box alerting the player. This program registers the reset_game function via the Turtle library’s onkeyrelease function. This allows a player to quit the current game and start a new one at any time by pressing the Q key. In addition to initializing the Turtle graphics environment, the reset_game calls the game engine’s initialize_board function to ensure the game engine removes any remnants of the abandoned game. Figure 8.6 shows a graphical 3×3 connect-the-dots game in progress. This separation of concerns, dividing the game control logic from the presentation, requires more effort to implement properly than does putting all the code together in one module. The payoff of this extra work is increased flexibility. This design allows us to decouple the engine from the presentation. We can “un- plug” this graphical user interface from the game engine and “plug in” a completely different presentation without touching the game engine code. Listing 8.14 (dot3x3text.py) uses the exact same game engine as Listing 8.13 (dot3x3turtle.py) but provides a text-output, keyboard-only-input interface to the players. Listing 8.14: dot3x3text.py from dot3x3logic import * ©2017 Richard L. Halterman Draft date: January 18, 2018 8.6. SEPARATING CONCERNS WITH PLUGGABLE MODULES 269 def show_player(p): ''' Determines the string to print in the context of a square's owner. p is a player. ''' if p: return ' ' + p else: return ' ' def draw_game(): ''' Draws the connect the dots game using text graphics ''' # 0---1---2 ------------------------------------ print(' 0', end='') if check_line('Northwest_North'): print('---', end='') else: print(' ', end='') print('1', end='') if check_line('North_Northeast'): print('---', end='') else: print(' ', end='') print('2') # | | | ------------------------------------ if check_line('Northwest_West'): print(' |', end='') else: print(' ', end='') print(show_player(square_owner('LeftTop')), end='') if check_line('North_Center'): print(' |', end='') else: print(' ', end='') print(show_player(square_owner('RightTop')), end='') if check_line('Northeast_East'): print(' |') else: print(' ') # 3---4---5 ------------------------------------ print(' 3', end='') if check_line('West_Center'): print('---', end='') else: print(' ', end='') print('4', end='') if check_line('Center_East'): print('---', end='') else: print(' ', end='') print('5') # | | | ------------------------------------ if check_line('West_Southwest'): ©2017 Richard L. Halterman Draft date: January 18, 2018 8.6. SEPARATING CONCERNS WITH PLUGGABLE MODULES 270 print(' |', end='') else: print(' ', end='') print(show_player(square_owner('LeftBottom')), end='') if check_line('Center_South'): print(' |', end='') else: print(' ', end='') print(show_player(square_owner('RightBottom')), end='') if check_line('East_Southeast'): print(' |') else: print(' ') # 6---7---8 ------------------------------------ print(' 6', end='') if check_line('Southwest_South'): print('---', end='') else: print(' ', end='') print('7', end='') if check_line('South_Southeast'): print('---', end='') else: print(' ', end='') print('8') def make_line(move): ''' Determines the line between two dots specified in the string move. The move parameter is one of '01', 12', '03', etc. representing a line connecting the dots in the pattern 0---1---2 | | | 3---4---5 | | | 6---7---8 The function returns the string that represents the line position between the dots, one of 'Northwest_North', 'North_Center', etc. If the dot1, dot2 pair represents an invalid combination, for example, (0, 4), the function returns the string 'NoLine'. ''' if move == '01' or move == '10': return 'Northwest_North' elif move == '12' or move == '21': return 'North_Northeast' elif move == '03' or move == '30': return 'Northwest_West' elif move == '14' or move == '41': return 'North_Center' elif move == '25' or move == '52': return 'Northeast_East' elif move == '34' or move == '43': return 'West_Center' elif move == '45' or move == '54': ©2017 Richard L. Halterman Draft date: January 18, 2018 8.6. SEPARATING CONCERNS WITH PLUGGABLE MODULES 271 return 'Center_East' elif move == '36' or move == '63': return 'West_Southwest' elif move == '47' or move == '74': return 'Center_South' elif move == '58' or move == '85': return 'East_Southeast' elif move == '67' or move == '76': return 'Southwest_South' elif move == '78' or move == '87': return 'South_Southeast' else: return 'NoLine' # Default return value # Start a new game initialize_board() draw_game() winning_player = None # No winner at start while not winning_player: prompt = 'Move for player ' + current_player() + ': ' move = input(prompt) # Get the dots to connect if move == 'Q' or move == 'q': # 'Q' quits the program break print() # Add the line, if possible new_line = make_line(move) if new_line != 'NoLine' and add_line(new_line): draw_game() else: print('Connection not possible') winning_player = winner() # Check for win # Determine winner, if either player X or player Y if winning_player == 'X': print('X won') elif winning_player == 'Y': print('Y won') else: print('Draw') print('\n*** G A M E O V E R ***') Listing 8.13 (dot3x3turtle.py) had to maintain a few global variables to keep track of the user’s graphical dot selections. Observe that Listing 8.14 (dot3x3text.py) needs no global variables of its own. This is because the user (players) simply type in the numbers of the dots to connect. The following shows an example of a complete game in one execution of Listing 8.14 (dot3x3text.py): 0 1 2 3 4 5 6 7 8 Move for player X: 12 0 1---2 ©2017 Richard L. Halterman Draft date: January 18, 2018 8.6. SEPARATING CONCERNS WITH PLUGGABLE MODULES 272 3 4 5 6 7 8 Move for player Y: 52 0 1---2 | 3 4 5 6 7 8 Move for player X: 47 0 1---2 | 3 4 5 | 6 7 8 Move for player Y: 34 0 1---2 | 3---4 5 | 6 7 8 Move for player X: 45 0 1---2 | 3---4---5 | 6 7 8 Move for player Y: 14 0 1---2 | Y | 3---4---5 | 6 7 8 Move for player Y: 58 0 1---2 | Y | 3---4---5 | | 6 7 8 Move for player X: 87 0 1---2 | Y | 3---4---5 | X | 6 7---8 Move for player X: 01 ©2017 Richard L. Halterman Draft date: January 18, 2018 8.7. LAMBDA EXPRESSIONS 273 0---1---2 | Y | 3---4---5 | X | 6 7---8 Move for player Y: 76 0---1---2 | Y | 3---4---5 | X | 6---7---8 Move for player X: 63 0---1---2 | Y | 3---4---5 | X | X | 6---7---8 Move for player X: 03 0---1---2 | X | Y | 3---4---5 | X | X | 6---7---8 X won *** G A M E O V E R *** The text-based version is not as natural to play as the graphical version, but it is playable. As far as the game logic is concerned, it behaves identically to our graphical version. This is because they share the same game engine. One benefit of this modularity is that if we detect and correct a logic error in our game engine, the change will repair both versions of the game. 8.7 Lambda Expressions One of the primary benefits of functions is that we can write a function’s code once and invoke it from many different places within the program (and even invoke it from other programs). Ordinarily, in order to call a function, we must know its name. Almost all the examples we have seen have invoked a function via its name. Listing 8.9 (arithmeticeval.py) in Section 8.5 provided examples of invoking functions without using their names directly. There we saw a function named evaluate that accepts a function as a parameter: def evaluate(f, x, y): return f(x, y) The evaluate function calls f. The question is, what function does evaluate call? The name f refers to one of evaluate’s parameters; there is no separate function named f specified by def within Listing 8.9 (arithmeticeval.py). The answer, of course, is that evaluate invokes the function passed in from the caller. The function named main in Listing 8.9 (arithmeticeval.py) calls evaluate passing the add function on one occasion and the multiply function on another. ©2017 Richard L. Halterman Draft date: January 18, 2018 8.7. LAMBDA EXPRESSIONS 274 The code in the evaluate function demands that callers send a function as the first parameter. Does this mean we have to write a separate function using def in order to call evaluate? What if we want to ensure that our function will execute exactly one time and only when invoked by evaluate? Python supports the definition of simple, anonymous functions via lambda expressions. The general form of a lambda expression is parameterlistlambda : expression where: • lambda is a reserved word that introduces a lambda expression. • parameterlist is a comma-separated list of parameters as you would find in the function definition (but notice the lack of parentheses). • expression is a single Python expression. The expression cannot be a complete statement, nor can it be a block of statements. The term lambda comes from lambda calculus (see http://en.wikipedia.org/wiki/Lambda calculus), a function-based mathematical system developed by Alonzo Church in the 1930s. Concepts from lambda calculus led to the development of the modern computer. We can use a lambda expression in a call to the evaluate function: evaluate(lambda x, y: x * y, 2, 3) The lambda keyword signifies the definition of an unnamed function; thus, the first argument being passed to evaluate is indeed a function. Notice that result of passing the lambda expression here is the same as passing the multiply function from Listing 8.9 (arithmeticeval.py)—both compute the product of the two parameters. The following interactive session shows some additional examples of lambda expressions: >>> def evaluate(f, x, y):
… return f(x, y)
…
>>> evaluate(lambda x, y: 3*x + y, 10, 2)
32
>>> evaluate(lambda x, y: print(x, y), 10, 2)
10 2
>>> evaluate(lambda x, y: 10 if x == y else 2, 5, 5)
10
>>> evaluate(lambda x, y: 10 if x == y else 2, 5, 3)
2

The expression following the colon (:) in a lambda expression cannot be a Python statement. The
conditional expression, for example, is acceptable, but an if/else statement is illegal. The expression’s
value is what the anonymous function returns, but the keyword return itself may not appear with the
expression. Assignments are not possible within lambda expressions, and loops are not allowed. Note
that a lambda expression can involve one or more function invocations, so the lambda expression in the
following statement is legal:

http://en.wikipedia.org/wiki/Lambda_calculus

8.7. LAMBDA EXPRESSIONS 275

evaluate(lambda x, y: max(x, y) + x – sqrt(y), 2, 3)

if the max and sqrt functions are available to the program.

One interesting aspect of lambda functions is that they form what is known as a closure. A closure is
a function that can capture the context of its surrounding environment. Listing 8.15 (closurein.py) demon-
strates a simple closure.

Listing 8.15: closurein.py

def evaluate(f, x, y):
return f(x, y)

def main():
a = int(input(‘Enter an integer:’))
print(evaluate(lambda x, y: False if x == a else True, 2, 3))

main()

Note that main creates a function (the lambda expression) that it passes to evaluate. It is important to note
that the statement

print(evaluate(lambda x, y: False if x == a else True, 2, 3))

passes just three parameters to evaluate: a function and two integer values. The main function’s local
variable a is not passed as a parameter; instead, it is embedded within the lambda code of the first parameter.
The variable a is encoded into the lambda expression. We say the function definition (lambda expression)
captures the variable a. When evaluate invokes the function sent by the caller, evaluate has no access to
a variable named a. The a involved in the conditional expression is captured from main. This is an example
of a closure transporting a captured variable into a function call.

For an example of a closure transporting a captured local variable out of a function, consider Listing 8.16
(makeadder.py) which includes a function that returns a function (lambda expression) to its caller.

Listing 8.16: makeadder.py

def make_adder():
loc_val = 2 # Local variable definition
return lambda x: x + loc_val # Returns a function

def main():
f = make_adder()
print(f(10))
print(f(2))

main()

Ordinarily when a function returns all of its local variables disappear. This means that after the following
statement in the main function executes:

f = make_adder()

8.7. LAMBDA EXPRESSIONS 276

make_adder’s loc_var local variable should no longer exist. The function that make_adder returns, how-
ever, uses loc_var in its computation. This means the function that make_adder returns forms a closure
that captures make_adder’s local variable loc_var. In the output of Listing 8.16 (makeadder.py) we can
see that function f still has knowledge of loc_val’s value:

12
4

We can assign a variable to a lambda expression:

>>> f = lambda x: 2*x
>>> f(10)
20

This gives the function a name, so the statement

f = lambda x: 2*x

is equivalent to the function definition

def f(x):
return 2*x

The function definition with def is much more powerful, however, because it can contain any number of
arbitrary Python statements.

While not a particularly useful application of lambda, to demonstrate the regularity of the Python lan-
guage, we can define an anonymous function and invoke it immediately; for example, the statement

print((lambda x, y: x * y)(2, 3))

prints 6. In this case the statement print(2*3) or, even better, print(6) produces the same result much
more simply.

Listing 8.17 (plotter.py) combines the concepts of lambda functions, functions as data (Section 8.5), and
Turtle graphics (Section 6.9). It defines several functions:

• initialize_plotter—calls appropriate Turtle graphics functions to initial the window size and
coordinate system based on the parameters passed by its caller. Draws an x- and y-axis to simulate a
Cartesian coordinate plane.

• plot—draws the graph of a two-dimensional mathematical function on the Cartesian coordinate
plane established by initialize_plotter. It accepts a mathematical function, expressed as a
Python function, as one of its parameters. Its other parameter is the drawing color for the curve.

• finish_plotting—finishes rendering the Turtle graphics.

• quad—represents the mathematical quadratic function f (x) =
1
2
x2 + 3. A caller can pass this to the

plot function for rendering.

The comments within Listing 8.17 (plotter.py) provide additional details about the functions’ operation.

Listing 8.17: plotter.py

8.7. LAMBDA EXPRESSIONS 277

“”” Provides the plot function that draws the graph of a mathematical
function on a Cartesian coordinate plane. “””

import turtle

def initialize_plotter(width, height, min_x, max_x, min_y, max_y):
“”” Initializes the plotter with a window with dimensions

width x height, the x-axis ranging from
min_x to max_x, and the y-axis ranging from
min_y to max_y. Establishes the global beginning and ending
x values for the plot and the global x_increment value.
Draws the x- and y-axes. “””

# Global variables that the plot function must access
global x_begin, x_end, x_increment

#turtle.tracer(1, 0) # Speed up rendering
turtle.delay(0) # Speed up rendering
# Establish global x and y ranges
x_begin, x_end = min_x, max_x
# Set up window size, in pixels
turtle.setup(width=width, height=height)
# Set up screen size, in pixels
turtle.screensize(width, height)
turtle.setworldcoordinates(min_x, min_y, max_x, max_y)

# x-axis distance that corresponds to one pixel in window distance
x_increment = (max_x – min_x)/width

turtle.hideturtle() # Make pen invisible
# Draw x axis
turtle.pencolor(‘black’)
turtle.penup()
turtle.setposition(min_x, 0) # Move the pen to the left, center
turtle.setheading(0) # Aim the pen right
turtle.pendown()
turtle.forward(max_x – min_x) # Draw a line left to right

# Draw y axis
turtle.penup()
turtle.setposition(0, min_y) # Move the pen to the center, bottom
turtle.setheading(90) # Aim the pen up
turtle.pendown() # Draw line bottom to top
turtle.forward(max_y – min_y)

def plot(f, color):
“”” Plots function f on the Cartesian coordinate plane

established by initialize_plotter. Plots (x, f(x)),
for all x in the range x_begin <= x < x_end. The color parameter dictates the curve's color. """ # Move pen to starting position turtle.penup() ©2017 Richard L. Halterman Draft date: January 18, 2018 8.8. GENERATORS 278 turtle.setposition(x_begin, f(x_begin)) turtle.pencolor(color) turtle.pendown() # Iterate over the range of x values for x_begin <= x < x_end x = x_begin while x < x_end: turtle.setposition(x, f(x)) x += x_increment # Next x def finish_plotting(): turtle.exitonclick() def quad(x): # Quadratic function (parabola) return 1/2 * x**2 + 3 def main(): """ Provides a simple test of the plot function. """ from math import sin initialize_plotter(600, 600, -10, 10, -10, 10) # Plot f(x) = 1/2*x + 3, for -10 <= x < 100 plot(quad, 'red') # Plot f(x) = x, for -10 <= x < 100 plot(lambda x: x, 'blue') # Plot f(x) = 3 sin x, for -10 <= x < 100 plot(lambda x: 3*sin(x), 'green') finish_plotting() if __name__ == '__main__': main() Listing 8.17 (plotter.py) contains a test function, main, that plots the following mathematical functions: f (x) = 1 2 x2 +3 f (x) = x f (x) = 3sinx The main function passes to plot the latter two functions as lambda functions. Observe that plot accepts both named functions and lambda functions with equal ease. Figure 8.7 provides a screenshot of the program’s execution. 8.8 Generators Ordinarily when a function returns to its caller the function relinquishes all of the memory for its local variables and parameters. The executing program then reuses this memory during calls to other functions, including re-calls to the same function. As a consequence, during every invocation a function begins fresh, ©2017 Richard L. Halterman Draft date: January 18, 2018 8.8. GENERATORS 279 Figure 8.7 A screenshot of the plot function rendering the mathematical functions f (x) = 1 2 x2 + 3 (red), f (x) = x (blue), and f (x) = 3sinx, all over the range −10≤ x < 10. ©2017 Richard L. Halterman Draft date: January 18, 2018 8.8. GENERATORS 280 with no traces of its past execution. This means a function normally cannot remember anything about past invocations. We could use global variables to allow a function to remember some information. The function remember in Listing 8.18 (funcmemory.py) uses a global variable to keep track of the number of times it has been in- voked. Listing 8.18: funcmemory.py count = 0 # A global count variable def remember(): global count count += 1 # Count this invocation print('Calling remember (#' + str(count) + ')') print('Beginning program') remember() remember() remember() remember() remember() print('Ending program') Listing 8.18 (funcmemory.py) prints Beginning program Calling remember (#1) Calling remember (#2) Calling remember (#3) Calling remember (#4) Calling remember (#5) Ending program Functions that access no global variables have precisely predictable behavior, which is a very desirable quality. In isolation we have no way to predict what the following statement will print: remember() We need to know the complete context. Certainly we need to know how many times the executing program previously called remember. Even that knowledge is insufficient in the context of a larger program that in- volves other functions. Other functions conceivably could manipulate the global count variable in between invocations to remember. In order to write functions with persistence we need to use programming objects. We consider objects in depth in Chapters 9 and beyond, but for now we will consider a Python programming feature that invisibly uses an object behind the scenes. A generator is a programming object that produces (that is, generates) a sequence of values. Code that uses a generator may obtain one value in the sequence at a time without the possibility of revisiting earlier values. We say the code that uses the generator consumes the generator’s product. Given only our current knowledge of functions, we can easily make and use generator objects. We create a generator within a function and “return” it. We do not use the return keyword; instead, we use ©2017 Richard L. Halterman Draft date: January 18, 2018 8.8. GENERATORS 281 the yield keyword. The code within the function definition specifies the behavior of the generator. A few simple examples illustrate how this works. First, consider the module defined in Listing 8.19 (yieldsequence.py). Listing 8.19: yieldsequence.py def gen(): yield 3 yield 'wow' yield -1 yield 1.2 The following interactive sequence reveals some information about the gen function within Listing 8.19 (yieldsequence.py): >>> from yieldsequence import gen
>>> gen

>>> type(gen)

>>> gen()

>>> type(gen())

>>> x = gen()
>>> x

>>> type(x)

We see that gen is just a function, and, when invoked, gen returns a generator object. What can we do with
a generator object?

Python has a built-in function named next that accepts a generator object and returns the next value in
the generator’s sequence. Consider the following interactive sequence:

>>> from yieldsequence import gen
>>> x = gen()
>>> next(x)
3
>>> next(x)
‘wow’
>>> next(x)
-1
>>> next(x)
1.2
>>> next(x)
Traceback (most recent call last):

File ““, line 1, in
StopIteration

The statement

x = gen()

8.8. GENERATORS 282

binds variable x to the generator object that gen returns. Once we have a generator object we can use the
next function to extract the values in its sequence. Observe that we get an error if we ask the generator to
provide a value after the final value in its sequence.

Programmers generally do not use the next function directly. Instead, they leave it to the for statement
to call next behind the scenes. A generator object is one example of an iterable object. We learned in Sec-
tion 5.3 that Python’s for statement is built to work with an iterable object. The for statement, therefore,
can iterate over the sequence of values produced by a generator object. Listing 8.20 (forgenerator.py) shows
that the for statement works naturally with the generator our gen function produces.

Listing 8.20: forgenerator.py

def gen():
yield 3
yield ‘wow’
yield -1
yield 1.2

for i in gen():
print(i)

Listing 8.20 (forgenerator.py) prints

3
wow
-1
1.2

The for statement basically receives the next value from the generator each time through the loop. The
loop stops automatically when the generator has no more values left.

The yield statement within the function generates the values of the sequence. It is uncommon to
provide separate yield statements for each value the generator is to produce. More likely, one yield
statement executes multiple times within a loop. Listing 8.21 (regulargenerator.py) shows a more common
scenario.

Listing 8.21: regulargenerator.py

def generate_multiples(m, n):
count = 0
while count < n: yield m * count count += 1 def main(): for mult in generate_multiples(3, 6): print(mult, end=' ') print() if __name__ == '__main__': main() ©2017 Richard L. Halterman Draft date: January 18, 2018 8.8. GENERATORS 283 Listing 8.21 (regulargenerator.py) prints the first six multiples of three: 0 3 6 9 12 15 The generate_multiples function in Listing 8.21 (regulargenerator.py) contains only one yield state- ment, but the loop executes the yield statement n times. Listing 8.22 (myrange.py) shows how we can use a generator to simulate the behavior of the built-in range expression. Listing 8.22: myrange.py def myrange(arg1, arg2=None, step=1): if arg2 != None: # Do we have at least two arguments? begin = arg1 end = arg2 else: # We must have just one argument begin = 0 # Begin value is zero by default end = arg1 i = begin while i != end: yield i i += step print('0 to 9:', end=' ') for i in myrange(10): print(i, end=' ') print() print('1 to 10:', end=' ') for i in myrange(1, 11): print(i, end=' ') print() print('2 to 18 by twos:', end=' ') for i in myrange(2, 20, 2): print(i, end=' ') print() print('20 down to 2 by twos:', end=' ') for i in myrange(20, 0, -2): print(i, end=' ') print() Listing 8.22 (myrange.py) prints 0 to 9: 0 1 2 3 4 5 6 7 8 9 1 to 10: 1 2 3 4 5 6 7 8 9 10 2 to 18 by twos: 2 4 6 8 10 12 14 16 18 20 down to 2 by twos: 20 18 16 14 12 10 8 6 4 2 While our myrange function works like Python’s built-in range expression, in fact, range is different. A simple exercise with the interactive shell reveals: ©2017 Richard L. Halterman Draft date: January 18, 2018 8.8. GENERATORS 284 >>> range

>>> range(10)
range(0, 10)
>>> type(range)

>>> type(range(10))

The expression range(0, 10) does not return a generator object but instead creates and returns a range
object. Furthermore, the interative sequence shows that range is not a function at all; it is a class. In reality,
the expression range(0, 10) calls the range class constructor. We will not be concerned with such details
about objects until Chapter 13. For now we will be content with the understanding that the for statement
is designed to work with iterable objects, and generators and range objects are both instances of iterable
objects.

Our myrange function may be interesting, but it offers no advantage over the built-in range expression.
It is time to use a generator in a more interesting way. Recall Listing 7.15 (primefunc.py) that uses a
function named is_prime in the course of printing the prime numbers within a range specified by the user.
What if we wish to print only the prime numbers within a range that end with the digit 3? What if wish
to add up all the prime numbers within a given range? A generator is ideal for implementing the more
modular and flexible code required to generate prime numbers independent of how a program uses them.
Listing 8.23 (generatedprimes.py) uses a generator function to produce the sequence of prime numbers.
The caller (main) then can select which values to print and sum the numbers in a sequence. In Listing 8.23
(generatedprimes.py) we further tune the is_prime function from the observations that two is the only even
prime number and that no prime number except two may have a factor that is even. Applying these facts
allows us to cut by one-half the potential factors to consider within the loop.

Listing 8.23: generatedprimes.py

# Contains the definition of the is_prime function
from math import sqrt

def is_prime(n):
“”” Returns True if nonnegative integer n is prime;

otherwise, returns false “””
if n == 2: # 2 is the only even prime number

return True
if n < 2 or n % 2 == 0: # Handle simple cases immediately return False # No evens and nothing less than 2 trial_factor = 3 root = sqrt(n) while trial_factor <= root: if n % trial_factor == 0: # Is trial factor a factor? return False # Yes, return right away trial_factor += 2 # Next potential factor, skip evens return True # Tried them all, must be prime def prime_sequence(begin, end): """ Generates the sequence of prime numbers between begin and end. """ for value in range(begin, end + 1): if is_prime(value): # See if value is prime ©2017 Richard L. Halterman Draft date: January 18, 2018 8.8. GENERATORS 285 yield value # Produce the prime number def main(): """ Experiments with the prime number generator """ min_value = int(input("Enter start of range: ")) max_value = int(input("Enter last of range: ")) print('Print all the primes from', min_value, 'to', max_value) for value in prime_sequence(min_value, max_value): print(value, end=' ') # Display the prime number print() # Move cursor down to next line print('Print all the primes in that range that end with digit 3') for value in prime_sequence(min_value, max_value): if value % 10 == 3: # See if value's ones digit is 3 print(value, end=' ') # Display the number print() # Move cursor down to next line # Add up all the primes in the range sum = 0 for value in prime_sequence(min_value, max_value): sum += value print('The sum of the primes in that range is', sum) # Decorate the output print('Fancier display') for value in prime_sequence(min_value, max_value): print('<' + str(value) + '>‘, end=”)

if __name__ == ‘__main__’:
main() # Run the program

Listing 8.23 (generatedprimes.py) prints

Enter start of range: 20
Enter last of range: 50
Print all the primes from 20 to 50
23 29 31 37 41 43 47
Print all the primes in that range that end with digit 3
23 43
The sum of the primes in that range is 251
Fancier display
<23><29><31><37><41><43><47>

Each call of the expression

prime_sequence(min_value, max_value)

creates a new generator object ready to use.

As Listing 8.23 (generatedprimes.py) demonstrates, a generator is useful when you need to centralize
and reuse code that produces a sequence of values and you cannot predict how consumers of the sequence
will use those values.

8.9. LOCAL FUNCTION DEFINITIONS 286

Figure 8.8 Decomposing a larger function into a collection of smaller functions. Callers now have access
to the individual functions do part1, do part2, and do part3, as well as to func.

part 2

part 1

part 3

def func():

Functional

decompositon
part 2

part 1

part 3

def do_part1():

def do_part2():

def do_part3():

def func():
do_part1()
do_part2()
do_part3()

8.9 Local Function Definitions

In Chapter 7 we introduced functional decomposition—a fancy term that means programmers can use
functions to break up a large, complex, monolithic program into smaller, more manageable pieces. The
code within a function is somewhat insulated from the rest of the program, in that a caller can influence the
behavior of a function only via the function’s parameters and any global variables the function may use.
Any local variables the function uses are invisible to code outside of the function.

Suppose we develop a function that itself becomes large and unwieldy. We further can break down
the large function into smaller pieces as Figure 8.8 shows. The perhaps unintended consequence of this
functional decomposition is that callers now can bypass the original function and access its pieces directly
and individually. Sometimes this more fine-grained access is desirable, but at other times programmers do
not want to expose that level of detail to callers.

Generalizing the concept of local variables, Python permits programmers to define functions within
other function definitions. These local functions are available to the code within their enclosing func-
tion but are inaccessible outside their enclosing function. Figure 8.9 shows how to restructure the func
function definition using local functions to enable functional decomposition without violating the code en-
capsulation of the original monolithic function. Listing 8.24 (boxmeasure.py) includes a function named
surface_area that computes the surface area of a rectangular box. The function expects the eight points
that represent the corners of the box. Note that the surface_area function uses a local function to compute
the area of each of its sides. Listing 8.24 (boxmeasure.py) also includes a function named volume also
computes the box’s volume.

Listing 8.24: boxmeasure.py

from math import fabs

def surface_area(x1, y1, z1, x2, y2, z2, x3, y3, z3, x4, y4, z4,
x5, y5, z5, x6, y6, z6, x7, y7, z7, x8, y8, z8):

“”” Computes the surface area of a rectangular box
(cuboid) defined by the 3D points (x,y,z) of
its eight corners:

8.9. LOCAL FUNCTION DEFINITIONS 287

Figure 8.9 The local functions do part1, do part2, and do part3 are available to function func but are
inaccessible outside the func function

part 2

part 1

part 3

def func():

Local

functional

decompositon

part 2

part 1

part 3

def do_part1():

def do_part2():

def do_part3():

def func():

do_part1()
do_part2()
do_part3()

7——8
/| /|
3——4 |
| | | |
| 5—-|-6
|/ |/
1——2

“””

# Local helper function to compute area
def area(length, width):

“”” Computes the area of a length x width rectangle “””
return length * width

# Main code for surface_area function
# Compute area of front face
length = fabs(x2 – x1)
height = fabs(y3 – y1)
front_area = area(length, height)
# Compute area of side face
width = fabs(z5 – z1)
side_area = area(width, height)
# Compute area of top face
top_area = area(length, width)
# Compute and return surface area: front/back,
# left side/right side, and top/bottom faces
return 2*front_area + 2*side_area + 2*top_area

def volume(length, width, height):
“”” Computes the volume of a rectangular box

(cuboid) defined by its length, width, and height “””
return length * width * height

8.9. LOCAL FUNCTION DEFINITIONS 288

def get_point(msg):
“”” Prints a message specified by msg and allows the user to

enter the (x, y, z) coordinates of a point. Returns the
point as a tuple. “””

print(msg)
x = float(input(“Enter x coordinate: “))
y = float(input(“Enter y coordinate: “))
z = float(input(“Enter z coordinate: “))
return x, y, z

# Get the coordinates of the box’s corners from the user
print(‘Enter the coordinates of each of the box\’s corners’)
print(”’

7——8
/| /|
3——4 |
| | | |
| 5—-|-6
|/ |/
1——2
”’)

x1, y1, z1 = get_point(‘Corner 1’)
x2, y2, z2 = get_point(‘Corner 2’)
x3, y3, z3 = get_point(‘Corner 3’)
x4, y4, z4 = get_point(‘Corner 4’)
x5, y5, z5 = get_point(‘Corner 5’)
x6, y6, z6 = get_point(‘Corner 6’)
x7, y7, z7 = get_point(‘Corner 7’)
x8, y8, z8 = get_point(‘Corner 8’)

# Compute the surface area of the box
print(‘Surface area:’, surface_area(x1, y1, z1, x2, y2, z2,

x3, y3, z3, x4, y4, z4,
x5, y5, z5, x6, y6, z6,
x7, y7, z7, x8, y8, z8))

# Compute the volume of the box
ln = fabs(x2 – x1) # Compute length
wd = fabs(z5 – z1) # Compute width
ht = fabs(y3 – y1) # Compute height
print(‘Volume:’, volume(ln, wd, ht))

The following shows a sample run of Listing 8.24 (boxmeasure.py):

Enter the coordinates of each of the box’s corners

7——8
/| /|
3——4 |
| | | |
| 5—-|-6
|/ |/
1——2

8.9. LOCAL FUNCTION DEFINITIONS 289

Corner 1
Enter x coordinate: 0
Enter y coordinate: 0
Enter z coordinate: 0
Corner 2
Enter x coordinate: 2
Enter y coordinate: 0
Enter z coordinate: 0
Corner 3
Enter x coordinate: 0
Enter y coordinate: 2
Enter z coordinate: 0
Corner 4
Enter x coordinate: 2
Enter y coordinate: 2
Enter z coordinate: 0
Corner 5
Enter x coordinate: 0
Enter y coordinate: 0
Enter z coordinate: 2
Corner 6
Enter x coordinate: 2
Enter y coordinate: 0
Enter z coordinate: 2
Corner 7
Enter x coordinate: 0
Enter y coordinate: 2
Enter z coordinate: 2
Corner 8
Enter x coordinate: 2
Enter y coordinate: 2
Enter z coordinate: 2
Surface area: 24.0
Volume: 8.0

Only code within the surface_area function can use the area function. If we wanted to, we could define
a function named area local to the volume function, and, if we did, the two like-named functions would be
completely separate functions.

Local functions can access the local variables and other local functions defined by enclosing function.
As with the global functions we have seen before this section, any variable defined within a local function
is a local variable of that function. If we need a local function to modify a variable defined in its outer
scope (its enclosing function), we must declare the variable as nonlocal. The global keyword declares a
variable as truly global, so we cannot use the global keyword in place of nonlocal in this situation.

Listing 8.25 (localcounter.py) uses a local function to mimic a generator.

Listing 8.25: localcounter.py

def create_counter(n):
“”” Creates a counting function that counts up to n “””
count = 0

def counter(): # Local function
“”” Increments the outer variable unless it

8.9. LOCAL FUNCTION DEFINITIONS 290

has reached its limit “””
nonlocal count
if count < n: count += 1 return count return counter # Returns a function ctr = create_counter(4) print(ctr()) print(ctr()) print(ctr()) print(ctr()) print(ctr()) print(ctr()) Listing 8.25 (localcounter.py) prints 1 2 3 4 4 4 Note that the create_counter function returns a function; it returns its own local function. This returned local function “remembers” the value of its enclosing function’s local variable count; thus, it represents a closure (see Section 8.7). Since the count variable in the enclosing function is not global, no outside code can modify the count variable except by calling the function that create_counter returns. It may appear that create_counter is similar to a generator function (see Section 8.8). Unfortunately the create_counter function in Listing 8.25 (localcounter.py) does not create a generator object, as it has no yield statement. This means we cannot use it in a for statement, and it does not work with the global next function. As another example of a function returning a local closure, consider the calculation of a derivative. Those familiar with basic calculus will recall the derivative of a function f at a is defined to be f ′(a) = lim h→0 f (a+h)− f (a) h If you are unfamiliar with calculus, all you need to know is that the derivative of a function is itself a function; the above formula shows how to transform a function into its derivative. The process of computing a derivative is known as differentiation. The limh→0 notation indicates that the answer becomes more precise as the value h gets closer to zero. Letting h be exactly zero would result in division by zero, which is undefined. The trick is to make h as small as possible, keeping in mind that the computer’s floating-point values have limitations. Based on the mathematical definition we can define a Python function that computes the derivative of another function, as shown here: def derivative(f, h): return lambda x: (f(x + h) - f(x)) / h ©2017 Richard L. Halterman Draft date: January 18, 2018 8.9. LOCAL FUNCTION DEFINITIONS 291 Note that the derivative function returns a function—a lambda expression is a simple function defini- tion (see Section 8.7). The function that derivative returns is a closure because it captures the function parameters f and h. Our derivative function allows us to compute the derivative of a function at a given value. This is known as numerical differentiation. Another approach (the one emphasized in calculus courses) uses symbolic differentiation. Symbolic differentiation transforms the formula for a function into a different formula. The details of symbolic differentiation are beyond the scope of this text, but we will use one of its results for a particular function to check our computed numerical results. A particular function f is defined as follows: f (x) = 3x2 +5 If you have studied calculus, you can confirm that f ’s derivative, f ′, is: f ′(x) = 6x Without a knowledge of calculus, we can just accept this as the correct answer so we can test our derivative function. Listing 8.26 (derivative.py) uses the derivative function on f (x) = 3x2 + 5 and compares its results with the known solution, f ′(x) = 6x. Listing 8.26: derivative.py def derivative(f, h): """ Approximates the derivative of function f given an h value. The closer h is to zero, the better the estimate. """ return lambda x: (f(x + h) - f(x)) / h def fun(x): # The function we wish to differentiate return 3*x**2 + 5 def ans(x): # The known derivative to function fun return 6*x # Difference: Approximation better as h -> 0
h = 0.0000001

# Compute the function representing an approximation
# of the derivative of function fun
der = derivative(fun, h)

# Compare the computed derivative to the exact derivative
# derived symbolically
x = 5.0
print(‘——————————————————‘)
print(‘ Approx. Actual’)
print(‘ x f(x) h f\'(x) f\'(x)’)
print(‘——————————————————‘)
while x < 5.1: ©2017 Richard L. Halterman Draft date: January 18, 2018 8.10. DECORATORS 292 print('{:.5f} {:.5f} {:.8f} {:.5f} {:.5f}'.format(x, fun(x), h, der(x), ans(x))) x += 0.01 With h = 0.0000001, Listing 8.26 (derivative.py) produces good results to the fifth decimal place: ------------------------------------------------------ Approx. Actual x f(x) h f'(x) f'(x) ------------------------------------------------------ 5.00000 80.00000 0.00000010 30.00000 30.00000 5.01000 80.30030 0.00000010 30.06000 30.06000 5.02000 80.60120 0.00000010 30.12000 30.12000 5.03000 80.90270 0.00000010 30.18000 30.18000 5.04000 81.20480 0.00000010 30.24000 30.24000 5.05000 81.50750 0.00000010 30.30000 30.30000 5.06000 81.81080 0.00000010 30.36000 30.36000 5.07000 82.11470 0.00000010 30.42000 30.42000 5.08000 82.41920 0.00000010 30.48000 30.48000 5.09000 82.72430 0.00000010 30.54000 30.54000 5.10000 83.03000 0.00000010 30.60000 30.60000 Even with h as large as 0.01, the results are not too bad: ------------------------------------------------------ Approx. Actual x f(x) h f'(x) f'(x) ------------------------------------------------------ 5.00000 80.00000 0.01000000 30.03000 30.00000 5.01000 80.30030 0.01000000 30.09000 30.06000 5.02000 80.60120 0.01000000 30.15000 30.12000 5.03000 80.90270 0.01000000 30.21000 30.18000 5.04000 81.20480 0.01000000 30.27000 30.24000 5.05000 81.50750 0.01000000 30.33000 30.30000 5.06000 81.81080 0.01000000 30.39000 30.36000 5.07000 82.11470 0.01000000 30.45000 30.42000 5.08000 82.41920 0.01000000 30.51000 30.48000 5.09000 82.72430 0.01000000 30.57000 30.54000 5.10000 83.03000 0.01000000 30.63000 30.60000 In Listing 8.26 (derivative.py), the statement der = derivative(fun, h) assigns der to the function returned by derivative; thus, der(x) returns the value of the derivative of fun at x. In order for der to compute its answer, it must have access to function fun. It has this access because der is a closure that captured fun during the call to derivative. 8.10 Decorators In Section 8.9 we saw how we can define a function within another function. That section also showed how we can write a function that returns a function as its result. We can use these two abilities in a clever way to add functionality to arbitrary functions, even functions that we ourselves have not written. ©2017 Richard L. Halterman Draft date: January 18, 2018 8.10. DECORATORS 293 As a simple example, suppose we are building an application that uses a number of functions that accept two integer parameters and return an integer; Listing 8.27 (undecorated.py) provides some code to illustrate. Listing 8.27: undecorated.py from random import randrange def max(x, y): """ Determine the maximum of x and y """ return x if x > y else y

def gcd(m, n):
“””
Uses Euclid’s method to compute the greatest common divisor
(also called greatest common factor) of m and n.
Returns the GCD of m and n.
“””
if n == 0:

return m
else:

return gcd(n, m % n)

def summation(begin, end):
“”” Add up the integers in the range begin…end – 1, inclusive “””
sum = 0
while begin != end:

sum += begin
begin += 1

return sum

def star_rect(length, width):
“”” Draw a length x width rectangle with asterisks “””
for row in range(length):

print(‘* ‘ * width)

print(“The maximum of 20 and 30 is”, max(20, 30))
print(“The maximum of 30 and 20 is”, max(30, 20))
print(“The maximum of 20 and 20 is”, max(20, 20))
print(‘————————‘)

print(“The GCD of 20 and 30 is”, gcd(20, 30))
print(“The GCD of 30 and 20 is”, gcd(30, 20))
print(“The GCD of 20 and 20 is”, gcd(20, 20))
print(‘————————‘)

print(“The summation from 20 to 30 is”, summation(20, 30))
print(‘————————‘)

star_rect(7, 3)
print(‘————————‘)
star_rect(4, 4)
print(‘————————‘)
star_rect(2, 5)

8.10. DECORATORS 294

print(‘————————‘)

print(randrange(10, 21), “is a pseudorandom integer in the range 10 to 20, inclusive”)

When executed, Listing 8.27 (undecorated.py) displays

The maximum of 20 and 30 is 30
The maximum of 30 and 20 is 30
The maximum of 20 and 20 is 20
————————
The GCD of 20 and 30 is 10
The GCD of 30 and 20 is 10
The GCD of 20 and 20 is 20
————————
The summation from 20 to 30 is 245
————————
* * *
* * *
* * *
* * *
* * *
* * *
* * *
————————
* * * *
* * * *
* * * *
* * * *
————————
* * * * *
* * * * *
————————
14 is a pseudorandom integer in the range 10 to 20, inclusive

The pseudorandom number displayed will vary, but the rest of the output will be the same whenever the
program runs.

During testing we would like every call to any of these functions (and any of the possibly hundreds
more functions that make up the application) to report the function’s arguments and return value. Ideally
we would write this information to a log file, but, here we simply will print the information. One approach
would be to modify each function temporarily for testing purposes, as Listing 8.28 (poorlydecorated.py)
demonstrates

Listing 8.28: poorlydecorated.py

from random import randrange

def max(x, y):
“”” Determine the maximum of x and y “””
call_string = “max({}, {})”.format(x, y)
print(“>>> Calling ” + call_string)
result = x if x > y else y
print(“<<< Returning {} from ".format(result) + call_string) return result ©2017 Richard L. Halterman Draft date: January 18, 2018 8.10. DECORATORS 295 def gcd(m, n): """ Uses Euclid's method to compute the greatest common divisor (also called greatest common factor) of m and n. Returns the GCD of m and n. """ call_string = "gcd({}, {})".format(m, n) print(">>> Calling ” + call_string)
if n == 0:

result = m
else:

result = gcd(n, m % n)
print(“<<< Returning {} from ".format(result) + call_string) return result def summation(begin, end): """ Add up the integers in the range begin...end - 1, inclusive """ call_string = "summation({}, {})".format(begin, end) print(">>> Calling ” + call_string)
sum = 0
while begin != end:

sum += begin
begin += 1

print(“<<< Returning {} from ".format(sum) + call_string) return sum def star_rect(length, width): """ Draw a length x width rectangle with asterisks """ call_string = "star_rect({}, {})".format(length, width) print(">>> Calling ” + call_string)
for row in range(length):

print(‘* ‘ * width)
print(“<<< Returning {} from ".format(None) + call_string) # This time just call the functions, and let each function print its # parameter and result details. max(20, 30) print('------------------------') max(30, 20) print('------------------------') max(20, 20) print('------------------------') gcd(20, 30) print('------------------------') gcd(30, 20) print('------------------------') gcd(20, 20) print('------------------------') summation(20, 30) print('------------------------') star_rect(7, 3) ©2017 Richard L. Halterman Draft date: January 18, 2018 8.10. DECORATORS 296 print('------------------------') star_rect(4, 4) print('------------------------') star_rect(2, 5) print('------------------------') print(randrange(10, 21), "is a pseudorandom integer in the range 10 to 20, inclusive") Note that we print information at the beginning of the function’s execution, indicated by the prefix >>>
(for entering the function). We also print some information prefixed with <<< at the end of the function’s execution (for leaving the function). This allows our output to be readable even for functions that do their own printing like star_rect. It also allows us to better track recursive function invocations like gcd. Listing 8.28 (poorlydecorated.py) displays >>> Calling max(20, 30)
<<< Returning 30 from max(20, 30) ------------------------ >>> Calling max(30, 20)
<<< Returning 30 from max(30, 20) ------------------------ >>> Calling max(20, 20)
<<< Returning 20 from max(20, 20) ------------------------ >>> Calling gcd(20, 30)
>>> Calling gcd(30, 20)
>>> Calling gcd(20, 10)
>>> Calling gcd(10, 0)
<<< Returning 10 from gcd(10, 0) <<< Returning 10 from gcd(20, 10) <<< Returning 10 from gcd(30, 20) <<< Returning 10 from gcd(20, 30) ------------------------ >>> Calling gcd(30, 20)
>>> Calling gcd(20, 10)
>>> Calling gcd(10, 0)
<<< Returning 10 from gcd(10, 0) <<< Returning 10 from gcd(20, 10) <<< Returning 10 from gcd(30, 20) ------------------------ >>> Calling gcd(20, 20)
>>> Calling gcd(20, 0)
<<< Returning 20 from gcd(20, 0) <<< Returning 20 from gcd(20, 20) ------------------------ >>> Calling summation(20, 30)
<<< Returning 245 from summation(20, 30) ------------------------ >>> Calling star_rect(7, 3)
* * *
* * *
* * *
* * *
* * *
* * *

8.10. DECORATORS 297

* * *
<<< Returning None from star_rect(7, 3) ------------------------ >>> Calling star_rect(4, 4)
* * * *
* * * *
* * * *
* * * *
<<< Returning None from star_rect(4, 4) ------------------------ >>> Calling star_rect(2, 5)
* * * * *
* * * * *
<<< Returning None from star_rect(2, 5) ------------------------ 17 is a pseudorandom integer in the range 10 to 20, inclusive Listing 8.28 (poorlydecorated.py) displays the information we need, but it comes at considerable cost: 1. We must modify every function with the augmented functionality, and it may involve hundreds of functions in the full application. 2. We must ensure we modify every one of the functions correctly; since each function has different parameter names we simply cannot copy and paste code and use it as is. For functions with return statements that involve an expression with multiple components (as in the original max function), we must introduce a local variable to print and then return that variable. We must be particularly careful, as mistakes here can alter the function’s logic. 3. Once we are finished testing we must put the functions back to their original state. This act of modifying the functions and then changing them back provides ample opportunities for introducing errors into a function that originally contained correct code. This process is labor intensive and too problematic to use as a general technique. Another serious problem involves functions over which we have no control. In our code, for example, we cannot (or, better, should not) modify the randrange function to provide the call details we seek. The randrange function is part of a library function maintained by someone else. If we attempt to change the contents of the random module’s source code, there is a good chance we could introduce an error. Modifying code within a library, therefore, reduces its trustworthiness. Enhancing randrange by modifying its source code is not a viable option. We really need a way to augment the functions in a uniform way without modifying them. This may seem like an impossible task, but Python’s ability to pass functions as arguments and define local functions makes it possible. Consider the following function: def show_call_and_return_details(f): """ f is a function that accepts two arguments. """ func_name = f.__name__ # Get the function's name def execute_augmented(x, y): call_string = "{}({}, {})".format(func_name, x, y) print(">>> Calling ” + call_string)
result = f(x, y)

8.10. DECORATORS 298

print(“<<< Returning {} from ".format(result) + call_string) return result return execute_augmented This show_call_and_return_details accepts a single function as a parameter. It “wraps” the func- tion in some additional code within a local function. The show_call_and_return_details function finally returns this local function to its caller. Listing 8.29 (simpledecorator.py) shows how we can use the show_call_and_return_details function to achieve our goal of printing details about function calls without modifying the code of the individual functions. Listing 8.29: simpledecorator.py from random import randrange def show_call_and_return_details(f): """ Decorates a function f so its call will display the parameter values and return value. """ func_name = f.__name__ # Get the function's name def execute_augmented(x, y): call_string = "{}({}, {})".format(func_name, x, y) print(">>> Calling ” + call_string)
result = f(x, y)
print(“<<< Returning {} from ".format(result) + call_string) return result return execute_augmented def max(x, y): """ Determine the maximum of x and y """ return x if x > y else y

def gcd(m, n):
“””
Uses Euclid’s method to compute the greatest common divisor
(also called greatest common factor) of m and n.
Returns the GCD of m and n.
“””
if n == 0:

return m
else:

return gcd(n, m % n)

def summation(begin, end):
“”” Add up the integers in the range begin…end – 1, inclusive “””
sum = 0
while begin != end:

sum += begin
begin += 1

return sum

def star_rect(length, width):
“”” Draw a length x width rectangle with asterisks “””
for row in range(length):

print(‘* ‘ * width)

8.10. DECORATORS 299

# Decorate the functions to provide information about their calls
# We can make up a new name
augmented_max = show_call_and_return_details(max)
# Or, more typically, simply redirect the original name to a new function!
gcd = show_call_and_return_details(gcd)
summation = show_call_and_return_details(summation)
star_rect = show_call_and_return_details(star_rect)
randrange = show_call_and_return_details(randrange)

augmented_max(20, 30)
print(‘————————‘)
augmented_max(30, 20)
print(‘————————‘)
augmented_max(20, 20)
print(‘————————‘)

gcd(20, 30)
print(‘————————‘)
gcd(30, 20)
print(‘————————‘)
gcd(20, 20)
print(‘————————‘)

summation(20, 30)
print(‘————————‘)

star_rect(7, 3)
print(‘————————‘)
star_rect(4, 4)
print(‘————————‘)
star_rect(2, 5)
print(‘————————‘)

print(randrange(10, 21), “is a pseudorandom integer in the range 10 to 20, inclusive”)

Listing 8.29 (simpledecorator.py) defines the original, unmodified functions from Listing 8.27 (undecorated.py)
and adds five statements that redirect each of the functions to their augmented equivalents. The first state-
ment creates a new function name, while the other four reassign the original function’s name. Listing 8.29
(simpledecorator.py) displays

>>> Calling max(20, 30)
<<< Returning 30 from max(20, 30) ------------------------ >>> Calling max(30, 20)
<<< Returning 30 from max(30, 20) ------------------------ >>> Calling max(20, 20)
<<< Returning 20 from max(20, 20) ------------------------ >>> Calling gcd(20, 30)
>>> Calling gcd(30, 20)
>>> Calling gcd(20, 10)
>>> Calling gcd(10, 0)
<<< Returning 10 from gcd(10, 0) ©2017 Richard L. Halterman Draft date: January 18, 2018 8.10. DECORATORS 300 <<< Returning 10 from gcd(20, 10) <<< Returning 10 from gcd(30, 20) <<< Returning 10 from gcd(20, 30) ------------------------ >>> Calling gcd(30, 20)
>>> Calling gcd(20, 10)
>>> Calling gcd(10, 0)
<<< Returning 10 from gcd(10, 0) <<< Returning 10 from gcd(20, 10) <<< Returning 10 from gcd(30, 20) ------------------------ >>> Calling gcd(20, 20)
>>> Calling gcd(20, 0)
<<< Returning 20 from gcd(20, 0) <<< Returning 20 from gcd(20, 20) ------------------------ >>> Calling summation(20, 30)
<<< Returning 245 from summation(20, 30) ------------------------ >>> Calling star_rect(7, 3)
* * *
* * *
* * *
* * *
* * *
* * *
* * *
<<< Returning None from star_rect(7, 3) ------------------------ >>> Calling star_rect(4, 4)
* * * *
* * * *
* * * *
* * * *
<<< Returning None from star_rect(4, 4) ------------------------ >>> Calling star_rect(2, 5)
* * * * *
* * * * *
<<< Returning None from star_rect(2, 5) ------------------------ >>> Calling randrange(10, 21)
<<< Returning 14 from randrange(10, 21) 14 is a pseudorandom integer in the range 10 to 20, inclusive In Listing 8.29 (simpledecorator.py), the show_call_and_return_details function is known as a deco- rator. A decorator does not change the way a function works; it simply adds some “decoration” to the function, usually to augment the function’s behavior. A decorator “wraps” a function passed to it. Observe that a decorator cannot modify the inner workings of a function. Our example shows that a decorator can do some preprocessing (activity before calling the function it wraps) and postprocessing (activity after calling the function it wraps). A particular decorator could call a different function instead of the function it wraps. This ability to decorate functions is so important that Python provides a special syntax to support it. We can use this special syntax for functions that we write. To see how it works, we will define our ©2017 Richard L. Halterman Draft date: January 18, 2018 8.10. DECORATORS 301 show_call_and_return_details function exactly as before. In the line before each function we wish to decorate we will add the following decoration: @show_call_and_return_details Our max function definition from Listing 8.29 (simpledecorator.py) would become @show_call_and_return_details def max(x, y): """ Determine the maximum of x and y """ return x if x > y else y

With the definition adjusted as shown the caller can use max as is without first calling the show_call_return_details
function. Listing 8.30 (decorator.py) updates Listing 8.29 (simpledecorator.py) with decorated functions.

Listing 8.30: decorator.py

from random import randrange

def show_call_and_return_details(f):
“”” Decorates a function f so its call will display the

parameter values and return value. “””
func_name = f.__name__ # Get the function’s name
def execute_augmented(x, y):

call_string = “{}({}, {})”.format(func_name, x, y)
print(“>>> Calling ” + call_string)
result = f(x, y)
print(“<<< Returning {} from ".format(result) + call_string) return result return execute_augmented @show_call_and_return_details def max(x, y): """ Determine the maximum of x and y """ return x if x > y else y

@show_call_and_return_details
def gcd(m, n):

“””
Uses Euclid’s method to compute the greatest common divisor
(also called greatest common factor) of m and n.
Returns the GCD of m and n.
“””
if n == 0:

return m
else:

return gcd(n, m % n)

@show_call_and_return_details
def summation(begin, end):

“”” Add up the integers in the range begin…end – 1, inclusive “””
sum = 0
while begin != end:

sum += begin
begin += 1

8.10. DECORATORS 302

return sum

@show_call_and_return_details
def star_rect(length, width):

“”” Draw a length x width rectangle with asterisks “””
for row in range(length):

print(‘* ‘ * width)

# Decorate the randrange function as before; we cannot alter its
# source code
randrange = show_call_and_return_details(randrange)

max(20, 30)
print(‘————————‘)
max(30, 20)
print(‘————————‘)
max(20, 20)
print(‘————————‘)

gcd(20, 30)
print(‘————————‘)
gcd(30, 20)
print(‘————————‘)
gcd(20, 20)
print(‘————————‘)

summation(20, 30)
print(‘————————‘)

star_rect(7, 3)
print(‘————————‘)
star_rect(4, 4)
print(‘————————‘)
star_rect(2, 5)
print(‘————————‘)

print(randrange(10, 21), “is a pseudorandom integer in the range 10 to 20, inclusive”)

When executed, Listing 8.30 (decorator.py) behaves exactly as Listing 8.29 (simpledecorator.py).

Since we do not control the definition of the randrange function we cannot decorate its definition using
the special @ syntax. As Listing 8.30 (decorator.py) shows, however, we can decorate it in the manner shown
earlier in Listing 8.29 (simpledecorator.py).

Decorators open the door to many interesting possibilities. Suppose you wish remove all functionality
from a function that accepts two parameters. The following decorator would work:

def nullify(f):
“”” A decorator that guts the functionality of a function that

requires two parameters. “””
def empty_func(x, y):

“”” This function does nothing and returns None “””
pass

return empty_func

8.11. PARTIAL APPLICATION 303

Our max function decorated as such:

@nullify
def max(x, y):

“”” Determine the maximum of x and y “””
return x if x > y else y

would do nothing when called! If in Listing 8.30 (decorator.py) we changed all the show_call_and_result_details
decorators to be nullify decorators, the program would print

————————
————————
————————
————————
————————
————————
————————
————————
————————
————————
None is a pseudorandom integer in the range 10 to 20, inclusive

[Add decorator to time a function.]

The necessity to define a particular number of parameters for the function that the decorator wraps
significantly reduces the decorator’s generality. Fortunately, we are limited now only by our current knowl-
edge of Python; Chapter 11 introduces the Python concepts that enable us to design decorators that apply
to functions accepting any number of parameters.

8.11 Partial Application

In Section 8.5 we saw how we can pass functions as arguments to other functions. Section 8.7 showed
how a function could serve as a return value from another function. The functools module provides
an interesting function named partial that accepts a function as its first parameter and one or more other
parameters. The partial function returns a new function that is behaviorally related to the original function
passed to it. To see what partial does, consider the function add:

def add(x, y):
return x + y

The add function expects two arguments. The interpreter will not allow a caller to pass fewer than two or
more than two parameters. Given the following import statement:

from functools import partial

we can use the partial function to make a new addition function that requires only one argument:

add5 = partial(add, 5)

This new add5 function accepts a single parameter. An example call would be

print(add5(3)) # Works like print(add(5, 3))

8.11. PARTIAL APPLICATION 304

The add5 invocation calls the original add function with 5 as the first argument and add5’s parameter, 3, as
the second argument.

This technique is known as partial application. Partial application allows us to make a new function
from an existing function with one or more of the original function’s actual parameters “hardwired” into
the definition. This new function exhibits the same behavior as the original function but requires fewer
parameters during its call.

Partial application can predetermine only leading parameters. It is not possible to predetermine a
parameter that follows a non-predetermined parameter.

Partial application is a rarely used, advanced Python feature, but we can illustrate its utility in a simple
program. Consider a program meant to compare a dice throw simulation to the behavior of a pair of real,
physical dice. Suppose a person performs an experiment with a pair of dice, rolling them hundreds of times
and recording the result each time. The number recorded is the sum of the numbers on both dice. Since
each die face contains one, two, three, four, five, or six spots, the outcome of a roll of two dice can be any
number in the range 2–12, inclusive. The person conducting the experiment records the results in a text file
named dicedata.data.

The following function opens a text file expecting a list of integer values representing the outcomes of
hundreds of dice rolls.

def read_file(filename, n, val):
“”” Reads n integers from the text file named filename.

Returns the number of times val appears in the file. “””
count, read = 0, 0
with open(filename, ‘r’) as f:

for value in f.readlines():
read += 1
# Have we read enough values in yet?
if read > n:

break
# Convert text integer into an actual integer
if int(value) == val:

count += 1
return count

The read_file’s parameters consist of the name of the file to process (filename), the number of outcomes
to consider (n), and the outcome value to count (val). By passing in the file name, read_file can flexibly
handle any data files of the proper format. The expectation is that the file will be very large, and the
parameter n limits how much of the data the function processes.

Now we need our program to perform the same experiment, simulating dice rolls using a pseudorandom
number generator (see Section 6.6 for a review of pseudorandom number generation). The following func-
tion simulates rolling a pair of dice a given number of times and counts the number of times a particular
value appears:

def roll(n, val):
“”” Simulates the roll of a pair of dice n times.

Returns the number of times a roll resulted in val. “””
count = 0
for i in range(n):

roll = randint(1, 6) + randint(1, 6)
if roll == val:

8.11. PARTIAL APPLICATION 305

count += 1
return count

The roll function does not need any file name since it generates the numbers itself. The function otherwise
behaves similarly to read_file.

The following run_trials function performs the experiment with a given number of throws and counts
the number of times each outcome occurs:

def run_trials(f, n):
“”” Performs n experiments using function f as the source of

outcomes. Counts the number of occurrences of each possible
outcome. “””

for value in range(2, 13):
print(“{:>3}:{:>5}”.format(value, f(n, value)))

Observe that run_trials invokes function f passing to it two values.

Our roll function is perfectly compatible as a potential f parameter for run_trials, but read_file is
not. The read_file function requires three parameters, not two. Is there any way we can make read_file
compatible with run_trials?

Partial application comes to our rescue. The read_file function flexibly works with any appropriate
data file, but run_trials cannot by itself handle this flexibility. The expression

partial(read_file, ‘dicedata.data’)

evaluates to a new function that, when invoked, will invoke read_file with the string ‘dicedata.data’
hardwired as the first parameter. This new function accepts just two parameters (the remaining parameters
n and val left over from read_file) and so will work perfectly as the first argument to run_trials.

Listing 8.31 (comparerolls.py) pulls everything together into an executable program.

Listing 8.31: comparerolls.py

from random import randint
from functools import partial

def read_file(filename, n, val):
“”” Reads n integers from the text file named filename.

Returns the number of times val appears in the file. “””
count, read = 0, 0
with open(filename, ‘r’) as f:

for value in f.readlines():
read += 1
# Have we read enough values in yet?
if read > n:

break
# Convert text integer into an actual integer
if int(value) == val:

count += 1
return count

8.12. EXERCISES 306

def roll(n, val):
“”” Simulates the roll of a pair of dice n times.

Returns the number of times a roll resulted in val. “””
count = 0
for i in range(n):

roll = randint(1, 6) + randint(1, 6)
if roll == val:

count += 1
return count

def run_trials(f, n):
“”” Performs n experiments using function f as the source of

outcomes. Counts the number of occurrences of each possible
outcome. “””

for value in range(2, 13):
print(“{:>3}:{:>5}”.format(value, f(n, value)))

# Compare the actual experiments to the simulation
number_of_trials = 100
print(‘— Pseudorandom number rolls —‘)
run_trials(roll, number_of_trials)
print(‘— Actual experimental data —‘)
run_trials(partial(read_file, ‘dicedata.data’), number_of_trials)

Given the simplicity of Listing 8.31 (comparerolls.py), you may be thinking of ways to rewrite the code
to avoid using partial application. Restructuring this code is indeed an option, since we have total control
over it. Partial application really shines when we need to interface with library functions over which we
have no control. Partial application is a tool that sometimes is handy for quickly adapting an existing
function to the requirements of a library developed by others.

8.12 Exercises

1. Consider the following Python code:

def sum1(n):
s = 0
while n > 0:

s += 1
n -= 1

return s

def sum2():
global val
s = 0
while val > 0:

s += 1
val -= 1

return s

8.12. EXERCISES 307

def sum3():
s = 0
for i in range(val, 0, -1):

s += 1
return s

def main():
# See each question below for details

main() # Call main function

(a) What is printed if main is written as follows?

def main():
global val
val = 5
print(sum1(5))
print(sum2())
print(sum3())

(b) What is printed if main is written as follows?

def main():
global val
val = 5
print(sum1(5))
print(sum3())
print(sum2())

def main():
global val
val = 5
print(sum2())
print(sum1(5))
print(sum3())

(d) Which of the functions sum1, sum2, and sum3 produce a side effect? What is the side effect?

(e) Which function may not use the val variable?

(f) What is the scope of the variable val? What is its lifetime?

(g) What is the scope of the variable i? What is its lifetime?

(h) Which of the functions sum1, sum2, and sum3 demonstrate good functional independence?
Why?

2. Consider the following Python code:

def next_int1():
cnt = 0
cnt += 1
return cnt

8.12. EXERCISES 308

global_count = 0

def next_int2():
global_count += 1
return global_count

def main():
for i = range(0, 5):

print(next_int1(), next_int2())

main()

(a) What does the program print?

(b) Which of the functions next_int1 and next_int2 is the best function for the intended purpose?
Why?

(d) The next_int2 function works in this context, but why is it not a good implementation of
function that always returns the next largest integer?

3. When is the global statement required?

4. What does the following Python program print?

def sum(m=0, n=0, r=0):
return m + n + r

def main():
print(sum())
print(sum(4))
print(sum(4, 5))
print(sum(5, 4))
print(sum(1, 2, 3))
print(sum(2.6, 1.0, 3))

main()

5. Consider the following function:

def proc(n):
if n < 1: return 1 else: return proc(n/2) + proc(n - 1) Evaluate each of the following expressions: (a) proc(0) ©2017 Richard L. Halterman Draft date: January 18, 2018 8.12. EXERCISES 309 (b) proc(1) (c) proc(2) (d) proc(3) (e) proc(5) (f) proc(10) 6. Rewrite the gcd function so that it implements Euclid’s method but uses iteration instead of recursion. 7. Classify the following functions as pure or impure. x is a global variable. (a) def f1(m, n): return 2*m + 3*n (b) def f2(n) return n - 2 (c) def f3(n): return n - x (d) def f4(n): print(2*n) (e) def f5(n): m = int(input()) return m * n (f) def f6(n): m = 2*n p = 2*m - 5 return p - n 8. Consider the following very simple module, found in the file mymod.py: """ Provides the increment function, increment. """ def increment(x): """ Increments x by 1 and returns the result. """ return x + 1 A programmer wishes to use the increment function from the mymod.py module. Indicate which, if any, of the following code snippets would work: (a) import mymod print(increment(4)) # Supposed to print 5 import from mymod import increment print(increment(4)) # Supposed to print 5 ©2017 Richard L. Halterman Draft date: January 18, 2018 8.12. EXERCISES 310 (b)(c) import mymod print(mymod.increment(4)) # Supposed to print 5 from mymod import increment print(mymod.increment(4)) # Supposed to print 5 (d)9. Modify the main function in Listing 8.23 (generatedprimes.py) that so that it prints all the prime numbers less than 1,000 that contain the digit 2 or digit 3 (or both). 10. Write a generator function named evens that enables the following code: for n in evens_less_than(12): print(n, end=' ') print() to print 2 4 6 8 10 that is, all positive even numbers less than 12. 11. Functions as data TODO Consider the following function definition: def f(): pass 12. Lambda expressions TODO 13. Write a generator function named oscillate that enables the following code: for n in oscillate(-3, 5): print(n, end=' ') print() to print -3 3 -2 2 -1 1 0 0 1 -1 2 -2 3 -3 4 -4 14. Local functions TODO 15. Partial application TODO ©2017 Richard L. Halterman Draft date: January 18, 2018 311 Chapter 9 Objects In the hardware arena, a personal computer is built by assembling a motherboard (a circuit board contain- ing sockets for a microprocessor and assorted support chips), a processor, memory, a video card, a disk controller, a disk drive, a case, a keyboard, a mouse, and a monitor. The video card by itself is a sophisti- cated piece of hardware containing a video processor chip, memory, and other electronic components. A technician does not need to assemble the card; the card is used as is off the shelf. The video card provides a substantial amount of functionality in a standard package. One video card can be replaced with another card from a different vendor or with another card with different capabilities. The overall computer will work with either card (subject to availability of drivers for the operating system) because standard interfaces allow the components to work together. Software development today is increasingly component based. Software components are used like hardware components. A software system can be built largely by assembling pre-existing software building blocks. Python supports various kinds of software building blocks. The simplest of these is the function that we investigated in Chapter 6 and Chapter 7. A more powerful technique uses software objects. Python is object oriented. Most modern programming languages support object-oriented (OO) develop- ment to one degree or another. An OO programming language allows the programmer to define, create, and manipulate objects. Objects bundle together data and functions. Like other variables, each Python object has a type, or class. The terms class and type are synonymous. In this chapter we explore some of the classes available in the Python standard library. 9.1 Using Objects An object is an instance of a class. We have been using objects since the beginning, but we have not taken advantage of all the capabilities that objects provide. Integers, floating-point numbers, strings, and functions are all objects in Python. With the exception of function objects, we have treated these objects as passive data. We can assign an integer value to a variable and then use that variable’s value. We can add two floating-point numbers and concatenate two strings with the + operator. We can pass objects to functions and functions can return objects. In object-oriented programming, rather than treating data as passive values and functions as active agents that manipulate data, we fuse data and functions together into software units called objects. A typical object consists of two parts: data and methods. An object’s data consists of its instance variables. The term ©2017 Richard L. Halterman Draft date: January 18, 2018 9.2. STRING OBJECTS 312 instance variable comes from the fact that the data is represented by a variable owned by an object, and an object is an instance of a class. Other names for instance variables include attributes and fields. Methods are like functions, and they are known also as operations. The instance variables and methods of an object constitutes the object’s members. The code that uses an object is called the object’s client. We say that an object provides a service to its clients. The services provided by an object can be more elaborate that those provided by simple functions because objects make it easy to store persistent data in their instance variables. 9.2 String Objects We have been using string objects—instamces of class str—for some time. Objects bundle data and functions together, and the data that comprise a string consist of the sequence of characters that make up the string. We now turn our attention to string methods. Listing 9.1 (stringupper.py) shows how a programmer can use the upper method available to string objects. Listing 9.1: stringupper.py name = input("Please enter your name: ") print("Hello " + name.upper() + ", how are you?") Listing 9.1 (stringupper.py) capitalizes (converts to uppercase) all the letters in the string the user enters: Please enter your name: Rick Hello RICK, how are you? The expression name.upper() within the print statement represents a method call. The general form of a method call is method nameobject . parameter list( ) • object is an expression that represents object. In the example in Listing 9.1 (stringupper.py), name is a reference to a string object. • The period, pronounced dot, associates an object expression with the method to be called. • methodname is the name of the method to execute. • The parameterlist is comma-separated list of parameters to the method. For some methods the pa- rameter list may be empty, but the parentheses always are required. The parameter list for a method call works exactly like the parameter list for a function call. ©2017 Richard L. Halterman Draft date: January 18, 2018 9.2. STRING OBJECTS 313 Except for the object prefix, a method call works like a function call. It can return a value to its caller. The upper method returns a new string. The upper method does not affect the object upon which it is called; this means name.upper() does not modify the name object. A method may accept parameters. Listing 9.2 (rjustprog.py), uses the rjust string method to right justify a string padded with a specified character. Listing 9.2: rjustprog.py word = "ABCD" print(word.rjust(10, "*")) print(word.rjust(3, "*")) print(word.rjust(15, ">“))
print(word.rjust(10))

The output of Listing 9.2 (rjustprog.py):

******ABCD
ABCD
>>>>>>>>>>>ABCD

ABCD

shows

• word.rjust(10, “*”) right justifies the string “ABCD” within a 10-character horizontal area padded
with * characters.

• word.rjust(3, “*”) does not return a different string from the original “ABCD” since the specified
width (3) is less than or equal to the length of the original string (4).

• word.rjust(10) shows that the default padding character is a space.

The following interactive sequence shows that we can call a method from a string literal:

>>> ‘aBcDeFgHiJ’.upper()
‘ABCDEFGHIJ’
>>> ‘This is a sentence.’.rjust(25, ‘-‘)
‘——This is a sentence.’

This syntax may look somewhat familiar; we introduced the string format method in Section 2.8 and
invoked it with a string literal. We also can use a string variable, as shown here:

>>> ‘{0} {1}’.format(23, 9)
’23 9′
>>> s = ‘{0} {1}’
>>> s.format(23, 9)
’23 9′

Table 9.1 lists some of the methods available to str objects.

9.2. STRING OBJECTS 314

Table 9.1 A few of the methods available to str objects
str Methods

upper
Returns a copy of the original string with all the characters converted to uppercase

lower
Returns a copy of the original string with all the characters converted to lower case

rjust
Returns a string right justified within an area padded with a specified character which de-
faults to a space

ljust
Returns a string left justified within an area padded with a specified character which de-
faults to a space

center
Returns a copy of the string centered within an area of a given width and optional fill
characters; fill characters default to spaces

strip
Returns a copy of the given string with the leading and trailing whitespace removed; if
provided an optional string, the strip function strips leading and trailing characters found
in the parameter string

startswith
Determines if the string parameter is a prefix of the invoking string

endswith
Determines if the string parameter is a suffix of the invoking string

count
Determines the number times the string parameter is found as a substring within the invok-
ing string; the count includes only non-overlapping occurrences

find
Returns the lowest index where the string parameter is found as a substring of the invoking
string; returns −1 if the parameter is not a substring of the invoking string

format
Embeds formatted values in a string using {0}, {1}, etc. position parameters

Listing 9.3 (stripandcount.py) demonstrates two of the string methods.

Listing 9.3: stripandcount.py

# Strip leading and trailing whitespace and count substrings
s = ” ABCDEFGHBCDIJKLMNOPQRSBCDTUVWXYZ ”
print(“[“, s, “]”, sep=””)
s = s.strip()
print(“[“, s, “]”, sep=””)

# Count occurrences of the substring “BCD”
print(s.count(“BCD”))

Listing 9.3 (stripandcount.py) displays:

[ ABCDEFGHBCDIJKLMNOPQRSBCDTUVWXYZ ]
[ABCDEFGHBCDIJKLMNOPQRSBCDTUVWXYZ]

9.2. STRING OBJECTS 315

The str class provides a __getitem__ method that returns the character at a given position within the
string. Since the method’s name begins with two underscores (__), the method is meant for internal class
use and not for clients. The __getitem__ method is special, as clients can access it via a special syntax:

>>> s = ‘ABCEFGHI’
>>> s
‘ABCEFGHI’
>>> s.__getitem__(0)
‘A’
>>> s.__getitem__(1)
‘B’
>>> s.__getitem__(2)
‘C’
>>> s[0]
‘A’
>>> s[1]
‘B’
>>> s[2]
‘C’

The square brackets when used with an object in the manner shown above invoke that object’s __getitem__
method. In the case of string objects the integer within the square brackets, known as an index, represents
the distance from the beginning of the string from which to obtain a character. For string s, s[0] is the first
character in the string, s[1] is the second character, as so forth.

Strings also provide a __len__ method that returns the number of characters that make up the string.
Again, since the name __len__ begins with two underscores, clients are supposed to invoke it in a different
way. The following shows the preferred way of determining a string’s length:

>>> s
‘ABCEFGHI’
>>> s = ‘ABCEFGHI’
>>> s
‘ABCEFGHI’
>>> len(s)
8
>>> s.__len__()
8

The expressions len(s) and s.__len__() are functionally equivalent. Instead of calling the __len__
method directly, clients should use the global len function. Listing 9.4 (printcharacters.py) uses the len
function and [] index operator to print the individual characters that make up a string.

Listing 9.4: printcharacters.py

s = “ABCDEFGHIJK”
print(s)
for i in range(len(s)):

print(“[“, s[i], “]”, sep=””, end=””)
print() # Print newline

for ch in s:

9.3. FILE OBJECTS 316

print(“<", ch, ">“, sep=””, end=””)
print() # Print newline

Strings are immutable objects. This means we cannot modify the contents of a string object:

s = ‘ABCDEFGHIJKLMN’
s[3] = ‘S’ # Illegal, strings are immutable

String immutability means a method such as strip may not change a given string:

s = ” ABC ”
s.strip() # s is unchanged
print(“<" + s + ">“) # Prints < ABC >, not

In order to strip the leading and trailing whitespace as far as the string bound to the variable s is concerned,
we must reassign s:

s = ” ABC ”
s = s.strip() # Note the reassignment
print(“<" + s + ">“) # Prints

The strip method returns a new string; the string on whose behalf strip is called is not modified. To
effectively strip the whitespace from a string, a client must, as in this example, reassign its variable to the
string passed back by the strip method.

When treated as a Boolean expression, the empty string (”) is interpreted as False, and all other strings
are considered True.

9.3 File Objects

So far all the programs we have seen lose their data at the end of their execution. Most useful applications,
however, require greater data persistence. Imagine using a word processor that does not allow you to save
your document and retrieve it later for further editing. Most modern operating systems store persistent data
in files. A word processor, for example, could store one of its documents in a file named thesis.doc.

Fortunately, Python’s standard library has a file class that makes it easy for programmers to make objects
that can store data to, and retrieve data from, disk. The formal name of the class of file objects we will be
using is TextIOWrapper, and it is found in the io module. Since file processing is such a common activity,
the functions and classes defined in the io module are available to any program, and no import statement
is required.

The statement

f = open(‘myfile.txt’, ‘r’)

creates and returns a file object (literally a TextIOWrapper object) named f. The first argument to open is
the name of the file, and the second argument is a mode. The open function supports the following modes:

• ‘r’ opens the file for reading

• ‘w’ opens the file for writing; creates a new file

• ‘a’ opens the file to append data to it

9.3. FILE OBJECTS 317

The statement

f = open(‘myfile.txt’, ‘r’)

creates a file object named f capable of reading the contents of the text file named myfile.txt. If the file does
not exist or the user of the program does not have adequate permissions to open the file, the open function
will raise an exception.

The statement

f = open(‘myfile.txt’, ‘w’)

creates and returns a file object named f capable of writing data to the text file named myfile.txt. If the file
does not exist, the function creates the file on disk. If a file by that name currently exists, new data will
replace the current data stored in the file. This means any pre-existing data in the file will be lost.

The statement

f = open(‘myfile.txt’, ‘a’)

creates and returns a file object named f capable of writing data to the text file named myfile.txt. If the file
does not exist, the function creates the file on disk. If a file by that name currently exists, new data will be
appended after the pre-existing data in that file. This means that the original data in the file is not lost.

If the second argument to the open function is missing, it defaults to ‘r’, so the statement

f = open(fname)

is equivalent to

f = open(fname, ‘r’)

Once you have a file object capable of writing (opened with ‘w’ or ‘a’) you can save data to the file
associated with that file object using the write method. For a file object named f, the statement

f.write(‘data’)

stores the string ‘data’ to the file. The three statements

f.write(‘data’)
f.write(‘compute’)
f.write(‘process’)

writes the text ‘datacomputeprocess’ to the file. If our intention is to retrieve the three separate original
strings, we must add delimiters to separate the pieces of data. Newline characters serve as good delimiters:

f.write(‘data\n’)
f.write(‘compute\n’)
f.write(‘process\n’)

This places each word on its own line in the text file. The advantage of storing each piece of data on its own
line of text is that it makes it easier to read the data from the file with a for statement. If f is a file object
created for reading, the following code:

for line in f:
print(line.strip())

9.3. FILE OBJECTS 318

reads in each line of text from the file and prints it out. The variable line is a string, and we use the strip
method to remove the trailing newline (‘\n’) character.

We also can read the contents of the entire file into a single string using the file object’s read method:

contents = f.read()

Given the text file from above, the code

in = open(‘compterms.txt’, ‘r’)
s = in.read()

assigns to s the string ‘data\ncompute\nprocess\n’.

The open method opens a file for reading or writing, and the read, write, and other such methods
enable the program to interact with the file. When the executing program is finished with its file processing
it must call the close method to close the file properly. Failure to close a file can have serious consequences
when writing to a file, as data meant to be saved could be lost. Every call to the open function should have
a corresponding call to the file object’s close method.

Listing 9.5 (simplefileread.py) opens a file named data.dat for reading and reads in and prints out each
line of text:

Listing 9.5: simplefileread.py

f = open(‘data.dat’) # f is a file object
for line in f: # Read each line as text

print(line.strip()) # Remove trailing newline character
f.close() # Close the file

If the file data.dat does not exist or there are issues such as the user does have sufficient permissions to read
the file, the executing program will raise an exception.

Since it is important to always close a file after opening it, Python offers a simpler way to express
Listing 9.5 (simplefileread.py) that automatically closes the file when finished. Listing 9.6 (simplerread.py)
uses the with/as statement to create what is known as a context manager that ensures the file is closed.

Listing 9.6: simplerread.py

with open(‘data.dat’) as f: # f is a file object
for line in f: # Read each line as text

print(line.strip()) # Remove trailing newline character
# No need to close the file

The general form of the with/as statement is

object

block

with as :object-creation

9.3. FILE OBJECTS 319

• The reserved word with begins the with/as statement.

• The expression object-creation attempts to create and return an object. If the object-creation expres-
sion is unsuccessful, the statement’s execution does not continue.

• The reserved word as binds the object created by the object-creation expression to a variable.

• object is bound to the object created by the object-creation expression.

• block contains the code that uses the object bound to object.

The with/as statement can work with classes like TextIOWrapper that provide a particular protocol
for initialization and finalization. In the case of our file object, if the call to open proceeds without an
error, the program will execute the code in the with/as block. When the code in the with/as has finished
executing, the statement executes any finalization actions the class requires. In this case, the finalization
code of the TextIOWrapper class closes the file associated with file object f. Only certain classes support
the initialization/finalization protocol in a way that is compatible with the with/as statement. Such classes
provide a method named __enter__ that performs the initialization and a method named __exit__ that
performs the finalization.

Listing 9.7 (numbersaver.py) allows the user to enter numbers from the keyboard and save them to a
file. It also allows the user retrieve the values previously saved to a file. The user can specify the name of
the file and, thus, work with multiple files.

Listing 9.7: numbersaver.py

“””
Uses Python’s file class to store data to and retrieve data from
a text file.
“””
def load_data(filename):

“”” Print the elements stored in the text file named filename. “””
# Open file to read
with open(filename) as f: # f is a file object

for line in f: # Read each line as text
print(int(line)) # Convert to integer and append to the list

def store_data(filename):
“”” Allows the user to store data to the text file named filename. “””
with open(filename, ‘w’) as f: # f is a file object

number = 0
while number != 999: # Loop until user provides magic number

number = int(input(‘Please enter number (999 quits):’))
if number != 999:

f.write(str(number) + ‘\n’) # Convert integer to string to save
else:

break # Exit loop

def main():
“”” Interactive function that allows the user to

create or consume files of numbers. “””
done = False

9.3. FILE OBJECTS 320

while not done:
cmd = input(‘S)ave L)oad Q)uit: ‘)
if cmd == ‘S’ or cmd == ‘s’:

store_data(input(‘Enter file name:’))
elif cmd == ‘L’ or cmd == ‘l’:

load_data(input(‘Enter filename:’))
elif cmd == ‘Q’ or cmd == ‘q’:

done = True

if __name__ == ‘__main__’:
main()

The following shows one particular run of Listing 9.7 (numbersaver.py):

S)ave L)oad Q)uit: s
Enter file name:numbers.txt
Please enter number (999 quits):10
Please enter number (999 quits):20
Please enter number (999 quits):30
Please enter number (999 quits):40
Please enter number (999 quits):50
Please enter number (999 quits):999
S)ave L)oad Q)uit: q

This run creates a file named numbers.txt. We can run the program again to retrieve the previously entered
values:

S)ave L)oad Q)uit: l
Enter filename:numbers.txt
10
20
30
40
50
S)ave L)oad Q)uit: q

The literal name of Python’s file class is TextIOWrapper from the io module. The kind of files pro-
cessed by this file class are known as text files. Text files store character data, and we can use a simple
editor to create and modify text files. Many applications prevent the easy modification of data files outside
of the application by encoding the data in a special way. Depending on the data, the application also may
encode the files to save space.

We can combine Python’s string objects and file objects to create some powerful file processing pro-
grams. In particular we can open one file, read its contents, and write a modified form of its contents to a
second file. Listing 9.8 (convertupper.py) is a module providing a simple utility function, capitalize, that
capitalizes the text within a file.

Listing 9.8: convertupper.py

“””
convertupper.py
“””
def capitalize(filename):

9.3. FILE OBJECTS 321

“”” Creates a new file with the prefix ‘upper_’
added to the name of the original file.
All the alphabetic characters in the new
are capitalized. This function does not
disturb the contents of the original file. “””

with open(filename, ‘r’) as infile:
with open(‘upper_’ + filename, ‘w’) as outfile:

for line in infile:
line = line.strip().upper()
print(line, file=outfile)

The capitalize function creates a new file, named with the upper prefix added to the name of the original
file.

Suppose we have a text file named declaration.txt containing the introduction and preamble to the United
States Declaration of Independence, as shown here:

When in the Course of human events, it becomes necessary for one people to dissolve
the political bands which have connected them with another, and to assume among the
powers of the earth, the separate and equal station to which the Laws of Nature and
of Nature’s God entitle them, a decent respect to the opinions of mankind requires
that they should declare the causes which impel them to the separation.

We hold these truths to be self-evident, that all men are created equal, that they are
endowed by their Creator with certain unalienable Rights, that among these are Life,
Liberty and the pursuit of Happiness.–That to secure these rights, Governments are
instituted among Men, deriving their just powers from the consent of the governed,
–That whenever any Form of Government becomes destructive of these ends, it is the
Right of the People to alter or to abolish it, and to institute new Government,
laying its foundation on such principles and organizing its powers in such form,
as to them shall seem most likely to effect their Safety and Happiness. Prudence,
indeed, will dictate that Governments long established should not be changed for
light and transient causes; and accordingly all experience hath shewn, that mankind
are more disposed to suffer, while evils are sufferable, than to right themselves by
abolishing the forms to which they are accustomed. But when a long train of abuses
and usurpations, pursuing invariably the same Object evinces a design to reduce them
under absolute Despotism, it is their right, it is their duty, to throw off such
Government, and to provide new Guards for their future security.–Such has been the
patient sufferance of these Colonies; and such is now the necessity which constrains
them to alter their former Systems of Government. The history of the present King
of Great Britain is a history of repeated injuries and usurpations, all having in
direct object the establishment of an absolute Tyranny over these States. To prove
this, let Facts be submitted to a candid world.

Listing 9.9 (runconvert.py) produces a new file named upper declaration.txt.

Listing 9.9: runconvert.py

from convertupper import capitalize

capitalize(‘declaration.txt’)

The file upper declaration.txt will contain the following text:

WHEN IN THE COURSE OF HUMAN EVENTS, IT BECOMES NECESSARY FOR ONE PEOPLE TO DISSOLVE
THE POLITICAL BANDS WHICH HAVE CONNECTED THEM WITH ANOTHER, AND TO ASSUME AMONG THE

9.3. FILE OBJECTS 322

POWERS OF THE EARTH, THE SEPARATE AND EQUAL STATION TO WHICH THE LAWS OF NATURE AND
OF NATURE’S GOD ENTITLE THEM, A DECENT RESPECT TO THE OPINIONS OF MANKIND REQUIRES
THAT THEY SHOULD DECLARE THE CAUSES WHICH IMPEL THEM TO THE SEPARATION.

WE HOLD THESE TRUTHS TO BE SELF-EVIDENT, THAT ALL MEN ARE CREATED EQUAL, THAT THEY ARE
ENDOWED BY THEIR CREATOR WITH CERTAIN UNALIENABLE RIGHTS, THAT AMONG THESE ARE LIFE,
LIBERTY AND THE PURSUIT OF HAPPINESS.–THAT TO SECURE THESE RIGHTS, GOVERNMENTS ARE
INSTITUTED AMONG MEN, DERIVING THEIR JUST POWERS FROM THE CONSENT OF THE GOVERNED,
–THAT WHENEVER ANY FORM OF GOVERNMENT BECOMES DESTRUCTIVE OF THESE ENDS, IT IS THE
RIGHT OF THE PEOPLE TO ALTER OR TO ABOLISH IT, AND TO INSTITUTE NEW GOVERNMENT,
LAYING ITS FOUNDATION ON SUCH PRINCIPLES AND ORGANIZING ITS POWERS IN SUCH FORM,
AS TO THEM SHALL SEEM MOST LIKELY TO EFFECT THEIR SAFETY AND HAPPINESS. PRUDENCE,
INDEED, WILL DICTATE THAT GOVERNMENTS LONG ESTABLISHED SHOULD NOT BE CHANGED FOR
LIGHT AND TRANSIENT CAUSES; AND ACCORDINGLY ALL EXPERIENCE HATH SHEWN, THAT MANKIND
ARE MORE DISPOSED TO SUFFER, WHILE EVILS ARE SUFFERABLE, THAN TO RIGHT THEMSELVES BY
ABOLISHING THE FORMS TO WHICH THEY ARE ACCUSTOMED. BUT WHEN A LONG TRAIN OF ABUSES
AND USURPATIONS, PURSUING INVARIABLY THE SAME OBJECT EVINCES A DESIGN TO REDUCE THEM
UNDER ABSOLUTE DESPOTISM, IT IS THEIR RIGHT, IT IS THEIR DUTY, TO THROW OFF SUCH
GOVERNMENT, AND TO PROVIDE NEW GUARDS FOR THEIR FUTURE SECURITY.–SUCH HAS BEEN THE
PATIENT SUFFERANCE OF THESE COLONIES; AND SUCH IS NOW THE NECESSITY WHICH CONSTRAINS
THEM TO ALTER THEIR FORMER SYSTEMS OF GOVERNMENT. THE HISTORY OF THE PRESENT KING
OF GREAT BRITAIN IS A HISTORY OF REPEATED INJURIES AND USURPATIONS, ALL HAVING IN
DIRECT OBJECT THE ESTABLISHMENT OF AN ABSOLUTE TYRANNY OVER THESE STATES. TO PROVE
THIS, LET FACTS BE SUBMITTED TO A CANDID WORLD.

Table 9.2 summarizes some of the functions and methods available to file objects.

Table 9.2 A few of the functions and methods available to file objects
TextIOWrapper Methods

open
A function that returns a file object (instance of io.TextIOWrapper).

read
A method that reads the contents of a text file into a single string.

write
A method that writes a string to a text file.

close
A method that closes the file from further processing. When writing to a file, the close
method ensures that all data sent to the file is saved to the file.

Objects usually contain data in addition to methods. TextIOWrapper objects store integer, string, and
Boolean information. The following interactive session reveals some of the data stored in file objects:

>>> f = open(‘temp.dat’, ‘w’)
>>> f.name
‘temp.dat’
>>> f._CHUNK_SIZE
8192
>>> f.mode
‘w’
>>> f.encoding
‘cp1252’
>>> f.line_buffering

9.4. FRACTION OBJECTS 323

False

We say that name, _CHUNK_SIZE, encoding, and line_buffering are all instance variables of the object
f. These are just like the variables we have been using, except that we must prefix their name with their
associated object and a dot (.). Since these names refer to data, not methods, no parentheses appear at the
end. If we have two different file objects, f and g, f.name may be different from g.name. The statement

x = 2

binds the variable x to the value 2, whereas the statement

obj.x = 2

binds the x instance variable of object obj to the value 2.

9.4 Fraction Objects

The fractions module provides the Fraction class. Fraction objects model mathematical rational num-
bers; that is, the ratio of two integers. Rational numbers contain a numerator and denominator. Listing 9.10
(fractionplay.py) makes and uses some Fraction objects.

Listing 9.10: fractionplay.py

from fractions import Fraction

f1 = Fraction(3, 4) # Make the fraction 3/4
print(f1) # Print it
print(f1.numerator) # Print numerator
print(f1.denominator) # Print denominator
print(float(f1)) # Floating-point equivalent
f2 = Fraction(1, 8) # Make another fraction, 1/8
print(f2) # Print the second fraction
f3 = f1 + f2 # Add the two fractions
print(f3) # 3/4 + 1/8 = 6/8 + 1/8 = 7/8

Listing 9.10 (fractionplay.py) prints

3/4
3
4
0.75
1/8
7/8

The statement

f1 = Fraction(3, 4)

creates a Fraction object and assigns the variable f1 to the object. The expression Fraction(3, 4) calls
a class constructor. Class constructors allow clients to supply data used in the formation of a new object. In
this case, the first parameter represents the numerator of the new fraction object, and the second parameter
represents the denominator of the object. The Fraction(3, 4) expression returns a reference to the newly
created fraction object, and the statement

9.4. FRACTION OBJECTS 324

f1 = Fraction(3, 4)

binds the variable f1 to this object.

We see from Listing 9.10 (fractionplay.py) that Fraction objects contain numerator and denominator
instance variables. The expression f1.numerator represents the numerator instance variable of object f1.

The program appears to be devoid of any method calls, but the addition statement involves a method
call behind the scenes. Python reserves special names for some methods. The Fraction class provides a
method named __add__. This allows clients to add together two fraction objects as shown in Listing 9.10
(fractionplay.py):

f3 = f1 + f2

This is a nicer way of expressing

f3 = f1.__add__(f2)

We say the former statement using the + operator is syntactic sugar for latter statement that uses the explicit
__add__ method. Most human readers prefer the version with +, but, in reality, both statements are identical
to the Python interpreter. The str class of string objects also provides an __add__ method. If s and t are
string objects, the string concatenation expression s + t is syntactic sugar for s.__add__(t).

The Fraction class includes a number of these special methods that exploit syntactic sugar; examples
include the following (f and g reference Fraction objects):

• __mul__, multiplication: f.__mul__(g) is equivalent to f * g

• __eq__, relational quality: f.__eq__(g) is equivalent to f == g

• __gt__, greater than: f.__gt__(g) is equivalent to f > g

• __sub__, subtraction: f.__sub__(g) is equivalent to f – g

• __neg__, unary minus: f.__neg__() is equivalent to -f

Any type that supports these operations must have these special methods. In fact, the familiar int,
float, and str types all have these methods, and we merely have been using their syntactic sugar-coatings.
Consider the following interactive sequence:

>>> (20).__add__(4)
24
>>> 0.25.__mul__(4)
1.0
>>> ‘hello’.__add__(‘there’)
‘hellothere’
>>> ‘hello’.__mul__(3)
‘hellohellohello’

In the first line of the interactive sequence we put 20 in parentheses so the interpreter interprets the period
as a dot instead of a numerical decimal point. We also could have put a space in front of the dot, as in

20 .__add__(4) # Note space before the dot

Calling __add__ instead of using the + operator offers no performance advantages and makes the code less
readable for humans. You therefore should use the more readable operator syntax in your code. We mention
the alternate syntax at this point more as interesting curiosity, but later in Chapter 13 we can take advantage
of these special methods when we are designing our own custom types.

9.5. TURTLE GRAPHICS OBJECTS 325

9.5 Turtle Graphics Objects

In Section 6.9, we introduced Python’s Turtle graphics functional interface. We saw how it is possible to
draw pictures within a graphical window via function calls. Behind the scenes the turtle module creates a
global Turtle object which models the pen doing the drawing. The Turtle graphics functions such as left
and pencolor manipulate this hidden Turtle object. We can create and use our own Turtle objects. This
is useful if we wish to manage multiple pens simultaneously.

To illustrate the use of Turtle objects, we will rewrite the programs that appeared in Section 6.9 but
use a Turtle object directly. We will call methods associated with our Turtle object instead of using the
global functions that operate on the hidden Turtle object.

Listing 9.11 (boxturtleobject.py) is the object version of Listing 6.18 (boxturtle.py), which draws a rect-
angular box within a graphical window.

Listing 9.11: boxturtleobject.py

# Draws a ractangular box in the window

from turtle import Turtle, mainloop

t = Turtle() # Create a turtle object named t
t.pencolor(‘red’) # t’s pen color is red
t.forward(200) # Move turtle t forward 200 units (create bottom of rectangle
t.left(90) # Turn turtle left by 90 degrees
t.pencolor(‘blue’) # Change t’s pen color to blue
t.forward(150) # Move turtle t forward 150 units (create right wall)
t.left(90) # Turn turtle left by 90 degrees
t.pencolor(‘green’) # Change t’s pen color to green
t.forward(200) # Move turtle t forward 200 units (create top)
t.left(90) # Turn turtle left by 90 degrees
t.pencolor(‘black’) # Change t’s pen color to black
t.forward(150) # Move turtle t forward 150 units (create left wall)
t.hideturtle() # Make turtle t invisible
mainloop() # Await user input

The behavior of Listing 9.11 (boxturtleobject.py) is identical to that of Listing 6.18 (boxturtle.py) (see Fig-
ure 6.6).

Observe that the methods of the Turtle class correspond exactly to the global functions we used before,
both in name and expected parameters.

Listing 9.12 (octogonobject.py) is an enhanced version of Listing 6.19 (octogon.py). Since introducing
Turtle graphics in Section 6.9 we have been writing our own functions. Besides using a Turtle object
instead of the global Turtle graphics functions, Listing 9.12 (octogonobject.py) organizes the code into
functions for greater modularity and the potential for reuse.

Listing 9.12: octogonobject.py

“”” Draws in the window a spiral surrounded with an octogon “””

from turtle import *

def octogon(t, x, y, color):
“”” Draws with turtle t an octogon centered at (x, y)

9.6. GRAPHICS WITH TKINTER OBJECTS 326

with the specified color “””
t.pencolor(color) # Set pen color
t.penup() # Lift pen to move it
t.setposition(x, y) # Move the pen to coordinates (x, y)
t.pendown() # Place pen to begin drawing
for i in range(8): # Draw the eight sides

t.forward(80)
t.right(45)

def spiral(t, x, y, color):
“”” Draws with turtle t a spiral centered at (x, y)

with the specified color “””
distance = 0.2
angle = 40
t.pencolor(color) # Set pen color
t.penup() # Left pen to move it
t.setposition(x, y) # Position the pen at coordinates (x, y)
t.pendown() # Set pen down to begin drawing
for i in range(100):

t.forward(distance)
t.left(angle)
distance += 0.5

t = Turtle() # Create a turtle object named t
octogon(t, -45, 100, ‘red’)
spiral(t, 0, 0, ‘blue’)
t.hideturtle() # Make turtle t invisible
done()

While Listing 9.12 (octogonobject.py) make look significantly different from Listing 6.19 (octogon.py), it
produces exactly the same picture with exactly the same algorithms (see Figure 6.8).

9.6 Graphics with tkinter Objects

The tkinter module provides classes for building graphical user interfaces via the cross-platform Tk
toolkit. Tk is available for the Microsoft Windows, Apple Mac, and Linux operating systems. The tkinter
module is much larger and more complex than the turtle module. In fact, the turtle module is built from
components the tkinter module provides.

Listing 9.13 (buttontester.py) is a simple example that exercises a graphical button. Figure 9.1 shows a
picture of the application’s window after the user has pressed the button three times.

Listing 9.13: buttontester.py

from tkinter import Tk, Button

count = 0 # Records the number of button presses

9.6. GRAPHICS WITH TKINTER OBJECTS 327

Figure 9.1 An very simple interactive graphical application using the Tk toolkit. The button keeps track of
how many times the user presses it. In this case the user has pressed the button three times.

def update():
“”” Updates the count label within the graphical button “””
global count, b
count += 1
b.config(text=”Click Count = ” + str(count))
print(“Updating”)

root = Tk()
b = Button(root)
b.configure(background=”yellow”, text=”Click Count = 0″, command=update)
b.pack()
root.mainloop()

Listing 9.13 (buttontester.py) uses two classes from the tkinter package:

• Tk: This class represents a graphical window. The statement

root = Tk()

creates a Tk object named root. The root object corresponds to the application’s main graphical
window.

The statement

root.mainloop()

calls the mainloop method on behalf of the root window object to start the graphical program. This
method starts the process in motion that enables the user to provide input to the application and allows
the application to provide visual feedback to the user.

• Button: This class represents a graphical button that a user can press. A Button is one many graphi-
cal user interface widgets the Tk toolkit provides. (Other Tk widgets include checkboxes, text labels,
radio buttons, text entry fields, and list boxes, scroll bars, progress bars, and spin boxes.) The state-
ment

b = Button(root)

creates a Button object named b that is associated with the root window.

The statement

b.configure(background=”yellow”, text=”Click Count = 0″, command=update)

configures the graphical button with a yellow background color, sets its displayed text, and assigns
a function to be called when the user presses the button. Recall from Section 6.3 that the print

9.6. GRAPHICS WITH TKINTER OBJECTS 328

function can accept up to four optional keyword arguments. We commonly use the end and sep
keyword arguments with print. The code here calls the configure method of the Button class with
background, text, and command keyword arguments. These names are only three of 35 different
keyword argument names that the configure method can accept. A few other characteristics of a
Button object that the configure method enables programmers to adjust include text font and color,
horizontal and vertical padding, text justification, and border thickness.

The statement

b.pack()

ensures the button will be placed in a visually pleasing location within the root window.

The code in Listing 9.13 (buttontester.py) calls the Button class constructor with one argument, root,
the main window of the application. Instead, it could have used the following statement:

b = Button(root, background=”yellow”, text=”Click Count = 0″, command=update)

and omitted the call to configure entirely. Here we see the class constructor accepting the required parent
window parameter (root) plus the three keyword arguments.

Note that in the update function of Listing 9.13 (buttontester.py) we must declare that count is a global
variable because the function reassigns it. Without the global declaration update would treat the name
color as a local variable. Since the code within update does not assign the b variable, the name b is
implicitly global within the function.

To explore the capabilities of Tk graphics a little more, Listing 9.14 (tkinterlight.py) provides a fully
functioning graphical interactive program that models a traffic light. The light changes from red to green to
yellow to red . . . , when the user presses the graphical button labeled Change.

Listing 9.14: tkinterlight.py

from tkinter import Tk, Canvas
from tkinter.ttk import Button, Frame

def do_button_press():
“”” The window manager will call this function when the user

presses the graphical button.
The variables color, canvas, red_lamp, yellow_lamp,
and green_lamp are global variables that this function
expects to exist.
Since we assign only to the color variable, it is the only
variable that needs explicit global declaration. “””

global color
if color == ‘red’:

color = ‘green’
canvas.itemconfigure(red_lamp, fill=’black’) # Turn red off
canvas.itemconfigure(green_lamp, fill=’green’) # Turn green on

elif color == ‘green’:
color = ‘yellow’
canvas.itemconfigure(green_lamp, fill=’black’) # Turn green off
canvas.itemconfigure(yellow_lamp, fill=’yellow’) # Turn yellow on

elif color == ‘yellow’:
color = ‘red’
canvas.itemconfigure(yellow_lamp, fill=’black’) # Turn yellow off

9.6. GRAPHICS WITH TKINTER OBJECTS 329

canvas.itemconfigure(red_lamp, fill=’red’) # Turn red on

# Create and initialize global variables
color = ‘red’ # The light’s current color
root = Tk() # Create the main window
root.title(“Traffic Light”)

frame = Frame(root) # Create a frame to hold the widgets
frame.pack() # Make the frame fill the entire window

# Create a drawing surface within the frame
canvas = Canvas(frame, width=150, height=300)

# Set up the visual aspects of the traffic light
# Traffic light frame
canvas.create_rectangle(50, 20, 150, 280, fill=’gray’)
# Red lamp
red_lamp = canvas.create_oval(70, 40, 130, 100, fill=’red’)
# Yellow lamp
yellow_lamp = canvas.create_oval(70, 120, 130, 180, fill=’black’)
# Green lamp
green_lamp = canvas.create_oval(70, 200, 130, 260, fill=’black’)

# Create a graphical button and ensure it calls the do_button_press
# function when the user presses it
button = Button(frame, text=’Change’, command=do_button_press)

# Position button in the containing frame’s first row, first column,
# and position canvas in the first row, second column (zero origin,
# like list indices).
button.grid(row=0, column=0)
canvas.grid(row=0, column=1)

# Start the GUI event loop
root.mainloop()

Figure 9.2 shows the result of running Listing 9.14 (tkinterlight.py).

Listing 9.14 (tkinterlight.py) uses two classes from the tkinter package and two classes from the
tkinter.ttk package:

• Tk: As before, this class represents a graphical window. The statement

root = Tk()

creates a Tk object named root. The root object corresponds to the application’s main graphical
window. The statement

root.title(“Traffic Light”)

sets the text in the window’s title bar. The statement

root.mainloop()

calls the mainloop method on behalf of the root window object to start the graphical program.

9.6. GRAPHICS WITH TKINTER OBJECTS 330

Figure 9.2 An interactive graphical traffic light. The user presses the Change button to cycle the traffic
signals.

• Frame: This class represents an invisible container that can hold other graphical objects. The state-
ment

frame = Frame(root)

creates a frame object and associates it with the graphical window. The statement

frame.pack()

makes this container widget fill the whole graphical window.

• Canvas: This class represents a drawing area within a graphical window. The statement

canvas = Canvas(frame, width=300, height=300)

creates a Canvas object named canvas placed in the frame widget container. The canvas objects
dimensions are 300 pixels wide and 300 pixels tall, as specified by the width and height keyword
arguments. The origin of the coordinate system of the canvas, the point (0,0), is found at the left-top
corner of the drawing area within the window, and the y axis is inverted, meaning it points down
instead of up. This means that while x values increase from left to right as expected, y increase from
top to bottom within the canvas. Figure 9.3 illustrates.

The statement

canvas.create_rectangle(150, 20, 250, 280, fill=’gray’)

invokes the create_rectangle method to add a gray rectangle of the given size to the canvas. The
first two parameters set the left-top corner of the rectangle to the location (150,20). The third and
fourth parameters locate the rectangle’s right-bottom corner to be exactly one pixel to the left and one
pixel above the point (250,280). The fill keyword argument specifies the rectangle’s background
color. This rectangle represents the traffic light’s frame that holds the lamps. The create_oval
method works similarly for creating the circles representing the lamps of the traffic light. Figure 9.4
shows how the arguments passed to create_oval bounds the oval shape within a rectangular area.

The statement

9.6. GRAPHICS WITH TKINTER OBJECTS 331

Figure 9.3 The Tk canvas coordinate system superimposed on a graphics window. x values increase from
left to right, and y values increase from top to bottom. The y axis is upside down compared to the Cartesian
coordinate system commonly used in mathematics.

(0, 0) x

Figure 9.4 The create oval method of the Tk Canvas class adds an oval shape to a canvas object. The
statement in the figure creates a circle shape on the canvas object referenced by c. The first two parameters
specify the left-top corner of a bounding rectangle, and the third and fourth parameters specify the bounding
rectangle’s right-bottom corner.

c.create_oval(10, 30, 60, 80, fill=”yellow”)

(10, 30)

(60, 80)

9.7. OTHER STANDARD PYTHON OBJECTS 332

canvas.itemconfigure(red_lamp, fill=’black’)

calls the itemconfigure method to change the color of the circle named red_lamp.

• Button: This class represents a graphical button the user can press. Unlike in Listing 9.13 (buttontester.py),
this class comes from the tkinter.ttk package. The visual appearance and functionality differs
slightly from Button objects from the tkinter package. Buttons from the tkinter.ttk package
have a more modern look and feel.

The statement

button = Button(canvas, text=’Change’, command=do_button_press)

creates a Button object named button attached to the canvas object. The button is labeled Change,
and it reacts to a user’s press by calling the do_button_press function. The statements

button.grid(row=0, column=0)
canvas.grid(row=0, column=1)

impose a one-row, two-column grid widget layout upon the root graphical window. The Tk toolkit
determines this configuration from the code, and we can too. Note that we add only the button and
canvas widgets to the root window. The two calls to the grid method specify only one row (both
are 0) but two columns (one is 0 and the other is 1). This means the button and canvas objects will
appear side by side (same row 0), and the button will be to the left of the canvas that draws the traffic
light image (0 is the first column, and 1 is the second column).

Note that in the do_button_press function of Listing 9.14 (tkinterlight.py) we must declare that color
is a global variable because the function reassigns it. Without the global declaration do_button_press
would treat color as a local variable. Since the code within do_button_press does not assign the canvas
variable, canvas is implicitly global within the function.

9.7 Other Standard Python Objects

Python provides many other standard classes. Among these, lists, tuples, dictionaries, and sets are particu-
larly useful. These classes are so general, useful, and widely-used that we devote the next few chapters to
exploring them in detail.

9.8 Object Mutability and Aliasing

Recall that a variable is a name that labels an object. We informally have treated a variable as the object it
represents; for example, given the following statement

frac1 = Fraction(1, 2)

we often refer to the object frac1. In fact, the object is the Fraction object representing the rational

number
1
2

, and frac1 is merely a name by which we can access the Fraction object. This informality has
not been a problem so far, but as we explore objects more deeply we need to be more careful in how we
talk about and use objects.

Consider Listing 9.15 (fractionassign.py) which uses Fraction variables.

9.8. OBJECT MUTABILITY AND ALIASING 333

Listing 9.15: fractionassign.py

from fractions import Fraction

# Assign some Fraction variables
f1 = Fraction(1, 2)
f2 = Fraction(1, 2)
f3 = f1

# Examine the objects involved
print(‘f1 =’, f1)
print(‘f2 =’, f2)
print(‘f3 =’, f3)

# Examine the numerators and denominators separately
print(‘f1 numerator, denominator:’, f1.numerator, f1.denominator)
print(‘f2 numerator, denominator:’, f2.numerator, f2.denominator)
print(‘f3 numerator, denominator:’, f3.numerator, f3.denominator)

# Compare the fractions
print(‘f1 == f2?’, f1 == f2)
print(‘f1 == f3?’, f1 == f3)
print(‘f1 is f2?’, f1 is f2)
print(‘f1 is f3?’, f1 is f3)

Listing 9.15 (fractionassign.py) prints

f1 = 1/2
f2 = 1/2
f3 = 1/2
f1 numerator, denominator: 1 2
f2 numerator, denominator: 1 2
f3 numerator, denominator: 1 2
f1 == f2? True
f1 == f3? True
f1 is f2? False
f1 is f3? True

To better understand the behavior of Listing 9.15 (fractionassign.py) we will examine each of its parts in
detail. The statement

f1 = Fraction(1, 2)

calls the Fraction class constructor which creates a new Fraction object with its numerator instance
variable set to 1 and its denominator instance variable set to 2. It assigns the variable f1 to this new
fraction object. The statement

f2 = Fraction(1, 2)

creates a new Fraction object with its numerator instance variable set to 1 and its denominator instance
variable set to 2. It assigns the variable f2 to this fraction object. The statement

f3 = f1

assigns the variable f3 to the same fraction object to which f1 is assigned. Note that since the statement does
not involve the Fraction class constructor, it does not create a new fraction object. At this point we have

9.8. OBJECT MUTABILITY AND ALIASING 334

Figure 9.5 An illustration of the relationships amongst the fraction objects and variables resulting from the
assignment statements in Listing 9.15 (fractionassign.py).

f1 1
2

1
2

two Fraction objects and three variables bound to Fraction objects. Figure 9.5 illustrates the relationships
amongst the Fraction objects and variables that result from these three assignment statements. The
variables f1 and f3 refer to the same object. We say that f1 aliases f3. Said another way, the variables
f1 and f3 are aliases. The Fraction class implements a method named __eq__ which enables clients to
compare two fraction objects for logical equality using the familiar == operator. The statements

print(‘f1 == f2?’, f1 == f2)
print(‘f1 == f3?’, f1 == f3)

reveal that all three variables refer to objects that are logically equal to each other. The Fraction.__eq__
method (==) compares the numerator and denominator instance variables of two fraction objects to deter-
mine equality.

Sometimes logical equality is not sufficient, and we may need to know if two variables refer to the same
object. Python’s is operator tests to see of two variables refer to the same object. The statements

print(‘f1 is f2?’, f1 is f2)
print(‘f1 is f3?’, f1 is f3)

show that the variables f1 and f2 reference two different objects, but f1 and f3 refer to the same object.
This proves that f1 and f3 are aliases. Python also has an id function that returns an integer that is unique
to a particular object. (For most Python implementations this number is the starting address in memory
where the executing program has placed the object.) If a and b are objects, a is b is true exactly when
id(a) == id(b).

Prior to this chapter we have restricted our attention to the classes int, float, str, and bool. Object
aliasing has no practical consequences for programmers restricted to these data types. Instances of these
classes are all immutable objects, which means an object of any these of these types cannot change its state
after its creation. The integer 3 always is 3, for example, and the string object ‘Fred’ cannot change to
‘Free’. Instances of the Fraction class are immutable also.

Aliasing can be an issue for mutable objects. In Python’s Turtle graphics library (Section 9.5), Turtle
objects are mutable. Programmers can move a turtle object, change its orientation, and change its pen color.
Each of these actions changes the state of the turtle and affects the way the turtle draws within the graphics
window.

Listing 9.16 (multiturtle.py) uses two Turtle objects.

9.8. OBJECT MUTABILITY AND ALIASING 335

Figure 9.6 The drawing that results from executing the first part of Listing 9.16 (multiturtle.py).

Figure 9.7 The final drawing rendered by Listing 9.16 (multiturtle.py).

Listing 9.16: multiturtle.py

“”” Uses two Turtle objects to draw on the screen “””

from turtle import *

# Part 1
t1 = Turtle() # Create a turtle object named t1
t2 = Turtle() # Create a second turtle object named t2
t1.pencolor(‘red’) # t1’s pen color is red
t2.pencolor(‘blue’) # t2’s pen color is blue
t2.left(90) # Point t2 up (t1 autoatically points to the right)
t1.forward(100) # Move turtle t1 forward 100 units
t2.forward(50) # Move turtle t2 forward 50 units

# Part 2
t2 = t1 # Make the second turtle just like the first?
t2.right(45) # Turn turtle 2 (but not turtle 1?)
t2.forward(50) # Move turtle 2 (why does turtle1 move instead?)

done()

The first part of Listing 9.16 (multiturtle.py) draws the picture shown in Figure 9.6. The beginning of Part 2
of Listing 9.16 (multiturtle.py) reassigns t2 to t1. At this point turtles t1 and t2 are aliases, and any further
actions taken either through t1 or t2 affect only one of the turtles. Figure 9.7 shows the final results of
Listing 9.16 (multiturtle.py). The turning and moving of t2 does not affect the original turtle 2. Instead,
changing t2 affects the t1’s turtle, as t2 and t1 refer to the same Turtle object.

Aliasing of mutable types can be a problem for beginning programmers because it is easy to believe the
statement

t2 = t1

makes t2 a copy of t1 and that they remain distinct objects. If the situation arises where your program
is managing what you believe to be similar but separate objects and changing the characteristics of one
object unexpectedly changes one or more of the other objects in exactly the same way, you likely have an
unintended aliasing problem.

9.9. GARBAGE COLLECTION 336

9.9 Garbage Collection

The following statement:

f = Fraction(2, 3)

creates a Fraction object representing
2
3

and assigns the variable f to the object. The Python interpreter acts
on this statement by reserving enough space in the computer’s memory to hold the object. It also performs
any initialization that the object requires; in this case it sets f.numerator to 2 and f.denominator to 3.

What happens to the object associated with f when we reassign the variable f? The following statement:

# f is the Fraction object created above
f = None

redirects f to refer to the special object None, which represents no object. At this point no variable refer-

ences the
2
3

fraction object created earlier. This means the object effectively is cut off from the remainder
of the program’s execution or the remainder of the interactive session. This abandoned object is classified
as garbage. The term garbage is a technical term used in computer science that refers to memory allo-
cated by an executing program that the program no longer can access. The Python interpreter cleans up
garbage through a process called garbage collection. Python uses a reference counting garbage collector
that automatically reclaims the space occupied by abandoned objects.

Reference counting garbage collection works as follows. All objects have an associated reference count.
When the executing program creates a new object and assigns a variable to it, it sets the object’s reference
count to 1. The following statement:

f = Fraction(2, 3) # The 2/3 object initially has a reference count of 1

assigns the variable f to a newly created Fraction object with a reference count of 1. A reference count
of 1 means that exactly one variable (in this case f) is assigned to the object. Making an alias, as in

g = f # The 2/3 object now has a reference count of 1 + 1 = 2

increments the
2
3

object’s reference count by one. If we make another alias, as in

h = f # The 2/3 object now has a reference count of 2 + 1 = 3

the assignment statement increases the object’s reference count to 3. If reassign f, g, or h, as in

g = Fraction(9/10) # Reassign a new object to g

the reference count of the
2
3

object decreases by one, and the reference count of the new
9

10
object be-

comes 1. If we reassign f:

f = None

this leaves only variable h referencing the
2
3

object, so the object’s reference count is 1. If we finally reassign
h:

h = 15

9.10. EXERCISES 337

the
2
3

object’s reference count drops to zero. An object with a reference count of zero is garbage, and the
garbage collector automatically will reclaim the space held by the object so it can be recycled and used
elsewhere.

9.10 Exercises

1. What is the difference between a class and an object?

2. What are some other names for the term instance variable?

3. What is another name for the term method?

4. What symbol associates an object with a method invocation?

5. How does a method differ from a function?

6. What method from the string class returns a new string with no leading or trailing whitespace?

7. What function returns the length of its string argument?

8. What type of object does the open function return?

9. What does the second parameter of the open function represent?

10. Write a program that stores the first 100 integers to a text file named numbers.txt. Each number
should appear on a line all by itself.

11. Complete the following function that reads a collection of integers from a text file named numbers.txt.
Each number in the file appears on a line all by itself. The function accepts a single parameter, a string
text file name. The function returns the sum of the integers in the file.

def sumfile(filename):
# Add your code here . . .

12. Provide the syntactic sugar for each of the following methods of the Fraction class:

(a) __sub__

(b) __eq__

(d) __gt__

13. How is using a Turtle object from Python’s Turtle graphics module different from using the free
functions; for example, t.penup() versus penup()?

14. For each of the drawings below write a program that draws the shape using a Turtle object from
Python’s Turtle graphics module.

9.10. EXERCISES 338

15. Does Python permit a programmer to change one symbol in a string object? If so, how?

16. What would be the consequences if a turtle.Turtle object were immutable?

17. In the context of programming, what is garbage?

18. What is garbage collection, and how does it work in Python?

19. Consider the following code:

a = “ABC”
b = a
c = b
a = “XYZ”

(a) At the end of this code’s execution what is the reference count for the string object “ABC”?

(b) At the end of this code’s execution is b an alias of a?

339

Chapter 10

Lists

The variables we have used to this point can bind to only one object at a time. As we have seen, we
can use individual variables to create some interesting and useful programs; however, variables that can
represent only one value at a time do have their limitations. Consider Listing 10.1 (averagenumbers.py)
which averages five numbers entered by the user.

Listing 10.1: averagenumbers.py

def main():
print(“Please enter five numbers: “)
# Allow the user to enter in the five values.
n1 = float(input(“Please enter number 1: “))
n2 = float(input(“Please enter number 2: “))
n3 = float(input(“Please enter number 3: “))
n4 = float(input(“Please enter number 4: “))
n5 = float(input(“Please enter number 5: “))
print(“Numbers entered:”, n1, n2, n3, n4, n5)
print(“Average:”, (n1 + n2 + n3 + n4 + n5)/5)

main()

A sample run of Listing 10.1 (averagenumbers.py) looks like:

Please enter five numbers:
Please enter number 1: 34.2
Please enter number 2: 10.4
Please enter number 3: 18.0
Please enter number 4: 29.3
Please enter number 5: 15.1
Numbers entered: 34.2 10.4 18.0 29.3 15.1
Average: 21.4

The program conveniently displays the values the user entered and then computes and displays their aver-
age.

Suppose the number of values to average must increase from five to 25. If we use Listing 10.1
(averagenumbers.py) as a guide, we would need to introduce twenty additional variables, and the over-

340

all length of the program necessarily would grow. Averaging 1,000 numbers using this approach would be
impractical.

Listing 10.2 (averagenumbers2.py) provides an alternative approach for averaging numbers that uses a
loop.

Listing 10.2: averagenumbers2.py

def main():
sum = 0.0
NUMBER_OF_ENTRIES = 5
print(“Please enter”, NUMBER_OF_ENTRIES, ” numbers: “)
for i in range(0, NUMBER_OF_ENTRIES):

num = float(input(“Enter number ” + str(i) + “: “))
sum += num

print(“Average:”, sum/NUMBER_OF_ENTRIES)

main()

Listing 10.2 (averagenumbers2.py) behaves slightly differently from Listing 10.1 (averagenumbers.py), as
the following sample run using the same data shows:

Please enter 5 numbers:
Enter number 0: 34.2
Enter number 1: 10.4
Enter number 2: 18.0
Enter number 3: 29.3
Enter number 4: 15.1
Average: 21.4

We can modify Listing 10.2 (averagenumbers2.py) to average 25 values much more easily than Listing 10.1
(averagenumbers.py) that must use 25 separate variables—just change the value of NUMBER_OF_ENTRIES.
In fact, the coding change to average 1,000 numbers is no more difficult. However, unlike the original
average program, this new version does not at the end display all the numbers entered. This is a significant
difference; it may be necessary to retain all the values entered for various reasons:

• All the values can be redisplayed after entry so the user can visually verify their correctness.

• The values may need to be displayed in some creative way; for example, they may be placed in a
graphical user interface component, like a visual grid (spreadsheet).

• The values entered may need to be processed in a different way after they are all entered; for example,
we may wish to display just the values entered above a certain value (like greater than zero), but the
limit is not determined until after all the numbers are entered.

In all of these situations we must retain all the values for future recall.

We need to combine the advantages of both of the above programs; specifically we want

• the ability to retain individual values, and

• the ability to dispense with creating individual variables to store all the individual values

These may seem like contradictory requirements, but Python provides a standard data structure that simul-
taneously provides both of these advantages—the list.

10.1. USING LISTS 341

10.1 Using Lists

A list is an object that holds a collection of objects; it represents a sequence of data. In that sense, a list is
similar to a string, except a string can hold only characters. A list can hold any Python object. A list need
not be homogeneous; that is, the elements of a list do not all have to be of the same type.

Like any other variable, a list variable can be local or global, and it must be defined (assigned) before
its use. The following code fragment defines a list named lst that holds the integer values 2,−3,0,4,−1:

lst = [2, -3, 0, 4, -1]

The right-hand side of the assignment statement is a literal list. The elements of the list appear within
square brackets ([ ]), and commas separate the elements. The following statement assigns the empty list to
a variable named a:

a = []

We can print list literals and lists referenced through variables:

lst = [2, -3, 0, 4, -1] # Assign the list
print([2, -3, 0, 4, -1]) # Print a literal list
print(lst) # Print a list via a variable

The above code prints

[2, -3, 0, 4, -1]
[2, -3, 0, 4, -1]

We may access the elements contained in a list via their position within the list. We access individual
elements of a list using square brackets:

lst = [2, -3, 0, 4, -1] # Assign the list
lst[0] = 5 # Make the first element 5
print(lst[1]) # Print the second element
lst[4] = 12 # Make the last element 12
print(lst) # Print a list variable
print([10, 20, 30][1]) # Print second element of literal list

This code prints

-3
[5, -3, 0, 4, 12]
20

The number within the square brackets is called the index. A nonnegative index indicates the distance from
the beginning of the list. The expression lst[0] therefore indicates the element at the very beginning (a
distance of zero from the beginning) of lst, and lst[1] is the second element (a distance of one away
from the beginning). We can read aloud the expression a[3] as “a sub three,” where the index 3 represents
a subscript. The subscript terminology is borrowed from mathematicians who use subscripts to reference
elements in a mathematical vector or matrix; for example, V2 represents the second element in vector V.
Unlike the convention often used in mathematics, however, the first element in a list is at position zero, not
one. As mentioned above, the index indicates the distance from the beginning; thus, the very first element
is at a distance of zero from the beginning of the list. The first element of list a is a[0]. As a consequence
of a zero beginning index, if list a holds n elements, the last element in a is a[n−1], not a[n].

10.1. USING LISTS 342

Figure 10.1 A simple list with three elements. The small number below a list element represents the index
of that element.

lst
5 3 12

1 20

‒

If a is a list with n elements, and i is an integer such that 0≤ i
19
-0.03
end
[24.2, 4, ‘word’, , 19, -0.03, ‘end’]

We clearly see that a single list can hold integers, floating-point numbers, strings, and even functions. A list
can hold other lists; the following code

col = [23, [9.3, 11.2, 99.0], [23], [], 4, [0, 0]]
print(col)

prints

[23, [9.3, 11.2, 99.0], [23], [], 4, [0, 0]]

Four of the elements of the list col are themselves lists.

The following interactive sequence shows how placing variables in a list actually copies the variable’s
values into the list:

>>> x = 5
>>> y = ‘ABC’
>>> z = [x, y]
>>> seq = [x, y, z]
>>> seq
[5, ‘ABC’, [5, ‘ABC’]]
>>> x = 0
>>> y = 10
>>> seq
[5, ‘ABC’, [5, ‘ABC’]]

As this sequence demonstrates, changing the variable x does not affect the list built from x’s original value.

We can treat the elements of a list we access via [] as any other variable; for example,

10.1. USING LISTS 344

nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]
# Print the fourth element
print(nums[3])
# Make the third element the average of two other elements
nums[2] = (nums[0] + nums[9])/2;
# Assign elements at indices 1 and 4 using tuple assignment
nums[1], nums[4] = sqrt(x), x + 2*y

The fact that we can write an assignment statement such as

lst[4] = 12

indicates that lists are mutable objects. In contrast, strings are immutable objects, so it is not possible to
modify the contents of a string object. We can, however, use the [] subscripting operator to access the
individual characters (actually strings of length one) that comprise a string; for example,

>>> s = ‘ABCEFGHI’
>>> s[0]
‘A’
>>> s[1]
‘B’

We know that string objects are immutable, so the following code generates an exception:

>>> s = ‘ABCEFGHI’
>>> s[0] = ‘a’
Traceback (most recent call last):

File ““, line 1, in
TypeError: ‘str’ object does not support item assignment

When an expression involving the supscripting operator appears on the side of the assignment operator, as
in

lst[0] = 4

the interpreter calls the object’s __setitem__ method. An equivalent statement is

lst.__setitem__(0, 4)

The str class has no __setitem__ method. All other situations that use the [] operator within an expres-
sion that do not attempt to modify the associated object correspond to the object’s __getitem__ method.
For example, the following two statements are equivalent:

# The following two statements are equivalent:
x = lst[3]
x = lst.__getitem__(3)

String and list objects both have a __getitem__ method. Programmers, of course, ordinarily should use the
syntactically sugared [] expressions and not invoke directly an object’s __setitem__ and __getitem__
methods.

The expression within [] must evaluate to an integer; some examples include

• an integer literal: a[34]

10.2. LIST TRAVERSAL 345

• an integer variable: a[x] (x must be an integer)

• an integer arithmetic expression: a[x + 3] (x must be an integer)

• an integer result of a function call that returns an integer: a[max(x, y)] (max must return an integer
when called with x and y)

• an element of another or the same list: a[b[3]] (element b[3] must be an integer)

10.2 List Traversal

The action of moving through a list visiting each element is known as traversal. A list is a kind of iterable
object, so we can use a for loop to visit each element in order within a list. Listing 10.5 (heterolistfor.py)
uses a for loop and behaves identically to Listing 10.4 (heterolist.py).

Listing 10.5: heterolistfor.py

collection = [24.2, 4, ‘word’, print, 19, -0.03, ‘end’]
for item in collection:

print(item) # Print each element

The built-in function len returns the number of elements in a list: The code segment

print(len([2, 4, 6, 8]))
a = [10, 20, 30]
print(len(a))

prints

4
3

The name len stands for length. The index of the last element in list lst is lst[len(lst) – 1].

If you have some experience in other programming languages, you may be tempted to use len and an
explicit list index with a for loop as shown in Listing 10.6 (heterolistforindex.py) instead of the code in
Listing 10.5 (heterolistfor.py).

Listing 10.6: heterolistforindex.py

collection = [24.2, 4, ‘word’, print, 19, -0.03, ‘end’]
for i in range(len(collection)): # Not the preferred way to traverse a list

print(collection[i]) # Print each element

Listing 10.6 (heterolistforindex.py) works identically to Listing 10.5 (heterolistfor.py), but Listing 10.5
(heterolistfor.py) demonstrates the preferred way to iterate over the elements of a list. Listing 10.5 (heterolistfor.py)
exploits a list object’s iterable property, and it more efficient and elegant than the technique used in List-
ing 10.6 (heterolistforindex.py).

How could we print the elements in a list in reverse order? We could use our familiar for i in range. . . construct
and use an explicit index to count backwards:

10.3. BUILDING LISTS 346

nums = [2, 4, 6, 8]
# Print last element to first (zero index) element
for i in range(len(nums) – 1, -1, -1):

print(nums[i])

This fragment prints

8
6
4
2

An even better way to iterate over list elements from back to front uses Python’s built-in function named
reversed:

nums = [2, 4, 6, 8]
# Print last element to first (zero index) element
for i in reversed(nums):

print(nums[i])

Not only is this version shorter, it actually is more efficient than the version that uses range and len. The
reversed expression creates an iterable object that enables the for statement to traverse the elements of
the list in reverse. The expression reversed(nums) does not affect the contents of the list nums; it simply
enables a backwards traversal of the elements. The reversed function returns a generator that works like
the following:

def my_reversed(lst):
“”” Generate the elements of list lst from back to front.

Works like the built-in reversed generator function. “””
for i in range(len(lst) – 1, -1, -1):

yield(lst[i])

Within the range expression, the first argument, len(lst) – 1, is the index of the last element in the list
lst. The second argument, -1, indicates−1 terminates, but is not included in, the range. The last argument,
-1 indicates the range counts backwards. Taken all together we see that the range spans the indices of all
the elements in the list, from the last to the first.

The reversed function is found in the __builtins__ module, so its use requires no special import
statement.

10.3 Building Lists

Python supports several other ways of building a list besides enumerating all the list’s elements in a list
literal. We can construct a new list from two existing lists using concatenation. The plus (+) operator
concatenates lists in the same way it concatenates strings. The following shows some experiments in the
interactive shell with list concatenation:

>>> a = [2, 4, 6, 8]
>>> a
[2, 4, 6, 8]
>>> a + [1, 3, 5]
[2, 4, 6, 8, 1, 3, 5]

10.3. BUILDING LISTS 347

>>> a
[2, 4, 6, 8]
>>> a = a + [1, 3, 5]
>>> a
[2, 4, 6, 8, 1, 3, 5]
>>> a += [10]
>>> a
[2, 4, 6, 8, 1, 3, 5, 10]
>>> a += 20
Traceback (most recent call last):

File ““, line 1, in
a += 20

TypeError: ‘int’ object is not iterable

The statement

a = [2, 4, 6, 8]

assigns the given list literal to the variable a. The expression

a + [1, 3, 5]

evaluates to the list [2, 4, 6, 8, 1, 3, 5], but the statement does not change the list to which a refers.
The statement

a = a + [1, 3, 5]

actually reassigns a to the new list [2, 4, 6, 8, 1, 3, 5]. The statement

a += [10]

updates a to be the new list [2, 4, 6, 8, 1, 3, 5, 10]. Observe that the + will concatenate two lists,
but it cannot join a list and something that is not a list. The following statement

a += 20

is illegal since a refers to a list, and 20 is an integer, not a list. If used within a program under these
conditions, this statement will produce a run-time exception.

If we wish to append a variable’s value to a list, we similarly must first enclose it within square brackets:

>>> x = 2
>>> a = [0, 1]
>>> a += [x]
>>> a
[0, 1, 2]

Listing 10.7 (builduserlist.py) shows how to build lists as the program executes.

Listing 10.7: builduserlist.py

# Build a custom list of nonnegative integers specified by the user

def make_list():
“””
Builds a list from input provided by the user.

10.3. BUILDING LISTS 348

“””
result = [] # List to return is initially empty
in_val = 0 # Ensure loop is entered at least once
while in_val >= 0:

in_val = int(input(“Enter integer (-1 quits): “))
if in_val >= 0:

result += [in_val] # Add item to list
return result

def main():
col = make_list()
print(col)

main()

A sample run of Listing 10.7 (builduserlist.py) produces

Enter integer (-1 quits): 23
Enter integer (-1 quits): 100
Enter integer (-1 quits): 44
Enter integer (-1 quits): 19
Enter integer (-1 quits): 19
Enter integer (-1 quits): 101
Enter integer (-1 quits): 98
Enter integer (-1 quits): -1
[23, 100, 44, 19, 19, 101, 98]

If the user enters a negative number initially, we get:

Enter integer (-1 quits): -1
[]

There are several ways to build a list without explicitly listing every element in the list. We can use
range to produce a regular sequence of integers. The range object returned by range is not itself a list, but
we can make a list from a range using the list function, as Listing 10.8 (makeintegerlists.py) demonstrates.

Listing 10.8: makeintegerlists.py

def main():
a = list(range(0, 10))
print(a)
a = list(range(10, -1, -1))
print(a)
a = list(range(0, 100, 10))
print(a)
a = list(range(-5, 6))
print(a)

main()

Listing 10.8 (makeintegerlists.py) prints

10.3. BUILDING LISTS 349

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
[10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]
[0, 10, 20, 30, 40, 50, 60, 70, 80, 90]
[-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5]

We can use the list conversion function to make a list out of any generator (see Section 8.8 for infor-
mation about generators). Listing 10.9 (generator2list.py) uses the prime_sequence generator we saw in
Listing 8.23 (generatedprimes.py) to make a list containing all the prime number in the range 20 to 50.

Listing 10.9: generator2list.py

from math import sqrt

def is_prime(n):
“”” Returns True if nonnegative integer n is prime;

otherwise, returns false “””
if n == 2: # 2 is the only even prime number

return True
if n < 2 or n % 2 == 0: # Handle simple cases immediately return False # No evens and nothing less than 2 trial_factor = 3 root = sqrt(n) while trial_factor <= root: if n % trial_factor == 0: # Is trial factor a factor? return False # Yes, return right away trial_factor += 2 # Next potential factor, skip evens return True # Tried them all, must be prime def prime_sequence(begin, end): """ Generates the sequence of prime numbers between begin and end. """ for value in range(begin, end + 1): if is_prime(value): # See if value is prime yield value # Produce the prime number def main(): """ Make a list from a generator """ # Build the list of prime numbers in the range 20 to 50 primes = list(prime_sequence(20, 50)) print(primes) if __name__ == '__main__': main() # Run the program Listing 10.9 (generator2list.py) displays the list built from our custom prime number generator: [23, 29, 31, 37, 41, 43, 47] It is easy to make a list in which all the elements are the same or a pattern of elements repeat. The * operator, when applied to a list and an integer, “multiplies” the elements of a list. The expression [0] * 5 ©2017 Richard L. Halterman Draft date: January 18, 2018 10.3. BUILDING LISTS 350 produces the list [0, 0, 0, 0, 0]. The integer multiplier may be any valid integer expression. List- ing 10.10 (makeuniformlists.py) builds several lists using the * list multiplication operator. Listing 10.10: makeuniformlists.py def main(): a = [0] * 10 print(a) a = [3.4] * 5 print(a) a = 3 * ['ABC'] print(a) a = 4 * [10, 20, 30] print(a) n = 3 # Use a variable multiplier a = n * ['abc', 22, 8.7] print(a) main() The output of Listing 10.10 (makeuniformlists.py) is [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] [3.4, 3.4, 3.4, 3.4, 3.4] ['ABC', 'ABC', 'ABC'] [10, 20, 30, 10, 20, 30, 10, 20, 30, 10, 20, 30] ['abc', 22, 8.7, 'abc', 22, 8.7, 'abc', 22, 8.7] Observe that the integer multiplier may appear either to left or the right of the * operator, and the effects are the same. This means the list multiplication * operator is commutative. The * multiplier operator works similarly with strings. Consider the following interactive sequence: >>> ‘abc’ * 3
‘abcabcabc’

We now have all the tools we need to build a program that flexibly averages numbers while retaining all
the values the user enters. Listing 10.11 (listaverage.py) uses an list and a loop to achieve the generality of
Listing 10.2 (averagenumbers2.py) with the ability to retain all input for later redisplay.

Listing 10.11: listaverage.py

def main():
# Set up variables
sum = 0.0
NUMBER_OF_ENTRIES = 5
numbers = []

# Get input from user
print(“Please enter”, NUMBER_OF_ENTRIES, “numbers: “)
for i in range(0, NUMBER_OF_ENTRIES):

10.4. LIST MEMBERSHIP 351

num = float(input(“Enter number ” + str(i) + “: “))
numbers += [num]
sum += num

# Print the numbers entered
print(end=”Numbers entered: “)
for num in numbers:

print(num, end=” “)
print() # Print newline

# Print average
print(“Average:”, sum/NUMBER_OF_ENTRIES)

main() # Execute main

The output of Listing 10.11 (listaverage.py) is similar to the original Listing 10.1 (averagenumbers.py)
program:

Please enter 5 numbers:
Enter number 0: 9.0
Enter number 1: 3.5
Enter number 2: 0.2
Enter number 3: 100.0
Enter number 4: 15.3
Numbers entered: 9.0 3.5 0.2 100.0 15.3
Average: 25.6

Unlike the original program, however, we now conveniently can extend this program to handle as many
values as we wish. We need only change the definition of the NUMBER_OF_ENTRIES variable to allow the
program to handle any number of values. This centralization of the definition of the list’s size eliminates
duplicating a literal numeric value and leads to a program that is more maintainable. Suppose every oc-
currence of NUMBER_OF_ENTRIES were replaced with the literal value 5. The program would work exactly
the same way, but changing the size would require touching many places within the program. When dupli-
cate information is scattered throughout a program, it is a common mistake to update some but not all of
the information when a change is to be made. If all of the duplicate information is not updated to agree,
the inconsistencies result in logic errors within the program. By faithfully using the NUMBER_OF_ENTRIES
variable throughout the program instead of the literal numeric value, we can avoid the problems of these
potential inconsistencies.

The first loop in Listing 10.11 (listaverage.py) collects all five input values from the user. The second
loop prints all the numbers the user entered.

When treated as a Boolean expression, the empty list ([]) is interpreted as False, and all other lists
are considered True. This means bool([[]]) evaluates to True, since [[]] is not empty; it contains one
element—the empty list.

10.4 List Membership

We can use the Python in operator to determine if an object is an element in a list. If lst is a list, the expres-
sion x in lst evaluates to True if x in an element in lst; otherwise, the expression is False. Similarly,
the expression x not in lst evaluates to True if x is not an element in lst; otherwise, the expression is

10.5. LIST ASSIGNMENT AND EQUIVALENCE 352

False. The expression x not in lst is equivalent to not(x in lst). Listing 10.12 (listmembership.py)
exercises Python’s in operator.

Listing 10.12: listmembership.py

lst = list(range(0, 21, 2))
for i in range(-2, 23):

if i in lst:
print(i, ‘is a member of’, lst)

if i not in lst:
print(i, ‘is NOT a member of’, lst)

Listing 10.12 (listmembership.py) prints

-2 is NOT a member of [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20]
-1 is NOT a member of [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20]
0 is a member of [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20]
1 is NOT a member of [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20]
2 is a member of [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20]
3 is NOT a member of [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20]
4 is a member of [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20]
5 is NOT a member of [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20]
6 is a member of [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20]
7 is NOT a member of [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20]
8 is a member of [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20]
9 is NOT a member of [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20]
10 is a member of [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20]
11 is NOT a member of [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20]
12 is a member of [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20]
13 is NOT a member of [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20]
14 is a member of [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20]
15 is NOT a member of [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20]
16 is a member of [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20]
17 is NOT a member of [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20]
18 is a member of [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20]
19 is NOT a member of [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20]
20 is a member of [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20]
21 is NOT a member of [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20]
22 is NOT a member of [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20]

Note that the in operator produces a Boolean result; it can reveal whether or not an object is a member of
a list. It cannot reveal the location (index) of the object it finds. We consider options for locating elements
in Section 15.4.

10.5 List Assignment and Equivalence

Given the assignment

lst = [2, 4, 6, 8]

the expression lst is very different from the expression lst[2]. The expression lst is a reference to
the list, while lst[2] is a reference to a particular element in the list, in this case the integer 6. The

10.5. LIST ASSIGNMENT AND EQUIVALENCE 353

Figure 10.2 State of Listing 10.13 (listassignment.py) as the assignment statements execute

a
10 20 30

1 20 3

a
10 20 30

1 20 3

a
10 20 30

1 20 3

b = [10, 20, 30, 40]

a = [10, 20, 30, 40]

b[2] = 35

integer 6 is immutable (see Section 7.2); a literal integer cannot change to be another value. Six is always
six. A variable, of course, can change its value and its type through assignment. Variable assignment
changes the object to which the variable is bound. Recall Figures 2.2–2.6, and consider the Listing 10.13
(listassignment.py).

Listing 10.13: listassignment.py

a = [10, 20, 30, 40]
b = [10, 20, 30, 40]
print(‘a =’, a)
print(‘b =’, b)
b[2] = 35
print(‘a =’, a)
print(‘b =’, b)

Figure 10.2 shows the consequences of each of the assignment statements in Listing 10.13 (listassignment.py),

As Figure 10.2 illustrates, variables a and b refer to two different list objects; however, the elements of
both lists bind to the same (immutable) values. Reassigning an element of list b does not affect list a. The
output of Listing 10.13 (listassignment.py) verifies this analysis:

a = [10, 20, 30, 40]

10.5. LIST ASSIGNMENT AND EQUIVALENCE 354

Figure 10.3 State of Listing 10.14 (listalias.py) as the assignment statements execute

a
10 20 30

1 20 3

a
10 20 30

1 20 3

b = a

a = [10, 20, 30, 40]

b[2] = 35
a

10 20 30

1 20 3

b = [10, 20, 30, 40]
a = [10, 20, 30, 40]
b = [10, 20, 35, 40]

Now consider Listing 10.14 (listalias.py), a subtle variation of Listing 10.13 (listassignment.py). At
first glance, the code in Listing 10.14 (listalias.py) looks like it may behave exactly like Listing 10.13
(listassignment.py).

Listing 10.14: listalias.py

a = [10, 20, 30, 40]
b = a
print(‘a =’, a)
print(‘b =’, b)
b[2] = 35
print(‘a =’, a)
print(‘b =’, b)

As Figure 10.3 illustrates, the second assignment statement causes variables a and b to refer to the same
list object. We say that a and b are aliases. Reassigning b[2] changes a[2] as well, as Listing 10.14
(listalias.py)’s output shows:

a = [10, 20, 30, 40]
b = [10, 20, 30, 40]
a = [10, 20, 35, 40]
b = [10, 20, 35, 40]

10.5. LIST ASSIGNMENT AND EQUIVALENCE 355

If a refers to a list, the statement

b = a

does not make a copy of a’s list. Instead it makes a and b aliases to the same list. Lists are mutable data
structures. We may reassign individual list elements via []. If more than one variable is bound to the same
list, any element modification through one of the variables will affect the list from the point of view of all
the aliased variables.

The familiar == equality operator determines if two lists contain the same elements. The is operator
determines if two variables alias the same list. Listing 10.15 (listequivalence.py) demonstrates the difference
between the two operators.

Listing 10.15: listequivalence.py

# a and b are distinct lists that contain the same elements
a = [10, 20, 30, 40]
b = [10, 20, 30, 40]
print(‘Is ‘, a, ‘ equal to ‘, b, ‘?’, sep=”, end=’ ‘)
print(a == b)

print(‘Are ‘, a, ‘ and ‘, b, ‘ aliases?’, sep=”, end=’ ‘)
print(a is b)

# c and d alias are distinct lists that contain the same elements
c = [100, 200, 300, 400]
d = c # Makes d an alias of c
print(‘Is ‘, c, ‘ equal to ‘, d, ‘?’, sep=”, end=’ ‘)
print(c == d)

print(‘Are ‘, c, ‘ and ‘, d, ‘ aliases?’, sep=”, end=’ ‘)
print(c is d)

Listing 10.15 (listequivalence.py) prints

Is [10, 20, 30, 40] equal to [10, 20, 30, 40]? True
Are [10, 20, 30, 40] and [10, 20, 30, 40] aliases? False
Is [100, 200, 300, 400] equal to [100, 200, 300, 400]? True
Are [100, 200, 300, 400] and [100, 200, 300, 400] aliases? True

When comparing lists lst1 and lst2, if the expression lst1 is lst2 evaluates to True, the expression
lst1 == lst2 is guaranteed to be True.

What if we wish to make a copy of an existing list? Listing 10.16 (listcopy.py) shows one way to
accomplish this.

Listing 10.16: listcopy.py

def list_copy(lst):
result = []
for item in lst:

result += [item]
return result

10.5. LIST ASSIGNMENT AND EQUIVALENCE 356

def main():
# a and b are distinct lists that contain the same elements
a = [10, 20, 30, 40]
b = list_copy(a) # Make a copy of a
print(‘a =’, a, ‘ b =’, b)

print(‘Is ‘, a, ‘ equal to ‘, b, ‘?’, sep=”, end=’ ‘)
print(a == b)

print(‘Are ‘, a, ‘ and ‘, b, ‘ aliases?’, sep=”, end=’ ‘)
print(a is b)

b[2] = 35 # Change an element of b
print(‘a =’, a, ‘ b =’, b)

main()

The output of Listing 10.16 (listcopy.py) reveals:

a = [10, 20, 30, 40] b = [10, 20, 30, 40]
Is [10, 20, 30, 40] equal to [10, 20, 30, 40]? True
Are [10, 20, 30, 40] and [10, 20, 30, 40] aliases? False
a = [10, 20, 30, 40] b = [10, 20, 35, 40]

The list_copy function is Listing 10.16 (listcopy.py) makes an actual copy of a. Changing an element of
b does not affect list a.

In Section 10.7 we will see a more effective way to copy a list.

We can use range to create a range of values that the for statement can consume, but this range object
is not a list. The following interactive sequence shows how we can use the list function to make a list out
of a range object:

>>> r = range(10)
>>> r
range(0, 10)
>>> type(r)

>>> list(r)
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
>>> lst = list(r)
>>> lst
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
>>> type(lst)

The expression list(range(5)), therefore, creates the list [0, 1, 2, 3, 4].

The flexibility of the range expression makes it easy to create a variety of different kinds of lists with
regular structure. Listing 10.17 (rangetolist.py) explores several possibilities.

Listing 10.17: rangetolist.py

print(list(range(11)))

10.6. LIST BOUNDS 357

print(list(range(10, 101, 10)))
print(list(range(10, -1, -1)))

Listing 10.17 (rangetolist.py) produces

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
[10, 20, 30, 40, 50, 60, 70, 80, 90, 100]
[10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]

10.6 List Bounds

In the following code fragment:

a = [10, 20, 30, 40]

All of the following expressions are valid: a[0], a[1], a[2] and a[3]. The expression a[4] does not
represent a valid element in the list. An attempt to use this expression, as in

a = [10, 20, 30, 40]
print(a[4]) # Out-of-bounds access

results in a run-time exception. The interpreter will insist that the programmer use an integral value for
an index, but in order to prevent a run-time exception the programmer must ensure that the index used is
within the bounds of the list. Consider the following code:

# Make a list containing 100 zeros
v = [0] * 100
# User enters x at run time
x = int(input(“Enter an integer: “))
v[x] = 1 # Is this OK? What is x?

Since a list index may consist of an arbitrary integer expression, the interpreter checks every attempt to
access a list. If the interpreter detects an out-of-bounds index, the interpreter raises an IndexError (list
index out-of-bounds) exception. The programmer must ensure the provided index is in bounds to prevent
such a run-time error.

The above unreliable code can be helped with conditional access:

# Make a list containing 100 zeros
v = [0] * 100
# User enters x at run time
x = int(input(“Enter an integer: “))
# Ensure index is within list bounds
if 0 <= x < len(v): v[x] = 1 # This should be fine else: print("Value provided is out of range") Listing 10.18 (badreverse.py) attempts to print the list’s elements in reverse order, but it fails to stay inside the bounds of the list. ©2017 Richard L. Halterman Draft date: January 18, 2018 10.7. SLICING 358 Listing 10.18: badreverse.py def make_list(): """ Builds a list from input provided by the user. """ result = [] # List to return is initially empty in_val = 0 # Ensure loop is entered at least once while in_val >= 0:

in_val = int(input(“Enter integer (-1 quits): “))
if in_val >= 0:

result = result + [in_val] # Add item to list
return result

def main():
col = make_list()
# Print the list in reverse
for i in range(len(col), 0, -1):

print(col[i], end=” “)
print()

main()

The for statement

for i in range(len(col), 0, -1):
print(col[i], end=” “)

considers first the element at col[len(col)], which is one index past the end of the list. The corrected for
statement is

for i in range(len(col) – 1, -1, -1):
print(col[i], end=” “)

10.7 Slicing

We can make a new list from a portion of an existing list using a technique known as slicing. A list slice is
an expression of the form

list [ begin : end : step ]

where

• list is a list—a variable referring to a list object, a literal list, or some other expression that evaluates
to a list,

• begin is an integer representing the starting index of a subsequence of the list, and

• end is an integer that is one larger than the index of the last element in a subsequence of the list.

10.7. SLICING 359

• step is an integer that specifies the stride size through the list. A step size of three, for example,
would include every third element in the list within the specified range. Negative step values reverse
the direction of the slice.

If missing, the begin value defaults to 0. A begin value less than zero is treated as zero. If the end value
is missing, it defaults to the length of the list. An end value greater than the length of the list is treated as
the length of the list. The default step value is 1. The examples provided in Listing 10.19 (listslice.py) best
illustrate how list slicing works.

Listing 10.19: listslice.py

lst = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120]
print(lst) # [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120]
print(lst[0:3]) # [10, 20, 30]
print(lst[4:8]) # [50, 60, 70, 80]
print(lst[2:5]) # [30, 40, 50]
print(lst[-5:-3]) # [80, 90]
print(lst[:3]) # [10, 20, 30]
print(lst[4:]) # [50, 60, 70, 80, 90, 100, 110, 120]
print(lst[:]) # [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120]
print(lst[-100:3]) # [10, 20, 30]
print(lst[4:100]) # [50, 60, 70, 80, 90, 100, 110, 120]
print(lst[2:-2:2]) # [30, 50, 70, 90]
print(lst[::2]) # [10, 30, 50, 70, 90, 110]
print(lst[::-1]) # [120, 110, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10]

Observe that when a slice involves a negative step value the first argument in the slice represents the end of
the reverse slice, and the second argument is the beginning of the slice.

Suppose variable a refers to a nonempty list. Note the difference between the expression a[0:1] and
the expression a[0]. The expression a[0:1] represents a new list that contains only the first element of
the original list a. The expression a[0] refers to the first element in a, which is not necessarily a list. The
following interactive sequence illustrates the difference:

>>> a = [34, -19, 20, 8, 12]
>>> print(a)
[34, -19, 20, 8, 12]
>>> print(a[0:1])
[34]
>>> print(a[0])
34
>>> b = [[2, 5], 7, [11, 4]]
>>> print(b)
[[2, 5], 7, [11, 4]]
>>> print(b[0:1])
[[2, 5]]
>>> print(b[0])
[2, 5]

Slicing is the easiest way to make a copy of a list. The expression lst[:] evaluates to a copy of the
entire list lst. The list_copy function we saw in Listing 10.16 (listcopy.py) made for an interesting exer-
cise, but list slicing is shorter, simpler way to achieve the same result. The last statement in Listing 10.19
(listslice.py) shows the expression lst[::-1] makes a copy of list lst with all of its elements appearing in
reverse order.

10.7. SLICING 360

Listing 10.20 (prefixsuffix.py) prints all the prefixes and suffixes of the list [1, 2, 3, 4, 5, 6, 7, 8].

Listing 10.20: prefixsuffix.py

a = [1, 2, 3, 4, 5, 6, 7, 8]
print(‘Prefixes of’, a)
for i in range(0, len(a) + 1):

print(‘<', a[0:i], '>‘, sep=”)
print(‘———————————-‘)
print(‘Suffixes of’, a)
for i in range(0, len(a) + 1):

print(‘<', a[i:len(a) + 1], '>‘, sep=”)

Listing 10.20 (prefixsuffix.py) prints

Prefixes of [1, 2, 3, 4, 5, 6, 7, 8]
<[]>
<[1]>
<[1, 2]>
<[1, 2, 3]>
<[1, 2, 3, 4]>
<[1, 2, 3, 4, 5]>
<[1, 2, 3, 4, 5, 6]>
<[1, 2, 3, 4, 5, 6, 7]>
<[1, 2, 3, 4, 5, 6, 7, 8]>
———————————-
Suffixes of [1, 2, 3, 4, 5, 6, 7, 8]
<[1, 2, 3, 4, 5, 6, 7, 8]>
<[2, 3, 4, 5, 6, 7, 8]>
<[3, 4, 5, 6, 7, 8]>
<[4, 5, 6, 7, 8]>
<[5, 6, 7, 8]>
<[6, 7, 8]>
<[7, 8]>
<[8]>
<[]>

When the slicing expression appears on the left side of the assignment operator it can modify the con-
tents of the list. This is known as slice assignment. A slice assignment can modify a list by removing or
adding a subrange of elements in an existing list. Listing 10.21 (listslicemod.py) demonstrates how to use
slice assignment to modify a list.

Listing 10.21: listslicemod.py

lst = [10, 20, 30, 40, 50, 60, 70, 80]
print(lst) # Print the list
lst[2:5] = [‘a’, ‘b’, ‘c’] # Replace [30, 40, 50] segment with [‘a’, ‘b’, ‘c’]
print(lst)
print(‘==================’)
lst = [10, 20, 30, 40, 50, 60, 70, 80]
print(lst) # Print the list
lst[2:6] = [‘a’, ‘b’] # Replace [30, 40, 50, 60] segment with [‘a’, ‘b’]
print(lst)
print(‘==================’)
lst = [10, 20, 30, 40, 50, 60, 70, 80]

10.8. LIST ELEMENT REMOVAL 361

print(lst) # Print the list
lst[2:2] = [‘a’, ‘b’, ‘c’] # Insert [‘a’, ‘b’, ‘c’] segment at index 2
print(lst)
print(‘==================’)
lst = [10, 20, 30, 40, 50, 60, 70, 80]
print(lst) # Print the list
lst[2:5] = [] # Replace [30, 40, 50] segment with [] (delete the segment)
print(lst)

Listing 10.21 (listslicemod.py) displays:

[10, 20, 30, 40, 50, 60, 70, 80]
[10, 20, ‘a’, ‘b’, ‘c’, 60, 70, 80]
==================
[10, 20, 30, 40, 50, 60, 70, 80]
[10, 20, ‘a’, ‘b’, 70, 80]
==================
[10, 20, 30, 40, 50, 60, 70, 80]
[10, 20, ‘a’, ‘b’, ‘c’, 30, 40, 50, 60, 70, 80]
==================
[10, 20, 30, 40, 50, 60, 70, 80]
[10, 20, 60, 70, 80]

10.8 List Element Removal

We have seen how to append elements to a list using the list concatenation operator (+). We can use del to
remove a specific element from a list via its index. The following sequence uses range to build a list and
del to remove one of the list’s elements:

>>> a = list(range(10, 51, 10))
>>> a
[10, 20, 30, 40, 50]
>>> del a[2]
>>> a
[10, 20, 40, 50]

We can remove a contiguous range of elements of a list using del with a slice, as shown here:

>>> b = list(range(20))
>>> b
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]
>>> del b[5:15]
>>> b
[0, 1, 2, 3, 4, 15, 16, 17, 18, 19]

As with scalar variables, you can del multiple list elements with one del statement, but it requires much
more care. Consider the following:

>>> c = list(range(20))
>>> c
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]
>>> del c[1], c[18]

10.9. LISTS AND FUNCTIONS 362

>>> c
[0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18]

You might expect the del statement to remove element 1 and element 18. Instead, it removed 1 and 19.
The deletion progresses from left to right, so the statement first removes 1, leaving the following list:

[0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]

The subsequent removal of c[18] occurs on this new list, not the original list. Element 19 now is at index
18, so the statement deletes element 19 instead of element 18. Consider the following list:

d = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]

suppose we wish to delete elements 2, 3, 4, 5, 6, and 18. We might try the following del statement:

del c[2:7], c[18]

This statement, however, produces a run-time exception. The error arises because removing the slice of
elements shortens the list so index 18 is out of range. Reordering the statement produces the desired
results:

del c[18], c[2:7]

since it removes elements from the back to the front.

Because faulty attempts at multiple list element deletions can lead to surprising results it is best to
restrict a list del statement to a single element or a single slice.

10.9 Lists and Functions

We can pass a list as an argument to a function, as shown in Listing 10.22 (listfunc.py)

Listing 10.22: listfunc.py

def sum(lst):
“””
Adds up the contents of a list of numeric values.
lst is the list to sum.
Returns the sum of all the elements or zero if the list is empty.
“””
result = 0
for item in lst:

result += item
return result

def make_zero(lst):
“””
Makes every element in list lst zero
“””
for i in range(len(lst)):

lst[i] = 0

10.10. LIST METHODS 363

def random_list(n):
“””
Builds a list of n integers, where each integer
is a pseudorandom number in the range 0…99.
Returns the random list.
“””
import random
result = []
for i in range(n):

rand = random.randrange(100)
result += [rand]

return result

def main():
a = [2, 4, 6, 8]
# Print the contents of the list
print(a)
# Compute and display sum
print(sum(a))
# Zero out all the elements of list
make_zero(a)
# Reprint the contents of the list
print(a)
# Compute and display sum
print(sum(a))
# Test empty list
a = []
print(a)
print(sum(a))
# Test pseudorandom list with 10 elements
a = random_list(10)
print(a)
print(sum(a))

main()

In Listing 10.22 (listfunc.py) the functions sum and make_zero accept a parameter of type list. Section 7.2
addressed the consequences of passing immutable types like integers and strings to functions. Since list
objects are mutable, passing to a function a reference to a list object binds the formal parameter to the list
object. This means the formal parameter becomes an alias of the actual parameter. The sum method does
not attempt to modify its parameter, but the make_zero method changes every element in the list to zero.
This means the make_zero function will modify the a list object in main.

10.10 List Methods

All Python lists are instances of the list class. Table 10.1 lists some of the methods available to list
objects.

10.10. LIST METHODS 364

Table 10.1 A few of the methods available to list objects
list Methods

count
Returns the number of times a given element appears in the list. Does not modify the list.

insert
Inserts a new element before the element at a given index. Increases the length of the list
by one. Modifies the list.

append
Adds a new element to the end of the list. Modifies the list.

index
Returns the lowest index of a given element within the list. Produces an error if the element
does not appear in the list. Does not modify the list.

remove
Removes the first occurrence (lowest index) of a given element from the list. Produces an
error if the element is not found. Modifies the list if the item to remove is in the list.

reverse
Physically reverses the elements in the list. The list is modified.

sort
Sorts the elements of the list in ascending order. The list is modified.

Since lists are mutable data structures, the list class has both __getitem__ and __setitem__ methods.
The statement

x = lst[2]

behind the scenes becomes the method call

x = list.__getitem__(lst, 2)

and the statement

lst[2] = x

maps to

list.__setitem__(lst, 2, x)

The str class does not have a __setitem__ method, since strings are immutable.

The code

lst = [“one”, “two”, “three”]
lst += [“four”]

is equivalent to

lst = [“one”, “two”, “three”]
lst.append(“four”)

but the version using append is more efficient.

Section 10.7 showed that if lst is a list, the slice lst[::-1] returns a copy of the list with all the
elements in reverse order. The expression lst.reverse() modifies lst, reversing the elements within lst

10.10. LIST METHODS 365

itself. Just to complicate the situation a bit more, Section 10.2 used to reversed function to create an
iterable object that allows programs to traverse a list in reverse order. Three ways different techniques that
involve reversing a list can be confusing. The following summarizes the differences:

• reversed is a function (not a method) that accepts a list (or, as we will see, any sequence object); it
returns an iterable object compatible with the for statement.

• list.reverse is a method of the list class (not a function) that mutates an existing list; it does not
return anything.

• The [::-1] slice notation returns a new list containing a copy of the original list with its elements in
reverse order.

Listing 10.23 (reversals.py) … exposes the major differences amongst the three reversal techniques.

Listing 10.23: reversals.py

lst = [1, 2, 3, 4, 5, 6, 7]
print(“—- Original list —-“)
print(“lst =”, lst)
print(“—- reversed function—-“)
obj1 = reversed(lst)
print(“lst =”, lst)
print(“obj1 =”, obj1)
print(“—- Slice —-“)
obj2 = lst[::-1]
print(“lst =”, lst)
print(“obj2 =”, obj2)
print(“—- list.reverse method —-“)
obj3 = lst.reverse()
print(“lst =”, lst)
print(“obj3 =”, obj3)

Listing 10.23 (reversals.py) produces the following output:

—- Original list —-
lst = [1, 2, 3, 4, 5, 6, 7]
—- reversed function—-
lst = [1, 2, 3, 4, 5, 6, 7]
obj1 = —- Slice —-
lst = [1, 2, 3, 4, 5, 6, 7]
obj2 = [7, 6, 5, 4, 3, 2, 1]
—- list.reverse method —-
lst = [7, 6, 5, 4, 3, 2, 1]
obj3 = None

Notice that neither the reversed function nor the slice alter the original list. Also observe that the
list.reverse method does not return a value (it implicitly returns None).

10.11. PRIME GENERATION WITH A LIST 366

10.11 Prime Generation with a List

Listing 10.24 (fasterprimes.py) uses an algorithm developed by the Greek mathematician Eratosthenes who
lived from 274 B.C. to 195 B.C. Called the Sieve of Eratosthenes, the principle behind the algorithm is
simple: Make a list of all the integers two and larger. Two is a prime number, but any multiple of two
cannot be a prime number (since a multiple of two has two as a factor). Go through the rest of the list and
mark out all multiples of two (4, 6, 8, …). Move to the next number in the list (in this case, three). If it is
not marked out, it must be prime, so go through the rest of the list and mark out all multiples of that number
(6, 9, 12, …). Continue this process until you have listed all the primes you want.

Listing 10.24 (fasterprimes.py) implements the Sieve of Eratosthenes in a Python function.

Listing 10.24: fasterprimes.py

# Display the prime numbers between 2 and 500

# Largest potential prime considered
MAX = 500

def main():
# Each position in the Boolean list indicates
# if the number of that position is not prime:
# false means “prime,” and true means “composite.”
# Initially all numbers are prime until proven otherwise
nonprimes = MAX * [False] # Initialize to all False

# First prime number is 2; 0 and 1 are not prime
nonprimes[0] = nonprimes[1] = True

# Start at the first prime number, 2.
for i in range(2, MAX + 1):

# See if i is prime
if not nonprimes[i]:

print(i, end=” “)
# It is prime, so eliminate all of its
# multiples that cannot be prime
for j in range(2*i, MAX + 1, i)

nonprimes[j] = True
print() # Move cursor down to next line

How much better is the algorithm in Listing 10.24 (fasterprimes.py) than the square-root-optimized
version we saw in Listing 6.8 (timemoreefficientprimes.py)? Listing 10.25 (timeprimes.py) compares the
execution speed of the two algorithms.

Listing 10.25: timeprimes.py

# Count the number of prime numbers less than
# 2 million and time how long it takes
# Compares the performance of two different
# algorithms.

from time import clock
from math import sqrt

10.11. PRIME GENERATION WITH A LIST 367

def count_primes(n):
“””
Generates all the prime numbers from 2 to n – 1.
n – 1 is the largest potential prime considered.
“””
start = clock() # Record start time

count = 0
for val in range(2, n):

root = round(sqrt(val)) + 1
# Try all potential factors from 2 to the square root of n
for trial_factor in range(2, root):

if val % trial_factor == 0: # Is it a factor?
break # Found a factor

else:
count += 1 # No factors found

stop = clock() # Stop the clock
print(“Count =”, count, “Elapsed time:”, stop – start, “seconds”)

def sieve(n):
“””
Generates all the prime numbers from 2 to n – 1.
n – 1 is the largest potential prime considered.
Algorithm originally developed by Eratosthenes.
“””

start = clock() # Record start time

# Each position in the Boolean list indicates
# if the number of that position is not prime:
# false means “prime,” and true means “composite.”
# Initially all numbers are prime until proven otherwise
nonprimes = n * [False] # Global list initialized to all False

count = 0

# First prime number is 2; 0 and 1 are not prime
nonprimes[0] = nonprimes[1] = True

# Start at the first prime number, 2.
for i in range(2, n):

# See if i is prime
if not nonprimes[i]:

count += 1
# It is prime, so eliminate all of its
# multiples that cannot be prime
for j in range(2*i, n, i):

nonprimes[j] = True
# Print the elapsed time
stop = clock()
print(“Count =”, count, “Elapsed time:”, stop – start, “seconds”)

10.12. COMMAND-LINE ARGUMENTS 368

def main():
count_primes(2000000)
sieve(2000000)

main()

Since printing to the screen takes up the majority of the time, Listing 10.25 (timeprimes.py) counts the
number of primes rather than printing each one. This allows us to better compare the behavior of the two
approaches. The square root version has been optimized slightly more: the floating-point root variable is
not an integer. The less than comparison between two integers is faster than the floating-point equivalent.

The output of Listing 10.25 (timeprimes.py) on one system reveals

Count = 148933 Elapsed time: 37.57788172418102 seconds
Count = 148933 Elapsed time: 1.028922514194747 seconds

Our previous “optimized” version requires almost 38 seconds to count the number of primes less than two
million, while the version based on the Sieve of Eratosthenes takes only about one second.

10.12 Command-line Arguments

The sys module provides a global variable named argv that is a list of extra text that the user can supply
when launching an application from the operating system shell (normally called the command prompt in
Windows and terminal in OS X and Linux). To run a program stored in the file myprog.py, the user would
type the command

python myprog.py

Some programs expect or allow the user to provide extra information. Listing 10.26 (cmdlineargs.py) is a
program meant to be executed from the command line with extra arguments. It simply reports the extra
information the user supplied.

Listing 10.26: cmdlineargs.py

import sys

for arg in sys.argv:
print(‘[‘ + arg + ‘]’)

The following shows one run of Listing 10.26 (cmdlineargs.py):

C:\Code>python cmdlineargs.py -h 45 extra
[cmdlineargs.py]
[-h]
[45]
[extra]

The shell printed C:
Code¿, and the user typed the remainder of the first line. In response, the program printed four lines that

10.13. LIST COMPREHENSIONS 369

follow. Notice that argv[0] is simply the name of the file containing the program. argv[1] is the string
‘-h’, argv[2] is the string ’45’, and argv[3] is the string ‘extra’.

In Listing 10.27 (sqrtcmdline.py), the user supplies a range of integers on the command line. The
program then prints all the integers in that range along with their square roots.

Listing 10.27: sqrtcmdline.py

from sys import argv
from math import sqrt

if len(argv) < 3: print('Supply range of values') else: for n in range(int(argv[1]), int(argv[2]) + 1): print(n, sqrt(n)) print() The following shows some sample runs of Listing 10.27 (sqrtcmdline.py): C:\Code>python sqrtcmdline.py
Supply range of values

C:\Code>python sqrtcmdline.py 2
Supply range of values

C:\Code>python sqrtcmdline.py 2 10
2 1.4142135623730951
3 1.7320508075688772
4 2.0
5 2.23606797749979
6 2.449489742783178
7 2.6457513110645907
8 2.8284271247461903
9 3.0
10 3.1622776601683795

10.13 List Comprehensions

Mathematicians often represent sets in two different ways:

1. set roster notation, which enumerates the elements in the set, and

2. set builder notation, which describes the contents of the set using a rule for constructing the set’s
elements

We can express P, the set of perfect squares less than 50, using both of these methods:

1. set roster notation: P = {0,1,4,9,16,25,36,49}

2. set builder notation: P = {x2 | x ∈ {0,1,2,3,4,5,6,7}}

10.13. LIST COMPREHENSIONS 370

The set roster notation example is obvious—it just lists the elements of the set. We read the set builder
notation example as “P is the set of all squares of x, such that x is taken from the set {0,1,2,3,4,5,6,7}.
Set builder notation in mathematics is essential for representing very large sets and infinite sets; for example,
consider S = {x2 | x ∈ Z}, the set of all perfect squares (Z is the infinite set of integers). Listing all the
elements is impossible. We could try to list the first few elements followed by an ellipsis (. . . ), but the
pattern may not be obvious to all readers.

We can compare Python’s lists to mathematical sets (with the important caveat that the order of the
elements in a list matters, but element order is irrelevant in a mathematical set). We have seen how to
express lists in Python in a manner similar to set roster notation in mathematics:

P = [1, 4, 9, 16, 25, 36, 49]

Python also supports a technique similar to set builder notation, called list comprehension. In Python, we
can express list P above as

P = [x**2 for x in [0, 1, 2, 3, 4, 5, 6, 7]]

or, using a range expression as

P = [x**2 for x in range(8)]

Observe the use of the keywords for and in within the square brackets. The for keyword takes the place
of the mathematical | symbol (usually pronounced “such that” or “where”), and in is the ∈ membership
relation. All list comprehensions use for within the square brackets.

We have seen that the range expression is useful for building lists with a regular, predictable ordering.
As another example, consider the following code that builds a list of the multiples of four from 4 to 40:

>>> lst = list(range(4, 41, 4))
>>> lst
[4, 8, 12, 16, 20, 24, 28, 32, 36, 40]

One limitation of range is that its arguments all must be integers. Suppose we wish to create succinctly a
list of floating-point numbers in a regular sequence. We cannot use the range expression by itself to express
such a list, but a list comprehension is ideal for the task. The following interactive sequence creates a list
containing the first ten multiples of one-half:

>>> halves = [x/2 for x in range(10)]
>>> halves
[0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5]

The single slash (/) performs floating-point division, populating the list with floating-point values.

We can use a list comprehension to filter certain elements out of a list. In the following example we
take a list containing integers and produce a new list with all the negative values omitted:

>>> lst = [9, -44, 0, 30, 2, -6, -8, 9, -8, 23]
>>> lst
[9, -44, 0, 30, 2, -6, -8, 9, -8, 23]
>>> [x for x in lst if x >= 0]
[9, 0, 30, 2, 9, 23]

The expression [x for x in lst if x >= 0] selects all the elements from list lst except for those less
than zero. If we instead want a list of the negative values, invert the logic of the condition:

10.13. LIST COMPREHENSIONS 371

>>> lst
[9, -44, 0, 30, 2, -6, -8, 9, -8, 23]
>>> [x for x in lst if x < 0] [-44, -6, -8, -8] The next example begins with a mixed list of numeric values and strings. The following interactive sequence shows how we can use list comprehensions to selectively filter out of the list all the strings or all the numbers: >>> lst = [‘ABC’, 23.4, 7, ‘Wow’, 16, ‘xyz’, 10]
>>> lst
[‘ABC’, 23.4, 7, ‘Wow’, 16, ‘xyz’, 10]
>>> [x for x in lst if type(x) != str]
[23.4, 7, 16, 10]
>>> lst
[‘ABC’, 23.4, 7, ‘Wow’, 16, ‘xyz’, 10]
>>> [x for x in lst if type(x) == str]
[‘ABC’, ‘Wow’, ‘xyz’]

Neither list comprehension expression affects the original list lst. A list comprehension expression evalu-
ates to a new list, and we can assign a variable to this list if we wish to retain it for later use:

>>> lst = [‘ABC’, 23.4, 7, ‘Wow’, 16, ‘xyz’, 10]
>>> lst2 = [x for x in lst if type(x) != str]
>>> lst
[‘ABC’, 23.4, 7, ‘Wow’, 16, ‘xyz’, 10]
>>> lst2
[23.4, 7, 16, 10]

The lists we build with list comprehension are not limited to elements with simple, single values. The
following interactive sequence builds a list containing tuples of the first 10 positive integers paired with
their squares:

>>> squares = [(x, x**2) for x in range(1, 11)]
>>> squares
[(1, 1), (2, 4), (3, 9), (4, 16), (5, 25), (6, 36), (7, 49), (8, 64), (9, 81), (10, 100)]

We can use multiple for expressions within a single list comprehension. This is useful for combining
elements from different lists. In the following example we make tuples out of the elements of two different
lists:

>>> pairs = [(x, y) for x in [1, 2, 3] for y in [‘a’, ‘b’]]
>>> pairs
[(1, ‘a’), (1, ‘b’), (2, ‘a’), (2, ‘b’), (3, ‘a’), (3, ‘b’)]

We can use the if keyword to add conditions for list membership. To start with, suppose we wish to
express the list containing the ordered pairs of elements taken from the list [1, 2, 3]. That is easy enough:

>>> points = [(x, y) for x in [1, 2, 3] for y in [1, 2, 3]]
>>> points
[(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)]

We can use variables within our list comprehension to shorten it a bit:

10.13. LIST COMPREHENSIONS 372

>>> V = [1, 2, 3]
>>> points = [(x, y) for x in V for y in V]
>>> points
[(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)]

Now suppose we wish to exclude pairs that contain the same elements. We can add an if expression to the
end of the list comprehension to impose additional conditions on the list members:

>>> V = [1, 2, 3]
>>> points = [(x, y) for x in V for y in V if x != y]
>>> points
[(1, 2), (1, 3), (2, 1), (2, 3), (3, 1), (3, 2)]

Here we see no number is paired with itself. The following list comprehension excludes pairs with compo-
nents that sum to an even number:

>>> points = [(x, y) for x in [1, 2, 3] for y in [1, 2, 3] if (x + y) % 2 != 0]
>>> points
[(1, 2), (2, 1), (2, 3), (3, 2)]

We see (1, 3) is missing because 1+3 = 4, and 4 is even.

Suppose we wish to build a list of factor pairs for a positive integer supplied by the user; for example, the
tuple (2, 15) is a factor pair for the number 30 because 2×15 = 30. We will begin with an easier problem:
create a list of all the factors for a positive integer supplied by the user. Listing 10.28 (factorsingles.py) uses
a list comprehension to create a such a list of factors.

Listing 10.28: factorsingles.py

n = int(input(“Please enter a positive integer: “))
factors = [x for x in range(1, n + 1) if n % x == 0]
print(“Factors of”, n, “:”, factors)

The following shows a sample run of Listing 10.28 (factorsingles.py) with the user entering the value 100:

Please enter a positive integer: 100
Factors of 100 : [1, 2, 4, 5, 10, 20, 25, 50, 100]

Observe that the program printed all the factors of 100. We want our list to contain factor pairs; that is, we
want to pair each factor with its mate so that the two values multiplied together equal the number the user
entered. We already have the first elements of the pairs, and we can compute their mates easily with integer
division. If x is a factor of n, then n//x will be its mate because x * n//x will equal n. The factor pair is
thus (x, n//x). Listing 10.29 (factorpairs.py) shows the resulting program which produces a list of factor
pairs.

Listing 10.29: factorpairs.py

n = int(input(“Please enter a positive integer: “))
factors = [(x, n//x) for x in range(1, n + 1) if n % x == 0]
print(“Factor pairs of”, n, “:”, factors)

The following shows a sample run of Listing 10.28 (factorsingles.py) with the user entering the value 100:

10.13. LIST COMPREHENSIONS 373

Please enter a positive integer: 100
Factor pairs of 100 : [(1, 100), (2, 50), (4, 25), (5, 20), (10, 10),
(20, 5), (25, 4), (50, 2), (100, 1)]

This is fine, but it would be nice to avoid adding redundant pairs pairs to the list; that is, we want just one of
the pairs (2, 50) and (50, 2) to appear in our list. Notice that once the first element reaches the square
root of the value supplied by the user, the remaining pairs are mirror images of earlier pairs. We can use this
fact to limit the range expression; we will choose xs in the range 1 . . .

√
n, inclusive. The Python imple-

mentation of this range is range(1, round(math.sqrt(n)) + 1). Listing 10.30 (uniquefactorpairs.py)
adds this finishing touch to avoid the redundant pairs.

Listing 10.30: uniquefactorpairs.py

import math
n = int(input(“Please enter a positive integer: “))
factors = [(x, n//x) for x in range(1, round(math.sqrt(n)) + 1) if n % x == 0]
print(“Factor pairs of”, n, “:”, factors)

The following shows a sample run of Listing 10.30 (uniquefactorpairs.py):

Please enter a positive integer: 100
Factor pairs of 100 : [(1, 100), (2, 50), (4, 25), (5, 20), (10, 10)]

We can use list comprehensions to filter elements from an existing list. In the following example we
build an almost regular list that omits a few elements:

>>> L = [x for x in range(20) if x not in [12, 8, 3, 17]]
>>> L
[0, 1, 2, 4, 5, 6, 7, 9, 10, 11, 13, 14, 15, 16, 18, 19]

This list contains all the elements in range(20) in order, but it specifically excludes the values 3, 8, 12,
and 17.

We can use a Boolean expression to build a list of Boolean values:

>>> [x > 2 for x in [5, 1, 0, 7, 2, 7, 3]]
[True, False, False, True, False, True, True]

We will see in Section 11.9 how to apply such Boolean conditions in a slightly different way to determine
quickly and easily if all the elements in a list possess a given property or if any elements in a list possess a
given property.

List comprehensions not essential to any program. Consider the list comprehension above:

L = [x for x in range(20) if x not in [12, 8, 3, 17]]

We can rewrite this as

L = []
for x in range(20):

if x not in [12, 8, 3, 17]:
L += [x]

10.13. LIST COMPREHENSIONS 374

While our expanded code is functionally equivalent to the list comprehension, in general a list comprehen-
sion will be more efficient than its equivalent expanded form.

Python list comprehensions are powerful and can be quite complex. When programming it sometimes
is easier to build the list without list comprehension and later discover a way to transform the code to use list
comprehension. As an example, consider the task of building a list that contains all the prime numbers less
than 100. For all n ≥ 2, the following list comprehension creates a list of all the factors of n, not including
1 and n itself:

[x for x in range(2, n) if n % x == 0]

The following expression evaluates to true if n is a prime number; otherwise, it evaluates to false:

[x for x in range(2, n) if n % x == 0] == []

(Note that this expression does not take advantage of the square root optimization we saw in Listing 6.4
(moreefficientprimes.py).) In Python, the empty list ([]) is considered false, and any nonempty list is
considered true, so the following expression reveals the primality of n as well:

not [x for x in range(2, n) if n % x == 0]

To make a list of all the prime numbers less than 80, we can use a list comprehension expression that begins
like the following:

[p for p in range(2, 80) if ???]

We then can replace the ??? with the list comprehension from above that determines if p is a prime number:

[p for p in range(2, 80) if not [x for x in range(2, p) if p % x == 0]]

In the Python shell we can see the list this expression produces:

>>> [p for p in range(2, 80) if not [x for x in range(2, p) if p % x == 0]]
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79]

List comprehensions are a valuable, powerful tool for creating lists. While the prime numbers example
demonstrates the power of Python’s list comprehensions, many programmers would consider the resulting
list comprehension expression above to be a bit too complex and tricky. Additionally, it is not very efficient.
It creates an internal, temporary list of factors for each number it must consider. Simpler list comprehension
expressions that avoid nested lists generally are efficient and readable. As a rule, you should use list
comprehensions when they make your code simpler and more readable, but do not go out of your way to
construct arcane list comprehension expressions just because you can.

If we replace the outer square brackets of a list comprehension with parentheses, the expression becomes
a generator expression (sometimes called a generator comprehension). A generator expression creates a
generator (Section 8.8) instead of a list. We can iterate over a generator with a for loop, as Listing 10.31
(generatorexpression.py) illustrates.

Listing 10.31: generatorexpression.py

for val in (2**x for x in range(10)):
print(val, end=’ ‘)

print()

Listing 10.31 (generatorexpression.py) prints

10.14. MULTIDIMENSIONAL LISTS 375

1 2 4 8 16 32 64 128 256 512

If you need to keep around the values of a sequence for additional processing, store them in a list and
possibly use a list comprehension to make the list. If you simply need to visit the elements in a sequence
once, building a list is overkill; use a generator to produce the sequence’s elements as needed. The list has
to store all of its elements in memory for the life of the list, but a generator produces only one element
at a time. This means the list [x for x in range(n)] will consume a large amount of the computer’s
memory if n is large. The generator (x for x in range(n)) uses a relatively small, constant amount of
memory regardless of n’s value.

Section 10.16 compares lists and generators in more detail.

10.14 Multidimensional Lists

A list represents a one-dimensional (1D), linear data structure. We can display a list’s elements from
beginning to end in a straight line; for example:

[9, 17, 88, 2, 17, 6, 45]

We can locate an element uniquely within the list via a single integer index, its offset from the beginning of
the list. In the example list above, element 88 is at index 2.

Some kinds of information are better represented two-dimensionally, in a rectangular array of elements,
also known as a matrix; for example,

100 14 8 22 71
0 243 68 1 30

90 21 7 67 112
115 200 70 150 8

Such a two-dimensional (2D) matrix has a particular number of rows and columns. The values in rows are
arranged horizontally, and the elements in columns are arranged vertically. The above matrix, therefore,
has four rows and five columns. We say its dimensions are 4×5. The first row of the example matrix above
consists of the elements 100, 14, 8, 22, and 71; the first column contains 100, 0, 90, and 115. We can locate
an element uniquely within the matrix with two integer indices—the first index represents the element’s
offset from the first row, and the second index represents the element’s offset from the first column. As with
1D lists, the index of the first row is zero, and the index of the first column is zero. The element 67 above
has a row index of 2 and a column index of 3.

How are 2D matrices used? Mathematicians can represent a system of equations in a matrix and use
techniques from linear algebra to solve the system. Computer scientists use 2D matrices to model the
articulation of robotic arms. Computer graphics programmers mathematically manipulate 2D matrices
to transform data in 3D space and project it onto a 2D screen giving users the illusion of depth, motion,
location. Many classic games such as chess, checkers, Go, and Scrabble involve a 2D grid of board positions
that naturally maps to a 2D matrix. A word search puzzle is a rectangular array of letters, and a maze is
simply a 2D arrangement of adjoining rooms, some of which are connected and others that are not.

In Python we can express a 2D matrix as a list of lists. We can model the matrix shown above with the
following statement:

matrix = [[100, 14, 8, 22, 71],
[ 0, 243, 68, 1, 30],

10.14. MULTIDIMENSIONAL LISTS 376

[ 90, 21, 7, 67, 112],
[115, 200, 70, 150, 8]]

While this arrangement of text best visually communicates the 2D nature of the object, as far as Python is
concerned it still is simply a linear list in which each element is itself a list. We can reveal this internal
linear representation with the following interactive sequence:

>>> matrix = [[100, 14, 8, 22, 71],
… [ 0, 243, 68, 1, 30],
… [ 90, 21, 7, 67, 112],
… [115, 200, 70, 150, 8]]
>>>
>>> print(matrix)
[[100, 14, 8, 22, 71], [0, 243, 68, 1, 30], [90, 21, 7, 67, 112], [115, 200, 70, 150, 8]]

Even though internally such a matrix ultimately must be linear, the good news is that we conceptually can
treat our list of lists as if it were a 2D structure, and everything will work as expected. Figure 10.4 conpares
our conceptual notion of a 2D list with its physical layout.

We must use two indices to access an element in our 2D list. We can print the element 67 from the
above 2D list named matrix as

print(matrix[2][3])

Note the double square brackets. The first index (2) selects the row, and the second index (3) specifies the
column. The expression matrix represents the whole 2D list. If we use just one index with a 2D list, it
selects an entire row. The expression matrix[x] represents the 1D list that constitutes row x in matrix;
for example, matrix[2] is the list [90, 21, 7, 67, 112]. That means we can interpret the expression
matrix[2][3] as (matrix[2])[3]; that is, the element at index 3 within the row at index 2. The expression
len(matrix) is the number of rows in matrix. The expression len(matrix[2]) represents the number of
elements in the row at index 2. For many applications, every row in the 2D list will have the same length;
we call such a 2D list a table. Python does not require that all rows have the same number of elements. The
following code creates what is called a ragged array, where each row potentially has a different length:

ragged = [[100, 14, 8, 22, 71],
[ 0, 243],
[ 90, 21, 7, 67],
[115, 200, 70, 150, 8, 45, 60]]

Listing 10.32 (prettyprint2d.py) demonstrates how to print a 2D list more attractively with a nested loop.

Listing 10.32: prettyprint2d.py

matrix = [[100, 14, 8, 22, 71],
[ 0, 243, 68, 1, 30],
[ 90, 21, 7, 67, 112],
[115, 200, 70, 150, 8]]

for row in matrix: # Process each row
for elem in row: # For each element in a given row

print(‘{:>4}’.format(elem), end=”)
print()

Listing 10.32 (prettyprint2d.py) displays the following,

10.14. MULTIDIMENSIONAL LISTS 377

Figure 10.4 A conceptual illustration of a two-dimensional list vs. its physical layout. In the conceptual
view the indices along the side locate the rows, and the indices across the top refer to the columns. When
programming it is safe to use the conceptual view as a mental model of a 2D list. The internal representation
of a 2D list’s physical layout shows that a 2D list is really just a list of lists.

matrix
1 20 3 4

115 200 70 150 8

90 21 7 67 112

0 243 68 1 30

100 14 8 22 710

100 14 8 22

matrix

1 20 3

Conceptual View

Internal Representation

0 243 68 1

1 20 3 4

90 21 7 67

1 20 3 4

112

115 200 70 150

1 20 3 4

10.14. MULTIDIMENSIONAL LISTS 378

100 14 8 22 71
0 243 68 1 30
90 21 7 67 112

115 200 70 150 8

The creation of a large 2D list with identical initial values merits special attention. Section 10.3 showed
how we can construct lists using the list element multiplier notation. The following statement:

a = [0] * 4

builds a 1D list named a that contains four zeros. This list element multiplier technique is straightforward
when the elements are immutable types (see Section 9.8). All the elements refer to the same object, but
since the object cannot be mutated, any reassignment of a list element will not effect any of the other
elements in the list. The following code produces no surprises:

a = [0] * 4 # Make a small list containing zeros
print(a) # Prints [0, 0, 0, 0]
a[1] = 5 # Replace element at index 1
print(a) # Prints [0, 5, 0, 0]

It prints, as expected,

[0, 0, 0, 0]
[0, 5, 0, 0]

If we attempt to build a 2D list the same way, we get a surprising result:

a = [[0] * 4] * 3 # Make a 3 x 4 2D list containing zeros
print(a) # Prints [[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]
a[1][2] = 5 # Replace element at row 1, column 2
print(a) # Prints what?!

This code prints

[[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]
[[0, 0, 5, 0], [0, 0, 5, 0], [0, 0, 5, 0]]

We expected the first line, but how did our attempt to change just one element in the list modify two other
elements at the same time?

To understand what is happening, we first will consider the simpler, 1D case that behaved as expected.
Figure 10.5 illustrates list creation and element reassignment in the 1D list. Figure 10.5 shows that after
the list multiplication statement that creates the list, all the elements in the list refer to the same object, the
integer zero. The object zero is immutable, so it cannot change, but we can redirect a reference in the list
to a different object, and that is exactly what the assignment statement does.

Figure 10.6 illustrates the attempt at 2D list creation and the subsequent element reassignment. As in
the 1D case from before, the list multiplication creates a list of elements that all refer to the same object.
In this case, however, instead of the integer zero, the object to which all the elements refer is a 1D list
containing zeros. Since all the references in the list of lists a refer to the same list, all the rows in our 2D
list alias the same list of zeros. Attempting the change the element at index 2 in row 1 changes the element
at index 2 in all the rows.

10.14. MULTIDIMENSIONAL LISTS 379

Figure 10.5 List multiplication creates a list of elements that all refer to the same object, the integer zero.
Reassignment of the element at index 1 redirects the index 1 reference to a different object, in this case five.

a
1 20 3

a = [0] * 4

a
1 20 3

a[1] = 5

List multiplication creation with immutable types such as integers, floating-point numbers, and strings is
always well behaved. The aliasing is not a problem, since immutable objects cannot change. Programmers
must be particularly careful using list multiplication when the elements are mutable types. Lists are mutable,
and we will encounter more mutable types later.

How can we easily create a 3×4 matrix of zeros? We can use a combination of list multiplication and
list comprehension, as follows:

a = [[0] * 4 for x in range(3)]

The effect of this statement is similar to the following code:

a = []
for x in range(3):

a.append([0] * 4)

The execution of list multiplication creates a new list each time through the loop. The list comprehension
example performs an optimized loop behind the scenes to achieve the result.

One thing to notice about the list comprehension example is the expression before the for keyword
does not contain the variable x; it contains only the expression [0] * 4:

a = [[0] * 4 for x in range(3)]

The for expression within the list comprehension requires a variable to control range’s iteration. Here
we gave it the name x. This variable x is local to the list comprehension. Section 2.3 emphasized that all
variables should have meaningful, descriptive names. Assignment attaches a name to an object so we can
access that object in the future via its name. The problem with x is this: we do not really do any thing with x.
It is difficult to provide a good name for a variable that we never actually use. Some programmers address

10.14. MULTIDIMENSIONAL LISTS 380

Figure 10.6 List multiplication creates a list of elements that all refer to the same object, a list containing
zeros. All the references in the outer list alias the same inner list, so the list actually contains just one,
shared physical row. The list at row 0 is the same list at row 1 and row 2. Due to the aliasing, reassignment
of the element at index 2 in row 1 affects the reference at index 2 in all the rows.

1 20 3

a = [[0] * 4] * 3

a[1][2] = 5 5

1 20

1 20 3

a 1 20

10.14. MULTIDIMENSIONAL LISTS 381

this situation by using a special variable name consisting of the single underscore (_). There is nothing
magical about the single underscore symbol—it is a legal identifier, and, therefore, is a valid variable name.
Its primary value lies in the fact that its name is ultimately non-descriptive! The name x may have a special
meaning in some contexts, like the first element in an (x,y) ordered pair, but it is difficult to attach meaning
to the name _.

The _ name is widely recognized as a “throw away” variable that is convenient to use in situations in
which both of the following are true:

1. the language requires a variable to appear in a particular context, and

2. the program otherwise has no use for the variable.

We can rewrite the 2D list creation statement as

a = [[0] * 4 for _ in range(3)]

Notice that the underscore is almost invisible or certainly less obvious than the original x variable. This
new version is less likely to prompt exprienced Python programmers to ask “What does that variable do?”

The _ symbol has special meaning in the interactive interpreter. The interpreter
automatically assigns _ to the value of its most recent evaluation. The following
interactive sequence illustrates:

>>> 10 + 4
14
>>> _
14
>>> 100 – 60
40
>>> 2 + _
42
>>>

The _ identifier has no special meaning in a Python program. As with any other
variable, a programmer can explicitly assign _ to any object.

Instead of mixing the list multiplication and list comprehension syntax, we can double up on list com-
prehension:

a = [[0 for _ in range(4)] for _ in range(3)]

Since the _ variable as used above is local to the code within the square brackets of its list comprehension,
the inner (left) _ is separate from, and does not conflict with, the outer (right) _. The two _ identifiers
represent two different integer objects and programmers are free to manipulate them independently.

Figure 10.7 illustrates the results of double-barreled list comprehension.

We will see another good use of the _ identifier in its role as a throw away variable in Section 11.1.

Python supports higher dimensional lists. A 2D list is a list of 1D lists. Similarly, a 3D list is a list 2D
lists. You can visualize a 3D list as a rectangular solid (like a cube), where each layer of the solid is 2D
plane (that is, a 2D list).

10.14. MULTIDIMENSIONAL LISTS 382

Figure 10.7 The double-barreled list comprehension creates independent lists for each row. Reassignment
of the element at index 2 in row 1 affects the only row 1.

a = [[0 for _ in range(4)] for _ in range(3)]

a[1][2] = 5
5

1 20

1 20 31 20 3

1 20 3

a 1 20

1 20 31 20 3

1 20 3

10.14. MULTIDIMENSIONAL LISTS 383

The number of list dimensions allowed by Python is limited only by available memory. Higher-
dimensional lists can consume an enormous amount of memory. Fortunately, most programmers rarely
need to deal with lists with dimensions greater than three. Only the most esoteric applications require lists
with more than three dimensions.

Consider the children’s game of Tic-Tac-Toe, sometimes called Noughts and Crosses (see https://en.
wikipedia.org/wiki/Tic-tac-toe for more information about the game). It consists of a 3 × 3 playing
grid in which two opposing players alternately place Xs and Os. A 3D variation uses a 4 × 4 × 4 cube
for placing Xs and Os (see https://en.wikipedia.org/wiki/3-D Tic-Tac-Toe for more information).
If we were to implement 3D Tic-Tac-Toe in Python, we could use a 4 × 4 × 4 list. As a visual proof of
concept, Listing 10.33 (threedlist.py) prints an intermediate state of a 3D Tic-Tac-Toe game in progress.

Listing 10.33: threedlist.py

# Make a 3D matrix representing the intermediate state
# of a 3D Tic-Tac-Toe game in progress.

matrix = [[[‘X’, ‘.’, ‘.’, ‘O’],
[‘.’, ‘.’, ‘.’, ‘.’],
[‘.’, ‘.’, ‘.’, ‘.’],

[‘.’, ‘.’, ‘.’, ‘.’]],
[[‘.’, ‘.’, ‘.’, ‘O’],

[‘.’, ‘X’, ‘.’, ‘.’],
[‘.’, ‘.’, ‘.’, ‘.’],

[‘.’, ‘.’, ‘.’, ‘.’]],
[[‘.’, ‘.’, ‘.’, ‘.’],

[‘.’, ‘.’, ‘.’, ‘.’],
[‘.’, ‘.’, ‘X’, ‘.’],

[‘.’, ‘.’, ‘.’, ‘.’]],
[[‘.’, ‘.’, ‘.’, ‘.’],

[‘.’, ‘.’, ‘.’, ‘.’],
[‘.’, ‘.’, ‘.’, ‘.’],

[‘.’, ‘.’, ‘.’, ‘O’]]]

# Pretty print the matrix
# Need the length of a row in order to adjust the indentation
row_length = len(matrix[0][0])
for layer in matrix: # Process each layer

for row in range(len(layer)): # For each row by its index
print(‘ ‘ * (row_length – row), end=”) # Print diminishing offset based on its index
for column in range(len(layer[row])): # For each element in a given row

print(‘{:>4}’.format(layer[row][column]), end=”)
print()

print()

Listing 10.33 (threedlist.py) prints

X . . O
. . . .

. . . .
. . . .

. . . O

https://en.wikipedia.org/wiki/Tic-tac-toe
https://en.wikipedia.org/wiki/Tic-tac-toe
https://en.wikipedia.org/wiki/3-D_Tic-Tac-Toe

10.15. SUMMARY OF LIST CREATION TECHNIQUES 384

. X . .
. . . .

. . . .

. . . .
. . . .

. . X .
. . . .

. . . .
. . . .

. . . .
. . . O

The dots represent empty positions. It appears that player O just moved into the bottom-right-front corner,
blocking a potential win by player X (the line from the top-left-back to the bottom-right-front).

10.15 Summary of List Creation Techniques

So far we have seen a variety of ways to create lists in Python. To recap, we will look at several different
ways to create the following list:

[2, 4, 6, 8, 10, 12, 14, 16, 18, 20]

• Literal enumeration:

L = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20]

• Piecemeal assembly:

L = []
for i in range(2, 21, 2):

L += [i]
L = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20]

• Creation from a generator or range expression:

L = list(range(2, 21, 2))

• List comprehension:

L = [x for x in range(1, 21) if x % 2 == 0]

• Combination of methods with list concatenation:

L = list(range(2, 9, 2)) + [10, 12, 14] + [x for x in range(16, 21, 2)]

Chapter 11 introduces several new ways to create lists from other Python data structures.

10.16. LISTS VS. GENERATORS 385

10.16 Lists vs. Generators

We now have seen two ways of expressing a sequence of values: generators and lists. How are they similar?
Generators and lists share the following characteristics:

• Both generators and lists represent a sequence of values. This means the order of the values matters.
There is a first element and a last element in a sequence. Except for the first element in the sequence,
every element has a predecessor. Except for the last element, every element in the sequence has a
successor.

• We can iterate over both generators and lists using the for statement.

How are generators and lists different? Generators and lists differ in the following ways:

• The elements in a list persist for the life of the list, but the elements produced by a generator become
available in turn as the iteration with the generator progresses. Once the iteration moves on from the
current element, previous elements are unavailable from that particular generator object.

• The memory required for a list generally will be greater than that for a generator that can produce the
same sequence of values. This is because the generator manages only one element at a time, while a
list must store simultaneously all the elements in the sequence.

• Lists provide random access. This means any value at any position in the list is available at any time.
A generator serves up values one at a time, in order from the first to the last. We cannot obtain the ith

element from a generator without first requesting all the elements that come before it. Any element
prior to the generator’s current element is no longer available.

• Lists support forward and backward traversal. Generators provide only forward traversal (reversed,
for example, does not work with a generator object).

If you need to create a sequence of values and random access is unnecessary, a generator may be the better
choice. The generator’s sequence behaves like a lazy list; that is, the sequence element exists only at the
time it is needed. If, on the other hand, your program needs to have all the values of a sequence available
at any time during the program’s execution, a list is the necessary choice. Unlike generators, a list usually
must be fully populated with all of its elements before it truly is useful to the program.

10.17 Exercises

1. Can a Python list hold a mixture of integers and strings?

2. What happens if you attempt to access an element of a list using a negative index?

3. What Python statement produces a list containing the values 45, −3, 16 and 8, in that order?

4. Given the statement

lst = [10, -4, 11, 29]

(a) What expression represents the very first element of lst?

(b) What expression represents the very last element of lst?

10.17. EXERCISES 386

(d) What is lst[3]?

(e) What is lst[1]?

(f) What is lst[-1]?

(g) What is lst[-4]?

(h) Is the expression lst[3.0] legal or illegal?

5. Given the statements

lst = [3, 0, 1, 5, 2]
x = 2

evaluate the following expressions:

(a) lst[0]?

(b) lst[3]?

(d) lst[-x]?

(e) lst[x + 1]?

(f) lst[x] + 1?

(g) lst[lst[x]]?

(h) lst[lst[lst[x]]]?

6. What function returns the number of elements in a list?

7. What expression represents the empty list?

8. Given the list

lst = [20, 1, -34, 40, -8, 60, 1, 3]

evaluate the following expressions:

(a) lst

(b) lst[0:3]

(d) lst[4:33]

(e) lst[-5:-3]

(f) lst[-22:3]

(g) lst[4:]

(h) lst[:]

(i) lst[:4]

(j) lst[1:5]

(k) -34 in lst

(l) -34 not in lst

(m) len(lst)

10.17. EXERCISES 387

9. An assignment statement containing the expression a[m:n] on the left side and a list on the right
side can modify list a. Complete the following table by supplying the m and n values in the slice
assignment statement needed to produce the indicated list from the given original list.

Slice indices
Original List Target List m n

[2, 4, 6, 8, 10] [2, 4, 6, 8, 10, 12, 14, 16, 18, 20]
[2, 4, 6, 8, 10] [-10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10]
[2, 4, 6, 8, 10] [2, 3, 4, 5, 6, 7, 8, 10]
[2, 4, 6, 8, 10] [2, 4, 6, ‘a’, ‘b’, ‘c’, 8, 10]
[2, 4, 6, 8, 10] [2, 4, 6, 8, 10]
[2, 4, 6, 8, 10] []
[2, 4, 6, 8, 10] [10, 8, 6, 4, 2]
[2, 4, 6, 8, 10] [2, 4, 6]
[2, 4, 6, 8, 10] [6, 8, 10]
[2, 4, 6, 8, 10] [2, 10]
[2, 4, 6, 8, 10] [4, 6, 8]

10. Write the list represented by each of the following expressions.

(a) [8] * 4

(b) 6 * [2, 7]

(d) 3 * [1, 2] + [4, 2]

(e) 3 * ([1, 2] + [4, 2])

11. Write the list represented by each of the following list comprehension expressions.

(a) [x + 1 for x in [2, 4, 6, 8]]

(b) [10*x for x in range(5, 10)]

(d) [(x, y) for x in range(3) for y in range(4)]

(e) [(x, y) for x in range(3) for y in range(4) if (x + y) % 2 == 0]

12. Provide a list comprehension expression for each of the following lists.

(a) [1, 4, 9, 16, 25]

(b) [0.25, 0.5, 0.75, 1.0, 1.25. 1.5]

13. If lst is a list, what expression indicates whether or not x is a member of lst?

14. What does reversed do?

15. Complete the following function that adds up all the positive values in a list of integers. For example,
if list a contains the elements 3,−3,5,2,−1, and 2, the call sum_positive(a) would evaluate to 12,
since 3+5+2+2 = 12. The function returns zero if the list is empty.

def sum_positive(a):
# Add your code…

10.17. EXERCISES 388

16. Complete the following function that counts the even numbers in a list of integers. For example, if
list a contains the elements 3,5,4,−1, and 0, the call count_evens(a) would evaluate to 2, since a
contains two even numbers: 4 and 0. The function returns zero if the list is empty. The function does
not affect the contents of the list.

def count_evens(lst):
# Add your code…

17. Write a function named print_big_enough that accepts two parameters, a list of numbers and a
number. The function should print, in order, all the elements in the list that are at least as large as the
second parameter.

18. Write a function named next_number that accepts a list of integer values. All the elements in the list
are unique, and all elements in the list are greater than or equal to one. (The caller must ensure that
these conditions are met before passing the list to next_number.) The next_number function should
return the smallest positive integer not in the list. (Note that 1 is the smallest positive integer.)
As examples,

• next_number([5, 3, 1]) would return 2

• next_number([5, 4, 1, 2]) would return 3

• next_number([2, 3]) would return 1

• next_number([]) would return 1

19. Write a function named reverse that reorders the contents of a list so they are reversed from their
original order. a is a list. Note that your function must physically rearrange the elements within the
list, not just print the elements in reverse order.

20. Write a Python program that creates the matrix

1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1

and assigns it to the variable m. Pretty print m to ensure the contents are correct. Next, reassign
m[2][4] to 0, and print m again to ensure your code modified the correct element.

21. Provide five different ways to create the list [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] and assign it to
the variable lst.

22. In a square 2D list the number of rows equals the nnumber of columns. Write a function that accepts
a square 2D list and returns True if the left to right contents of any row equals the top to bottom
contents of any column. If no row matches any column, the function returns False.

23. We can represent a Tic-Tac-Toe board as a 3 × 3 grid in which each position can hold one of the
following three strings: “X”, “O”, or ” “. Write a function named check_winner that accepts a
3 × 3 list as a parameter. If “X” appears in a winning Tic-Tac-Toe pattern, the function should return
the string “X”. If “O” appears in a winning Tic-Tac-Toe pattern, the function should return the string
“O”. If no winning pattern exists, the function should return the string ” “.

389

Chapter 11

Tuples, Dictionaries, and Sets

Lists, introduced in Chapter 10, are convenient data structures for representing sequences of data. In this
chapter we examine several other ways that Python provides for storing aggregate data: tuples, dictionaries,
and sets.

11.1 Tuples

Tuples are similar to lists, except tuples are immutable. Listing 11.1 (tupletest.py) compares the usage of
lists versus tuples.

Listing 11.1: tupletest.py

my_list = [1, 2, 3, 4, 5, 6, 7] # Make a list
my_tuple = (1, 2, 3, 4, 5, 6, 7) # Make a tuple
print(‘The list:’, my_list) # Print the list
print(‘The tuple:’, my_tuple) # Print the tuple
print(‘The first element in the list:’, my_list[0]) # Access an element
print(‘The first element in the tuple:’, my_tuple[0]) # Access an element
print(‘All the elements in the list:’, end=’ ‘)
for elem in my_list: # Iterate over the elements of a list

print(elem, end=’ ‘)
print()
print(‘All the elements in the tuple:’, end=’ ‘)
for elem in my_tuple: # Iterate over the elements of a tuple

print(elem, end=’ ‘)
print()
print(‘List slice:’, my_list[2:5]) # Slice a list
print(‘Tuple slice:’, my_tuple[2:5]) # Slice a tuple
print(‘Try to modify the first element in the list . . .’)
my_list[0] = 9 # Modify the list
print(‘The list:’, my_list)
print(‘Try to modify the first element in the list . . .’)
my_tuple[0] = 9 # Is tuple modification possible?
print(‘The tuple:’, my_tuple)

11.1. TUPLES 390

Table 11.1 Python lists versus tuples
Feature List Tuple

Mutability mutable immutable
Creation lst = [i, j] tpl = (i, j)
Element access a = lst[i] a = tpl[i]
Element modification lst[i] = a Not possible
Element addition lst += [a] Not possible
Element removal del lst[i] Not possible
Slicing lst[i:j:k] tpl[i:j:k]
Slice assignment lst[i:j] = [] Not possible
Iteration for elem in lst:. . . for elem in tpl:. . .

Listing 11.1 (tupletest.py) prints

The list: [1, 2, 3, 4, 5, 6, 7]
The tuple: (1, 2, 3, 4, 5, 6, 7)
The first element in the list: 1
The first element in the tuple: 1
All the elements in the list: 1 2 3 4 5 6 7
All the elements in the tuple: 1 2 3 4 5 6 7
List slice: [3, 4, 5]
Tuple slice: (3, 4, 5)
Try to modify the first element in the list . . .
The list: [9, 2, 3, 4, 5, 6, 7]
Try to modify the first element in the list . . .
Traceback (most recent call last):

File “tupletest.py”, line 26, in
main()

File “tupletest.py”, line 22, in main
my_tuple[0] = 9

TypeError: ‘tuple’ object does not support item assignment

We see that Listing 11.1 (tupletest.py) does not run to completion. The next to the last statement in the
program:

my_tuple[0] = 9

generates a run-time exception because tuples are immutable. Once we create tuple object, we cannot
change that object’s contents.

Table 11.1 compares lists to tuples.

Unlike with lists, we cannot modify an element within a tuple, we cannot add elements to a tuple, nor
can we remove elements from a tuple. If we have a variable assigned to a tuple, we always can reassign that
variable to a different tuple. Such an assignment simply binds the variable to a different tuple object—it
does not modify the tuple to which the variable originally was bound.

The parentheses are optional in the following statement:

my_tuple = (1, 2, 3)

The following statement is equivalent:

11.1. TUPLES 391

my_tuple = 1, 2, 3

Lists can hold heterogeneous data types, and so too can tuples:

>>> t = (2, ‘Fred’, 41.2, [30, 20, 10])
>>> t
(2, ‘Fred’, 41.2, [30, 20, 10])

In general practice, however, many Python programmers favor storing only homogeneous types in lists and
prefer tuples for holding heterogeneous types.

Section 7.1 introduced tuple unpacking. The following code unpacks a tuple into separate variables:

t = 3, ‘A’, 99
val, letter, quant = t

After this code executes val will refer to 3, letter will be assigned to the string ‘A’, and quant will be
another name for the integer 99.

Tuple unpacking is convenient if you need to extract most, if not all, of the elements from a tuple. If
you need only one element from a potentially large tuple, the index operator is a better choice, as shown
here:

t = 3, ‘A’, 99
letter = t[1]

Here letter is assigned to the string ‘A’.

If you wish to extract several components from a tuple and ignore others, tuple extraction with “throw
away” _ variables (see Section 10.14) can be a good choice. The following code illustrates:

t = 3, ‘A’, 99, 16, 0, 42
_, letter, _, _, quant, rating = t

The nameless _ variable will end up with the value 16, but this variable is meant to be ignored. The code
that follows these statements would be interested only in the variables letter, quant, and rating.

We can convert a tuple to a list using the list function, and the tuple function performs the reverse
conversion. The following interactive sequence demonstrates the use of the conversion functions:

>>> tpl = 1, 2, 3, 4, 5, 6, 7, 8
>>> tpl
(1, 2, 3, 4, 5, 6, 7, 8)
>>> list(tpl)
[1, 2, 3, 4, 5, 6, 7, 8]
>>> lst = [‘a’, ‘b’, ‘c’, ‘d’]
>>> lst
[‘a’, ‘b’, ‘c’, ‘d’]
>>> tuple(lst)
(‘a’, ‘b’, ‘c’, ‘d’)

Neither the list nor tuple function actually modifies its argument; that is, tuple(lst) does not modify
lst, and list(tpl) does not modify tuple (since tuples are immutable, any modification would be impos-
sible anyway). The list function makes a new list out of the contents of a tuple, and the tuple function
makes a new tuple out of the elements in a list.

11.1. TUPLES 392

We can use the built-in zip function to generate a sequence of tuples from two lists. Consider the
following interactive sequence:

>>> lst1 = [1, 2, 3, 4, 5, 6, 7, 8]
>>> lst2 = [‘a’, ‘b’, ‘c’, ‘d’, ‘e’, ‘f’, ‘g’, ‘h’]
>>> for t in zip(lst1, lst2):
… print(t)
…
(1, ‘a’)
(2, ‘b’)
(3, ‘c’)
(4, ‘d’)
(5, ‘e’)
(6, ‘f’)
(7, ‘g’)
(8, ‘h’)

You can think of the zip function working like a physical zipper. A physical zipper pairs up two sets of
interlocking (usually metal) teeth, closing an opening in a garment or bag. The Python zip function pairs
up elements from two different sequences. The paired-up elements are tuples, and the sequences can be
lists or sequences constructed from generators (see Section 8.8). If one of the sequences is shorter than the
other, the zip function stops at the shorter sequence and ignores the remainder of the longer sequence.

Listing 11.2 (zipseq.py) constructs a sequence of tuples with their first elements derived from a list and
their second elements obtained from a generator. Note that the generator’s sequence is shorter than the list.

Listing 11.2: zipseq.py

def gen(n):
“”” Generates the first n perfect squares, starting with zero:

0, 1, 4, 9, 16,…, (n – 1)ˆ2. “””
for i in range(n):

yield i**2

for p in zip([10, 20, 30, 40, 50, 60], gen(4)):
print(p, end=’ ‘)

print()

Listing 11.2 (zipseq.py) prints

(10, 0) (20, 1) (30, 4) (40, 9)

The zip function does not return a list; like range, it returns an object over which we can iterate. We
can make a list from a zip object using the list conversion function:

>>> list(zip(range(5), range(10, 0, -1)))
[(0, 10), (1, 9), (2, 8), (3, 7), (4, 6)]

We can use the zip function and list comprehension to build elaborate lists. Suppose we wish to make
a new list from two existing lists. The first element in our new list will be the sum of the first elements from
the two original lists. Similarly, the second element in our new list will be the sum of the second elements
in the two original lists, and so forth. We can use zip to pair up the elements, as the following interactive
sequence illustrates:

11.2. ARBITRARY ARGUMENT LISTS 393

>>> for p in zip([1, 2, 3, 4, 5], [10, 11, 12, 13, 14]):
… print(p)
…
(1, 10)
(2, 11)
(3, 12)
(4, 13)
(5, 14)

We want to add together the components of each tuple. To print each sum we could write

>>> for (x, y) in zip([1, 2, 3, 4, 5], [10, 11, 12, 13, 14]):
… print(x + y)
…
11
13
15
17
19

We can reassemble these pieces into a list comprehension to build our list of sums:

>>> [x + y for (x, y) in zip([1, 2, 3, 4, 5], [10, 11, 12, 13, 14])]
[11, 13, 15, 17, 19]

When treated as a Boolean expression, the empty tuple (()) is interpreted as False, and any other tuple
is considered True.

Since they are so similar, why does Python have both lists and tuples? Under some circumstances an
executing program can perform optimizations on immutable objects that would be impossible with mutable
objects. These optimizations can increase the program’s performance. Also, it is easier in general to reason
about the behavior of programs that use immutable objects. The fact that some objects cannot change makes
it easier to understand how a section of code works, or, during debugging, why the section of code does not
work.

11.2 Arbitrary Argument Lists

We can easily write a function that adds two numbers; consider the following sum function:

def sum(a, b):
return a + b

What if we need sum to be flexible enough to add two or three numbers? We can implement such a function
with default arguments (Section 8.2). Listing 11.3 (add2or3.py) illustrates such a function

Listing 11.3: add2or3.py

def sum(a, b, c=0):
return a + b + c # Adding zero will not affect a + b

print(sum(3, 4))

11.2. ARBITRARY ARGUMENT LISTS 394

print(sum(3, 4, 5))

The sum function in Listing 11.3 (add2or3.py) handles two and three arguments equally well:

7
12

A function that is capable of adding up to five numbers is equally easy:

def sum(a, b=0, c=0, d=0, e=0):
return a + b + c + d + e

Suppose we wish to write a sum function that can add as many numbers as the caller can supply? The default
parameter approach is not practical in this situation. Our function must be able to handle 1,000 numbers or
more, and these numbers must be separate arguments—not a single list containing 1,000 numbers.

When we define a function we specify the individual parameters it accepts, providing default values as
needed. In the function definitions we have seen to this point the number of parameters is fixed. We need
a way to define a function in such a way so that it can accept an arbitrary number of parameters. Fortu-
nately Python has a mechanism for specifying that a function can accept an arbitrary number of parameters.
Listing 11.4 (addmany.py) illustrates how write such a function.

Listing 11.4: addmany.py

def sum(*nums):
s = 0 # Initialize sum to zero
for num in nums: # Consider each argument passed to the function

s += num # Accumulate their values
return s # Return the sum

print(sum(3, 4))
print(sum(3, 4, 5))
print(sum(3, 3, 3, 3, 4, 1, 9, 44, -2, 8, 8))

The sum function in Listing 11.4 (addmany.py) handles as many actual parameters as the client can provide;
the program prints

7
12
84

The single asterisk (*) before the formal parameter nums indicates the parameter is not necessarily a single
value but potentially a collection of values. Listing 11.5 (addmanyaugmented.py) reveals what really is
going on behind the scenes.

Listing 11.5: addmanyaugmented.py

def sum(*nums):
print(nums) # See what nums really is
s = 0 # Initialize sum to zero
for num in nums: # Consider each argument passed to the function

s += num # Accumulate their values
return s # Return the sum

11.2. ARBITRARY ARGUMENT LISTS 395

print(sum(3, 4))
print(sum(3, 4, 5))
print(sum(3, 3, 3, 3, 4, 1, 9, 44, -2, 8, 8))

The sum function in Listing 11.5 (addmanyaugmented.py) prints the following:

(3, 4)
7
(3, 4, 5)
12
(3, 3, 3, 3, 4, 1, 9, 44, -2, 8, 8)
84

Listing 11.5 (addmanyaugmented.py) exposes the fact that the formal parameter nums is a tuple wrapping
all the actual parameters sent by the caller. Since nums is simply a tuple, we can iterate over it with the for
statement to extract all the actual parameters provided by the caller.

A function definition may contain at most one of these parameters that represents a tuple of arguments,
and, if present, this parameter must appear after all the named, single formal parameters, if any. In the
following sum function, callers must provide at least two parameters but may pass more:

def sum(num1, num2, *extranums):
s = num1 + num2
for n in extranums:

s += n
return s

Note that the formal parameters num1 and num2 must appear before *nums in sum’s formal parameter list.

As we have seen, a formal parameter declared with an asterisk is really a tuple from the function’s
perspective. The caller can pass individual arguments not packed within a tuple. The Python interpreter
takes care of the packing the caller’s arguments into a tuple during the call.

This process works in reverse also. Consider the following function that accepts four parameters:

def f(a, b, c, d):
print(‘a =’, a, ‘ b = ‘, b, ‘ c = ‘, c, ‘ d = ‘, d)

We can pass a single argument to function f if we express it in the proper way:

args = (10, 20, 30, 40)
f(*args)

The variable args is a tuple, but f does not accept a single tuple; it accepts four parameters. Expressing the
actual parameter as *args enables the interpreter to unpack the tuple into the four parameters the function
expects. Note that the tuple must contain exactly the number of parameters that the function expects.

Given the definition of function f above, the following call is legal:

f(*(10, 20, 30, 40)) # Legal, unpacks the tuple into separate args

but the following is illegal:

f((10, 20, 30, 40)) # Illegal, function does not accept a tuple

11.2. ARBITRARY ARGUMENT LISTS 396

because the actual parameter is a single object—a tuple—and the function requires four parameters, not
just one. We must use the * tuple unpacking operator during the call. Of course the easiest way to call the
function in this case is simply

f(10, 20, 30, 40) # Why use a literal tuple anyway?

Python supports a concept known as generalized unpacking. It extends simple unpacking by using the
asterisk to represent a collection of elements not covered by individual variables during the unpacking. The
following interactive sequence shows how generalized unpacking can extract a prefix of a tuple, storing the
remainder of the tuple’s elements in a list:

>>> a = 1, 2, 3, 4, 5, 6, 7, 8
>>> a
(1, 2, 3, 4, 5, 6, 7, 8)
>>> x, y, *rest = a
>>> x
1
>>> y
2
>>> rest
[3, 4, 5, 6, 7, 8]

Curiously, the elements in the remainder of the tuple are copied into a list, not a tuple.

Prefer extracting a suffix of the tuple instead? Try the following:

>>> a = 1, 2, 3, 4, 5, 6, 7, 8
>>> a
(1, 2, 3, 4, 5, 6, 7, 8)
>>> *start, x, y = a
>>> start
[1, 2, 3, 4, 5, 6]
>>> x
7
>>> y
8

The next sequence unpacks a prefix and a suffix of the elements:

>>> a = 1, 2, 3, 4, 5, 6, 7, 8
>>> a
(1, 2, 3, 4, 5, 6, 7, 8)
>>> x1, x2, *middle, x3, x4 = a
>>> x1
1
>>> x2
2
>>> middle
[3, 4, 5, 6]
>>> x3
7
>>> x4
8
>>> a
(1, 2, 3, 4, 5, 6, 7, 8)

11.2. ARBITRARY ARGUMENT LISTS 397

At most one * expression may appear in a generalized unpacking expression.

Generalized unpacking works with lists as well:

>>> a = [1, 2, 3, 4, 5, 6, 7, 8]
>>> a
[1, 2, 3, 4, 5, 6, 7, 8]
>>> x1, x2, *midlist, x3, x4 = a
>>> x1
1
>>> x2
2
>>> midlist
[3, 4, 5, 6]
>>> x3
7
>>> x4
8
>>> x, y, z = [‘a’, ‘b’, ‘c’]
>>> x
‘a’
>>> y
‘b’
>>> z
‘c’

The print function knows how to handle a list argument, and it also accepts a variable number of
arguments. Consider Listing 11.6 (speciallistprinting.py) which demonstrates the power of the * unpacking
operator for flexible list printing:

Listing 11.6: speciallistprinting.py

lst = [2*i for i in range(6)]

# Typical list printing
print(lst)

# Print just the list elements
print(*lst)

# Print the list in a special way
print(*lst, sep=” and “, end=”–that’s all folks!\n”)

Listing 11.6 (speciallistprinting.py) prints

[0, 2, 4, 6, 8, 10]
0 2 4 6 8 10
0 and 2 and 4 and 6 and 8 and 10–that’s all folks!

While we are on the subject of unpacking tuples, we can unpack a tuple directly from a range object
without the need to involve a for statement:

>>> x, y, z = range(10, 31, 10)
>>> x
10

11.3. DICTIONARIES 398

>>> y
20
>>> z
30

You must ensure the number of values match exactly:

>>> x, y, z = range(0, 100)
Traceback (most recent call last):

File ““, line 1, in
ValueError: too many values to unpack (expected 3)
>>> x, y, z = range(0, 2)
Traceback (most recent call last):

File ““, line 1, in
ValueError: need more than 2 values to unpack

11.3 Dictionaries

Lists and tuples are convenient for storing collections of data, but they have some limitations. For one, we
locate an element within a list or tuple based on its position (index). While this approach is fine for many
applications, in other situations this access-by-index approach is awkward or inefficient.

A Python dictionary is an associative container which permits access based on a key, rather than an
index. Unlike an index, a key is not restricted to an integer expression. The following interactive sequence
builds a simple dictionary that uses string keys:

>>> d = {} # Make an empty dictionary
>>> d
{}
>>> # Add an element
… d[‘Fred’] = 44
>>> d
{‘Fred’: 44}
>>> # Add another element
… d[‘Ella’] = 31
>>> d
{‘Fred’: 44, ‘Ella’: 31}
>>> print(d)
{‘Fred’: 44, ‘Ella’: 31}
>>> d[‘Fred’]
44
>>> d[‘Ella’]
31
>>> d[‘Zach’]
Traceback (most recent call last):

File ““, line 1, in
KeyError: ‘Zach’
>>> d[0]
Traceback (most recent call last):

File ““, line 1, in
KeyError: 0

11.3. DICTIONARIES 399

Notice that, unlike a list which uses square brackets ([]), the contents of a dictionary appear within curly
braces ({}). To access an element within a dictionary, however, we use square brackets exactly as we would
with a list. In a dictionary every key has an associated value. The dictionary d from the interactive sequence
above pairs the key ‘Fred’ with the value 44. It also pairs the key ‘Ella’ with the value 31.

The following assignment statement associates a value with a key:

d[‘Fred’] = 44 # Associate value 44 with key ‘Fred’

The string ‘Fred’ is the key, and 44 is its associated value. If the key within the square brackets does not
exist in the dictionary, the statement adds the key and pairs it with the value on the right of the assignment
operator. If the key already exists in the dictionary, the statement replaces the value previously associated
with the key with the new value on the right of the assignment operator.

Accessing a value with a given key is a different story. In the statement

x = d[‘Fred’]

‘Fred’ must be a valid key in dictionary d, or the program will raise an exception. A valid key is a key that
is present in the dictionary. At the end of the interaction sequence above ‘Fred’ is a valid key but ‘Zach’
is not. We see the interpreter’s reaction when we attempt to use an invalid key: the interpreter generates a
KeyError exception.

We can check to see if a key is present in a dictionary with the in operator:

if ‘Fred’ in d: # Check to see if ‘Fred’ is a valid key
print(d[‘Fred’]) # Print the value associated with key ‘Fred’

else:
print(‘\’Fred\’ is not a key in d’) # Warn user of missing key

A dictionary key may be of any immutable type. This means all of the following can serve as keys
within a dictionary: integers, floating-point numbers, strings, Booleans, and tuples. Since lists are mutable
objects, a list may not be a key. A dictionary is a mutable object, so a dictionary cannot use itself or another
dictionary object as a key. A value within a dictionary may be any valid Python type, immutable or mutable.

The keys within a given dictionary may be of mixed types; consider the following interactive sequence:

>>> s = {}
>>> s[8] = 44
>>> s[8]
44
>>> s[‘Alpha’] = ‘up’
>>> s[‘Alpha’]
‘up’
>>> s[True] = ‘right’
>>> s[True]
‘right’
>>> s[10 < 20] 'right' >>> s[‘Beta’] = 100
>>> s
{8: 44, True: ‘right’, ‘Beta’: 100, ‘Alpha’: ‘up’}
>>> s[3.4] = True
>>> s
{8: 44, True: ‘right’, ‘Beta’: 100, 3.4: True, ‘Alpha’: ‘up’}
>>> s[2 == -2] = ‘wrong’

11.3. DICTIONARIES 400

>>> s[False]
‘wrong’
>>> s
{False: ‘wrong’, True: ‘right’, ‘Beta’: 100, ‘Alpha’: ‘up’, 3.4: True,
8: 44}
>>> x = 8
>>> s[x]
44
>>> y = 15
>>> s[y] = ‘down’
>>> lst = [1, 2, 3]
>>> s[17] = lst
>>> s
{False: ‘wrong’, True: ‘right’, ‘Beta’: 100, ‘Alpha’: ‘up’, 3.4: True,
17: [1, 2 , 3], 8: 44, 15: ‘down’}

This interactive sequence reveals several dictionary characteristics:

• The keys in a dictionary may have different types

• The values in a dictionary may have different types

• The values in a dictionary may be mutable objects

• The order of key:value pairs in a dictionary are independent of the order of their insertion into the
dictionary

We can initialize a dictionary using the same syntax as the output that the print function displays. The
following statement populates the dictionary d with four key:value entries:

d = {‘Fred’: 44, ‘Ella’: 39, ‘Owen’: 40, ‘Zoe’: 41}
print(d)

Despite the order supplied during d’s initialization, on one system the code above prints

{‘Fred’: 44, ‘Ella’: 39, ‘Zoe’: 41, ‘Owen’: 40}

Observe that the print function neither lists the keys in lexicographical order nor lists the values in numer-
ical order. While an executing program must store a dictionary’s contents in memory in some particular
order, the exact internal ordering of the elements within a dictionary can vary from one program execution
to the next. This example further demonstrates that programmers cannot depend on a specific ordering of
the elements within a dictionary. Unlike in a list or other sequence type, the notions of order and position
have no meaning within a dictionary.

The keys method of the dictionary class returns a sequence of all the keys in d. The following code
demonstrates:

d = {‘Fred’: 44, ‘Ella’: 39, ‘Owen’: 40, ‘Zoe’: 41}
for k in d.keys():

print(k, end=’ ‘)
print()

Upon one execution of this code it prints

Zoe Owen Fred Ella

11.3. DICTIONARIES 401

The exact order of the printed keys will vary, even between executions of the same program. The following
code behaves similarly:

d = {‘Fred’: 44, ‘Ella’: 39, ‘Owen’: 40, ‘Zoe’: 41}
for k in d:

print(k, end=’ ‘)
print()

This code produces the same output as iterating over d.keys():

Zoe Owen Fred Ella

with the above noted caveat that the exact order of the printed keys will vary.

The values method of the dictionary class returns a sequence of all the values in d. The following code
illustrates:

d = {‘Fred’: 44, ‘Ella’: 39, ‘Owen’: 40, ‘Zoe’: 41}
for v in d.values():

print(v, end=’ ‘)
print()

This code prints

39 40 44 41

We can obtain a sequence of tuples of key:value pairs of a dictionary with the items method:

d = {‘Fred’: 44, ‘Ella’: 39, ‘Owen’: 40, ‘Zoe’: 41}
for k, v in d.items():

print(k, v)

This code fragment prints

Fred 44
Owen 40
Zoe 41
Ella 39

Suppose we have the list [‘Fred’, ‘Ella’, ‘Owen’, ‘Zoe’] and the list [4174, 2287, 5003, 2012].
We know we can zip them together into a sequence of tuples using zip (Section 11.1). We can use the dict
function to create a dictionary of key:value pairs formed from the tuples, as the following interactive se-
quence shows:

>>> names = [‘Fred’, ‘Ella’, ‘Owen’, ‘Zoe’]
>>> numbers = [4174, 2287, 5003, 2012]
>>> names
[‘Fred’, ‘Ella’, ‘Owen’, ‘Zoe’]
>>> numbers
[4174, 2287, 5003, 2012]
>>> d = dict(zip(names, numbers))
>>> d
{‘Zoe’: 2012, ‘Owen’: 5003, ‘Fred’: 4174, ‘Ella’: 2287}

11.4. USING DICTIONARIES 402

The elements of the list specified as the first actual parameter to zip become the dictionary keys, and the
elements of the list specified as the second argument to zip form the values in the dictionary. As we noted
earlier, the ordering of the key:value pairs is different from their order in the original lists, but the first
element from the names list is paired with the first element of the numbers list, the second element from
names is paired with the second element of numbers, and so forth.

A dictionary is sometimes called an associative array because its elements (values) are associated with
keys instead of indices. The placement and lookup of an element within a dictionary uses a process known
as hashing. A hash function maps a key to a location within the dictionary where the key’s associated value
resides. Python dictionaries are related to hash tables in computer science. See http://en.wikipedia.
org/wiki/Hash table for more information about hash functions and hash tables. The important thing to
know about the hashing process is that it makes value lookup via a key very fast.

When treated as a Boolean expression, the empty dictionary ({}) is interpreted as False, and any other
dictionary is considered True.

11.4 Using Dictionaries

You should use a dictionary when you need fast and convenient access to an element of a collection based
on a search key rather than an index. Consider the problem of implementing a simple telephone contact
list. Most people are very familiar with the names of their friends, family, and business contacts but can
remember only a handful of telephone numbers. A contact list associates a name with a telephone number.

It would be inappropriate to place the names in a list and locate a name using the associated phone
number as an index into the list. This look-up method is backwards—we do not want to find a name given a
phone number; we want to look up a number based on a name. Besides, each phone number contains many
digits, and we would not need or want to have a list with indices with values that large—most of the space
in the list would be unused.

In our situation a person or company’s name is a unique identifier for that contact. In this case the
name is a key to that contact. A Python dictionary is the ideal data structure for mapping keys to values. A
dictionary allows for the fast retrieval of a value given its associated key. Listing 11.7 (phonelist.py) uses
a Python dictionary to implement a simple telephone contact database with a rudimentary command line
interface.

Listing 11.7: phonelist.py

contacts = {} # The global telephone contact list

running = True

while running:
command = input(‘A)dd D)elete L)ook up Q)uit: ‘)
if command == ‘A’ or command == ‘a’ :

name = input(‘Enter new name:’)
print(‘Enter phone number for’, name, end=’:’)
number = input()
contacts[name] = number

elif command == ‘D’ or command == ‘d’:
name = input(‘Enter name to delete :’)
del contacts[name]

elif command == ‘L’ or command == ‘l’:
name = input(‘Enter name :’)

http://en.wikipedia.org/wiki/Hash_table
http://en.wikipedia.org/wiki/Hash_table

11.4. USING DICTIONARIES 403

print(name, contacts[name])
elif command == ‘Q’ or command == ‘q’:

running = False
elif command == ‘dump’: # Secret command

print(contacts)
else:

print(command, ‘is not a valid command’)

The following shows a sample run of Listing 11.7 (phonelist.py):

A)dd D)elete L)ook up Q)uit: a
Enter new name:Fred
Enter phone number for Fred:222-555-0134
A)dd D)elete L)ook up Q)uit: dump
{‘Fred’: ‘222-555-0134’}
A)dd D)elete L)ook up Q)uit: a
Enter new name:Ella
Enter phone number for Ella:222-555-9434
A)dd D)elete L)ook up Q)uit: l
Enter name :Ella
Ella 222-555-9434
A)dd D)elete L)ook up Q)uit: l
Enter name :Fred
Fred 222-555-0134
A)dd D)elete L)ook up Q)uit: dump
{‘Fred’: ‘222-555-0134’, ‘Ella’: ‘222-555-9434’}
A)dd D)elete L)ook up Q)uit: d
Enter name to delete :Ella
A)dd D)elete L)ook up Q)uit: dump
{‘Fred’: ‘222-555-0134’}
A)dd D)elete L)ook up Q)uit: q

Listing 11.8 (translateif.py) translates some Spanish words into English.

Listing 11.8: translateif.py

word = ‘*’ # Initial word to ensure loop entry
while word != ”: # Loop until user presses return by itself

# Obtain word from the user
word = input(‘Enter Spanish word:’)
if word == ‘uno’:

print(‘one’)
elif word == ‘dos’:

print(‘two’)
elif word == ‘tres’:

print(‘three’)
elif word == ‘cuatro’:

print(‘four’)
elif word == ‘cinco’:

print(‘five’)
elif word == ‘seis’:

print(‘six’)
elif word == ‘siete’:

print(‘seven’)
elif word == ‘ocho’:

11.5. COUNTING WITH DICTIONARIES 404

print(‘eight’)
else: # Unknown word

print(‘???’)

Listing 11.8 (translateif.py) can successfully translate eight Spanish words into English. If we wish to
increase the program’s vocabulary, we must modify the program’s logic by adding another elif block for
each new word. Listing 11.9 (translatedictionary.py) uses a dictionary to assist the translation.

Listing 11.9: translatedictionary.py

translator = {‘uno’:’one’,
‘dos’:’two’,
‘tres’:’three’,
‘cuatro’:’four’,
‘cinco’:’five’,
‘seis’:’six’,
‘siete’:’seven’,
‘ocho’:’eight’}

word = ‘*’
while word != ”: # Loop until user presses return by itself

# Obtain word from the user
word = input(‘Enter Spanish word:’)
if word in translator:

print(translator[word])
else:

print(‘???’) # Unknown word

We do not need to touch the program’s logic at all to expand the program’s vocabulary; all we need do
is add the appropriate key:value item to the dictionary. This is a significant difference if wish to include
enough words to make the program practical.

11.5 Counting with Dictionaries

Dictionaries are useful for counting things. We have experience using variables to count; recall Listing 5.3
(countup.py), Listing 5.15 (countvowels.py), Listing 5.34 (startree.py), Listing 6.7 (measureprimespeed.py),
Listing 7.19 (treefunc.py), or Listing 10.25 (timeprimes.py). These programs all have counted one thing at
a time, so they each use just one counter variable. In general, we need to use a separate variable for each
count we manage. The following code counts the number of negative and nonnegative numbers in a list of
numbers and returns a tuple with the results:

def count_neg_nonneg(nums):
# Initialize counters
neg_count, nonneg_count = 0, 0
for num in nums:

if num < 0: neg_count += 1 else: nonneg_count += 1 return neg_count, nonneg_count Since we needed to count two different kinds of things, we had to use two separate counter variables. ©2017 Richard L. Halterman Draft date: January 18, 2018 11.5. COUNTING WITH DICTIONARIES 405 What if we face a situation in which we must count multiple kinds of things, but we cannot know ahead of time how many kinds of things there will be to count? How can we determine how many counter variables to use in a program that attempts to solve such a problem? The answer is this: We cannot know how many counter variables we will need, so we must use a differ- ent approach. If all the things we need to count are immutable objects, like numbers or strings, we can use the objects as keys in a dictionary and associate with each key a count. As a concrete example, Listing 11.10 (wordcount.py) reads the content of a text file containing words. After reading the file the program prints a count of each word. To simplify things, the text file contains only words with no punctuation. The user supplies the file name on the command line when launching the program (see Section 10.12). Listing 11.10: wordcount.py """ Uses a dictionary to count the number of occurrences of each word in a text file. """ import sys # For sys.argv global command line arguments list def main(): """ Counts the words in a text file. """ if len(sys.argv) < 2: # Did the user not supply a file name? print('Usage: python wordcount ‘)
print(‘ where is the name of a text file.’)

else: # User provided file name
filename = sys.argv[1]
counters = {} # Initialize counting dictionary
with open(filename, ‘r’) as f: # Open the file for reading

content = f.read() # Read in content of the entire file
words = content.split() # Make list of individual words
for word in words:

word = word.upper() # Make the word all caps
if word not in counters:

counters[word] = 1 # First occurrence, add the counter
else:

counters[word] += 1 # Increment existing counter
# Report the counts for each word
for word, count in counters.items():

print(word, count)

if __name__ == ‘__main__’:
main()

The following paragraph appears in the Declaration of Independence of the United States (all punctuation
has been removed):

When in the Course of human events it becomes necessary for one people to dissolve the political bands which have connected them with another and to assume among the powers of the
earth the separate and equal station to which the Laws of Nature and of Nature’s God entitle them a decent respect to the opinions of mankind requires that they should declare the causes
which impel them to the separation

The following shows a sample run of Listing 11.10 (wordcount.py) when presented with the above text file:

THEY 1
COURSE 1
AMONG 1

11.5. COUNTING WITH DICTIONARIES 406

OPINIONS 1
SEPARATE 1
DECENT 1
NATURE 1
NECESSARY 1
THAT 1
IMPEL 1
IN 1
NATURE’S 1
PEOPLE 1
ANOTHER 1
STATION 1
REQUIRES 1
CONNECTED 1
ASSUME 1
CAUSES 1
EVENTS 1
TO 5
A 1
GOD 1
FOR 1
POWERS 1
BANDS 1
IT 1
THE 9
EQUAL 1
DISSOLVE 1
RESPECT 1
EARTH 1
LAWS 1
WHEN 1
MANKIND 1
ONE 1
SHOULD 1
WHICH 3
POLITICAL 1
THEM 3
AND 3
OF 5
HUMAN 1
BECOMES 1
SEPARATION 1
WITH 1
ENTITLE 1
DECLARE 1
HAVE 1

In Listing 11.10 (wordcount.py), since we cannot predict what words will appear in the document, we cannot
use a separate variable for each counter. Instead, we use the user’s words as keys in a dictionary. For each
key in the dictionary we associate an integer value that keeps track of the number of times the word appears
in the file.

The following expression in Listing 11.10 (wordcount.py):

content.split()

11.5. COUNTING WITH DICTIONARIES 407

exercises a method of the str class that separates the very long string composed of all the words in the file
into separate strings. The split method divides the string based on whitespace (spaces, tabs, and newlines)
and returns the individual words in a list. The following interactive sequence shows how the split method
works:

>>> s = ‘ ABC def GHI JKLM-nop, aaa ‘
>>> s
‘ ABC def GHI JKLM-nop, aaa ‘
>>> s.split()
[‘ABC’, ‘def’, ‘GHI’, ‘JKLM-nop,’, ‘aaa’]

With no arguments, str.split method splits the string based on whitespace (spaces, tabs, and newlines).
Whitespace separates the words to place in the list. The split function accepts an optional string parameter
that contains the characters used to separate the words (or tokens); for example,

>>> x = ‘ABC:xyz.122:prst’
>>> x
‘ABC:xyz.122:prst’
>>> x.split()
[‘ABC:xyz.122:prst’]
>>> x.split(‘:’)
[‘ABC’, ‘xyz.122’, ‘prst’]

We can put the string split method to good use with list comprehension (see Section 10.13). Suppose
we have string containing comma-separated integer data. The string could contain spaces as well. The
following represents a typical string:

s = ” 85, 54 , 13, 17, 44 ,31, 80, 35, 30, 54, 78 ”

Notice that the location of the spaces is arbitrary, but commas faithfully separate one integer from another.
We wish to produce from this string a list containing its integers in the order they appear within the string:

[85, 54, 13, 17, 44, 31, 80, 35, 30, 54, 78]

The interactive interpreter reveals how we can split the string into its comma-separated components:

>>> s = ” 85, 54 , 13, 17, 44 ,31, 80, 35, 30, 54, 78 ”
>>> s.split(“,”)
[‘ 85’, ‘ 54 ‘, ‘ 13’, ‘ 17’, ‘ 44 ‘, ’31’, ‘ 80’, ‘ 35’,
‘ 30’, ‘ 54’, ‘ 78 ‘]

This leaves us a list of strings, many containing extraneous leading or trailing spaces (or both). We need
to remove the spaces with the string strip method and then convert the results to integers. The following
interactive session shows how to use a one-line list comprehension to do exactly what we need:

>>> s = ” 85, 54 , 13, 17, 44 ,31, 80, 35, 30, 54, 78 ”
>>> s
‘ 85, 54 , 13, 17, 44 ,31, 80, 35, 30, 54, 78 ‘
>>> int_list = [int(x.strip()) for x in s.split(“,”)]
>>> int_list
[85, 54, 13, 17, 44, 31, 80, 35, 30, 54, 78]

Consider using a list comprehension expression similar to this one when writing code to read numerical
data from a text file. Consider a very common task: reading comma-separated integer data from a text

11.6. GROUPING WITH DICTIONARIES 408

file. Spaces and newlines can litter the file at random, but commas definitely separate the numbers. The
following file named monitor.data is typical:

92,50 , 77, 50 , 40,
36 , 52, 92,77, 77 , 93 ,

14, 42,
19, 52 ,75 ,
42, 23 ,14

This file contains five lines of text. Each line may have trailing spaces that are not visible in the listing
above, and each line certainly has a newline (“\n”) at its end. We must strip the newline from each line and
strip the final comma and trailing spaces. The string rstrip will accomplish this end-of-line clean up with
the match string ” ,\n” (space, comma, newline). Listing 11.11 (readtextfile.py) provides the complete
code.

Listing 11.11: readtextfile.py

def readfile(filename):
“”” Read the comma-separated integer data from the text file

named filename and return the data in a list. “””
result = [] # List initially empty
with open(filename, “r”) as f:

for line in f:
# Remove any trailing spaces, comma, and newline
result += [int(x.strip()) for x in line.rstrip(” ,\n”).split(“,”)]

return result

def main():
lst = readfile(“monitor.data”)
print(lst)

if __name__ == “__main__”:
main()

Listing 11.11 (readtextfile.py) reads in the file monitor.data and prints

[92, 50, 77, 50, 40, 36, 52, 92, 77, 77, 93, 14, 42, 19, 52, 75, 42, 23, 14]

11.6 Grouping with Dictionaries

Dictionaries are useful for grouping items. Like Listing 11.10 (wordcount.py), Listing 11.12 (groupwords.py)
reads in the contents of a text file. Instead of counting the words, Listing 11.12 (groupwords.py) groups the
words into lists based on the number of letters in the word. All the words containing only one letter are in
one list, all the words containing two letters are in another list, etc.

Listing 11.12: groupwords.py

“”” Uses a dictionary to group the words in a text file according to
their length (number of letters). “””

11.6. GROUPING WITH DICTIONARIES 409

import sys # For argv global command line arguments list

def main():
“”” Group the words by length in a text file. “””
if len(sys.argv) < 2: # Did the user not supply a file name? print('Usage: python groupwords.py ‘)
print(‘ where is the name of a text file.’)

else: # User provided file name
filename = sys.argv[1]
groups = {} # Initialize grouping dictionary
with open(filename, ‘r’) as f: # Open the file for reading

content = f.read() # Read in content of the entire file
words = content.split() # Make list of individual words
for word in words:

word = word.upper() # Make the word all caps
# Compute the word’s length
size = len(word)
if size in groups:

if word not in groups[size]: # Avoid duplicates
groups[size] += [word] # Add the word to its group

else:
groups[size] = [word] # Add the word to a new group

# Show the groups
for size, group in groups.items():

print(size, ‘:’, group)

if __name__ == ‘__main__’:
main()

The following shows a sample run of Listing 11.12 (groupwords.py) on our snippet from the Declaration of
Independence:

1 : [‘A’]
2 : [‘IN’, ‘OF’, ‘IT’, ‘TO’]
3 : [‘THE’, ‘FOR’, ‘ONE’, ‘AND’, ‘GOD’]
4 : [‘WHEN’, ‘HAVE’, ‘THEM’, ‘WITH’, ‘LAWS’, ‘THAT’, ‘THEY’]
5 : [‘HUMAN’, ‘BANDS’, ‘WHICH’, ‘AMONG’, ‘EARTH’, ‘EQUAL’, ‘IMPEL’]
6 : [‘COURSE’, ‘EVENTS’, ‘PEOPLE’, ‘ASSUME’, ‘POWERS’, ‘NATURE’, ‘DECENT’, ‘SHOULD’, ‘CAUSES’]
7 : [‘BECOMES’, ‘ANOTHER’, ‘STATION’, ‘ENTITLE’, ‘RESPECT’, ‘MANKIND’, ‘DECLARE’]
8 : [‘DISSOLVE’, ‘SEPARATE’, “NATURE’S”, ‘OPINIONS’, ‘REQUIRES’]
9 : [‘NECESSARY’, ‘POLITICAL’, ‘CONNECTED’]
10 : [‘SEPARATION’]

Each key represents the length of all the strings in the list it oversees.

In this example the need for a dictionary object is not as compelling as in Listing 11.10 (wordcount.py),
because in practice the length of English words is limited. We could instead use a list of 50 sets. Only rarely
used, highly technical words exceed 50 letters. We could handle these “too-long” words in a special way,
perhaps storing them in the set in the last position in the list with other words of more than 49 letters. Our
program could use special processing for this set of long words if it ever becomes nonempty. This approach
under typical circumstances would result in a number of empty sets at higher indices because most English

11.6. GROUPING WITH DICTIONARIES 410

text contains words of at most about 20 letters. The advantage of a dictionary is that it stores only what it
needs. Listing 11.13 (groupwordslist.py) is close transliteration of Listing 11.12 (groupwords.py) that uses
a list in place of a dictionary.

Listing 11.13: groupwordslist.py

“”” Uses a list to group the words from a text file according to
their length (number of letters). “””

import sys # For argv global command line arguments list

def main():
“”” Group the words by length in a text file. “””
if len(sys.argv) < 2: # Did the user not supply a file name? print('Usage: python groupwordslist.py ‘)
print(‘ where is the name of a text file.’)

else: # User provided file name
filename = sys.argv[1]
groups = [] # Initialize grouping list
for i in range(20):

groups.append(set()) # Add new empty set to the list
with open(filename, ‘r’) as f: # Open the file for reading

content = f.read() # Read in content of the entire file
words = content.split() # Make list of individual words
for word in words:

word = word.upper() # Make the word all caps
# Compute the word’s length
size = len(word)
groups[size].add(word)

# Show the groups
for size, group in enumerate(groups):

print(size, ‘:’, group)

if __name__ == ‘__main__’:
main()

We can see the unused space in the output of Listing 11.13 (groupwordslist.py):

0 : set()
1 : {‘A’}
2 : {‘IT’, ‘TO’, ‘OF’, ‘IN’}
3 : {‘ONE’, ‘AND’, ‘FOR’, ‘GOD’, ‘THE’}
4 : {‘THEY’, ‘WHEN’, ‘HAVE’, ‘LAWS’, ‘THEM’, ‘WITH’, ‘THAT’}
5 : {‘EQUAL’, ‘BANDS’, ‘HUMAN’, ‘EARTH’, ‘WHICH’, ‘IMPEL’, ‘AMONG’}
6 : {‘SHOULD’, ‘DECENT’, ‘POWERS’, ‘NATURE’, ‘COURSE’, ‘ASSUME’, ‘EVENTS’, ‘PEOPLE’, ‘CAUSES’}
7 : {‘RESPECT’, ‘STATION’, ‘BECOMES’, ‘DECLARE’, ‘ANOTHER’, ‘ENTITLE’, ‘MANKIND’}
8 : {‘REQUIRES’, “NATURE’S”, ‘DISSOLVE’, ‘OPINIONS’, ‘SEPARATE’}
9 : {‘NECESSARY’, ‘POLITICAL’, ‘CONNECTED’}
10 : {‘SEPARATION’}
11 : set()
12 : set()
13 : set()
14 : set()

11.7. KEYWORD ARGUMENTS 411

15 : set()
16 : set()
17 : set()
18 : set()
19 : set()

The expression set() is how Python prints the empty set (to distinguish it from an empty dictionary). In
a different document there could be empty sets in the groups representing the words with fewer than 11
letters.

11.7 Keyword Arguments

The following function specifies formal parameters named a, b, and c:

def process(a, b, c):
print(‘a =’, a, ‘ b =’, b, ‘ c =’, c)

The following code uses function process, passing actual parameters 2, x (that is, 14), and 10:

x = 14
process(2, x, 10)

It prints

a = 2 b = 14 c = 10

The calling code assigns the value of the first actual parameter to the first formal parameter. It assigns the
value of the second parameter to the second formal parameter. Finally, it assigns the value of the third
actual parameter to the third formal parameter. By default, the association of actual parameter to formal
parameter during a function invocation is strictly positional. This is the shortest, simplest way for the caller
to pass parameters.

Python allows the caller to pass its actual parameters in any order using a technique known as keyword
arguments. We introduced the end and sep keyword arguments for the print function in Section 2.7.
In order to use keyword arguments, the caller must know the names of the function’s formal parameters.
Listing 11.14 (namedparams.py) shows how callers can use keyword parameters.

Listing 11.14: namedparams.py

def process(a, b, c):
print(‘a =’, a, ‘ b =’, b, ‘ c =’, c)

x = 14
process(1, 2, 3)
process(a=10, b=20, c=30)
process(b=200, c=300, a=100)
process(c=3000, a=1000, b=2000)
process(10000, c=30000, b=20000)

Listing 11.14 (namedparams.py) prints the following:

11.7. KEYWORD ARGUMENTS 412

a = 1 b = 2 c = 3
a = 10 b = 20 c = 30
a = 100 b = 200 c = 300
a = 1000 b = 2000 c = 3000
a = 10000 b = 20000 c = 30000

The statement

process(10000, c=30000, b=20000)

shows that keywords arguments may appear in the same call as non-keyword arguments, but in such mixed-
parameter calls all non-keyword arguments must appear before any keyword arguments. The function
invocation mechanism assigns the non-keyword arguments as usual: the first actual parameter to the first
formal parameter, second actual parameter to the second formal parameter, etc. It assigns the keyword
arguments that follow to the formal parameters of the same name.

We can define a function to require keyword parameters by prefixing a formal parameter with two
asterisks (**). The following function requires the caller to pass three actual parameters named a, b, and c:

def f(**args):
a = args[‘a’]
b = args[‘b’]
c = args[‘c’]
return 2*a*a + 3*b + c

Given this definition of f, a caller can invoke f as

x = f(a=4, b=11, c=3)

and the following statement:

x = f(4, 11, c) # Illegal, f requires keyword arguments

is illegal.

The following function prints the names of the keyword arguments passed in by the caller:

def process(**args):
for arg in args:

print(arg)

This process function is designed to accept any keyword arguments the caller chooses to pass. Consider
the following interactive sequence:

>>> def process(**args):
… for arg in args:
… print(arg, ‘–>’, args[arg])
… print(‘args =’, args)
…
>>> process(num=5, x=’Hello’, value=True, zz=100)
num –> 5
zz –> 100
value –> True
x –> Hello
args = {‘num’: 5, ‘zz’: 100, ‘value’: True, ‘x’: ‘Hello’}

11.7. KEYWORD ARGUMENTS 413

As we can see, the formal parameter **args is really a dictionary. All the keyword arguments become keys
and values in the dictionary. The parameter’s name becomes a key, and the associated value is the caller’s
value assigned to the keyword argument name.

As with arbitrary argument lists, we can mix regular positional parameters with the special ** key-
word argument parameter. We actually can mix regular parameters, arbitrary argument lists, and keyword
arguments as long as we use the proper order:

def f(x, y, z, *a, **b):
pass

In this function x, y, and z are regular positional arguments, a is the arbitrary arguments tuple, and b is the
keywords arguments dictionary. The positional arguments, if any, must appear before any arbitrary argu-
ments and keyword arguments. The arbitrary arguments, if any, must appear after the positional arguments
and before the keyword arguments. The keyword arguments, if any, must appear after the positional and
arbitrary argument list parameters.

As with arbitrary argument list arguments, we can use keyword arguments on the caller side. List-
ing 11.15 (callerkeyword.py) shows how we can send a dictionary as a parameter to a function that expects
regular positional parameters.

Listing 11.15: callerkeyword.py

def f(a, b, c):
print(‘a =’, a, ‘ b =’, b, ‘ c =’, c)

f(1, 2, 3) # Pass three parameters
dict = {}
dict[‘b’] = 22
dict[‘a’] = 11
dict[‘c’] = 33
f(**dict)
f(**{‘a’:10, ‘b’:20, ‘c’:30}) # Pass a dictionary

Listing 11.15 (callerkeyword.py) prints

a = 1 b = 2 c = 3
a = 11 b = 22 c = 33
a = 10 b = 20 c = 30

Observe that the caller must use the ** prefix when passing the dictionary in the place of the expected
positional parameters.

Recall that we saw several methods in the in the tkinter package that accept keyword arguments; for
example, the following is a statement from Listing 9.13 (buttontester.py):

b.configure(background=”yellow”, text=”Click Count = 0″, command=update)

Keyword arguments are very convenient for functions and methods that can accept a large number of ar-
guments. The configure method in the Button class is defined to accept a dictionary via the ** notation.
It accepts up to 35 keyword arguments. Keyword arguments in general enable a caller to supply just a
few arguments, in any order. There is no need for the programmer to remember which argument comes
first, then second, etc. as with positional arguments. The function or method can accept the caller-supplied
arguments and use predetermined default values for any optional arguments the caller omitted.

11.8. SETS 414

Section 14.4 shows how keyword arguments are invaluable for implementing multiple inheritance, an
advanced object-oriented design technique.

Recall the nullify decorator we examined in Section 8.10. It removed the functionality from any
function that accepts two parameters. Armed with our knowledge of arbitrary argument lists and keyword
arguments we now can write a more comprehensive nullify decorator as

def nullify(f):
“”” A decorator that guts the functionality of a function “””
def empty_func(*args, **kwargs):

“”” This function does nothing and returns None “””
pass

return empty_func

When used as a decorator this version of nullify effectively removes the functionality of any function
regardless of the number and kinds of parameters the function to be nullified expects.

11.8 Sets

Python provides a data structure that represents a mathematical set. As with mathematical sets, we use curly
braces ({}) in Python code to enclose the elements of a literal set. Python distinguishes between set literals
and dictionary literals by the fact that all the items in a dictionary are colon-connected (:) key-value pairs,
while the elements in a set are simply values. Unlike Python lists, sets are unordered and may contain no
duplicate elements. The following interactive sequence demonstrates these set properties:

>>> S = {10, 3, 7, 2, 11}
>>> S
{2, 11, 3, 10, 7}
>>> T = {5, 4, 5, 2, 4, 9}
>>> T
{9, 2, 4, 5}

Note the element ordering of the input is different from the ordering in the output. Also observe that sets
do not admit duplicate elements.

We can make a set out of a list using the set conversion function:

>>> L = [10, 13, 10, 5, 6, 13, 2, 10, 5]
>>> S = set(L)
>>> L
[10, 13, 10, 5, 6, 13, 2, 10, 5]
>>> S
{10, 2, 13, 5, 6}

As you can see, the element ordering is not preserved, and duplicate elements appear only once in the set.

Python set notation exhibits one important difference with mathematics: the expression {} does not
represent the empty set. In order to use the curly braces for a set, the set must contain at least one element.
The expression set() produces a set with no elements, and thus represents the empty set. Python reserves
the {} notation for empty dictionaries (see Section 11.3).

Unlike in mathematics, all sets in Python must be finite. Python supports the standard mathematical set
operations of intersection, union, set difference, and symmetric difference. Table 11.2 shows the Python

11.9. SET QUANTIFICATION WITH ALL AND ANY 415

Table 11.2 Python set operations. A and B are sets. Figure 11.1 illustrates how the set operations work.
Operation Mathematical Python Result Meaning

Notation Syntax Type
Union A∪B A | B set Elements in A or B or both
Intersection A∩B A & B set Elements common to both A and B
Set Difference A−B A – B set Elements in A but not in B
Symmetric Difference A⊕B A ˆ B set Elements in A or B, but not both
Set Membership x ∈ A x in A bool x is a member of A
Set Membership x /∈ A x not in A bool x is not a member of A
Set Equality A = B A == B bool Sets A and B contain exactly the

same elements
Subset A⊆ B A <= B bool Every element in set A also is a member of set B Proper Subset A⊂ B A < B bool A is a subset B, but B contains at least one element not in A syntax for these operations. Figure 11.1 illustrates how the set operations work. The following interactive sequence computes the union and intersection and two sets and tests for set membership: >>> S = {2, 5, 7, 8, 9, 12}
>>> T = {1, 5, 6, 7, 11, 12}
>>> S | T
{1, 2, 5, 6, 7, 8, 9, 11, 12}
>>> S & T
{12, 5, 7}
>>> 7 in S
True
>>> 11 in S
False

As with list comprehensions and generator expressions (Section 10.13), we can use set comprehension
to build sets. The syntax is the same as for list comprehension, except we use curly braces rather than
square brackets. The following interactive sequence constructs the set of perfect squares less than 100:

>>> S = {x**2 for x in range(10)}
>>> S
{0, 1, 64, 4, 36, 9, 16, 49, 81, 25}

The displayed order of elements is not as nice as the list version, but, again, element ordering is meaningless
with sets.

When treated as a Boolean expression, the empty set (set()) is interpreted as False, and any other set
is considered True.

11.9 Set Quantification with all and any

Python provides functions named all and any that respectively correspond to mathematical universal and
existential quantification. These fancy mathematical terms label relatively simple concepts. Universal

11.9. SET QUANTIFICATION WITH ALL AND ANY 416

Figure 11.1 Python’s set operations: union, intersection, set difference, and symmetric difference. The
shaded area in each diagram indicates the elements that are included in the set that results from applying
the indicated operator.

0 1

3
4

20
30

31 24

S T

S = {0, 1, 2, 3, 4, 5, 6, 11, 12, 20}

T = {1, 4, 6, 7, 8, 24, 31}

S | T

0 1

3
4

20
30

31 24

S T

S & T

0 1

3
4

20
30

31 24

S T

S – T

0 1

3
4

20
30

31 24

S T

S ^ T

11.9. SET QUANTIFICATION WITH ALL AND ANY 417

quantification means that a particular property is true for all the elements of a set. Existential quantification
means that at least one element is the set exhibits a particular property. In mathematics the ∀ symbol
represents universal quantification, and the ∃ symbol represents existential quantification. The ∀ symbol
usually is pronounced “for all,” and the ∃ symbol is read as “there exists.”

To see how we can use these quantifiers in a Python program, consider the set S = {1,2,3,4,5,6,7,8}.
In the interactive shell we can type

>>> S = {1, 2, 3, 4, 5, 6, 7, 8}
>>> S
{1, 2, 3, 4, 5, 6, 7, 8}

To express in mathematics the fact that all the elements in set S are greater than zero, we can write

(∀x ∈ S)(x > 0)

This is a statement that is either true or false, and we can see that it is a true statement. In Python, we first
will use a list comprehension to see which elements in S are greater than zero. We can do this by building
a list of Boolean values by using a Boolean expression in the list comprehension:

>>> [x > 0 for x in S]
[True, True, True, True, True, True, True, True]

We can see that all the entries in this list are True, but the best way to determine this in code is to use
Python’s all function:

>>> all([x > 0 for x in S])
True

The all function returns True if all the elements in a list, set, or other iterable possesses a particular quality.
We do not need to create a list; a generator expression is better (note that parentheses replace the square
brackets):

>>> all((x > 0 for x in S))
True

and in this case the inner parentheses are superfluous. We can write the expression as

>>> all(x > 0 for x in S)
True

The expression

all(x > 0 for x in S)

is Python’s way of checking the mathematical predicate (∀x ∈ S)(x > 0).

The any function returns True if any element in a list, set, or other iterable possesses a particular quality.
This means the any function represents the mathematical existential quantifier, ∃:

>>> any(x > 0 for x in S)
True

The expression

11.9. SET QUANTIFICATION WITH ALL AND ANY 418

any(x > 0 for x in S)

is Python’s way of checking the mathematical predicate (∃x ∈ S)(x > 0). Certainly if the property holds for
all the elements in set S, there is at least one element for which it holds.

Are all the elements of S greater than 5?

>>> all(x > 5 for x in S)
False

The answer is false, of course, because the set contains 1, 2, 3, 4, and 5, none of which are greater than 5.
There are some elements in S that are greater than 5:

>>> any(x > 5 for x in S)
True

The elements 6, 7, and 8 are all greater than 5. Is it true that the set contains an element greater than 10?

>>> any(x > 10 for x in S)
False

We can see that none of the elements in S are greater than 10. If none of the set’s elements possess the
particular property, it certainly cannot be true for all the elements in the set:

>>> all(x > 10 for x in S)
False

The all and any functions work with any iterable object: sets, lists, dictionaries, and generated se-
quences.

In most Python programming, sets play a much smaller role than lists and dictionaries. Sets are most
similar to lists, and the ordering of data is important in many applications. If order does not matter and all
elements are unique, the set type does offer a big advantage over the list type: testing for membership
using in is much faster on sets than lists. Listing 11.16 (setvslistaccess.py) creates both a set and a list,
each containing the first 1,000 perfect squares. It then searches both data structuures for, and does nothing
with, all the integers from 0 to 999,999. It reports the time required for the efforts.

Listing 11.16: setvslistaccess.py

# Data structure size
size = 1000

# Make a big set
S = {x**2 for x in range(size)}
# Make a big list
L = [x**2 for x in range(size)]

# Verify the type of S and L
print(‘Set:’, type(S), ‘ List:’, type(L))

from time import clock

# Search size
search_size = 1000000

11.10. ENUMERATING THE ELEMENTS OF A DATA STRUCTURE 419

# Time list access
start_time = clock()
for i in range(search_size):

if i in L:
pass

stop_time = clock()
print(‘List elapsed:’, stop_time – start_time)

# Time set access
start_time = clock()
for i in range(search_size):

if i in S:
pass

stop_time = clock()
print(‘Set elapsed:’, stop_time – start_time)

The results of Listing 11.16 (setvslistaccess.py) are dramatic. A run on one system reports:

Set: List:
List elapsed: 44.99767441164282
Set elapsed: 0.48652052551967984

The 1,000,000 list accesses required about three-quarters of a minute, while the set accesses needed less than
one-half second. The set membership test was almost 100 times faster than the exact same test performed
on the list.

Listing 11.10 (wordcount.py) grouped words from a text file according to their length. The program
contained a check to avoid duplicate entries:

if size in groups:
if word not in groups[size]: # Avoid duplicates

groups[size] += [word] # Add the word to its group
else:

groups[size] = [word] # Add the word to a new group

We know now that if we used sets of words rather than lists of words we could have eliminated the check
for duplicate entries.

if size in groups:
groups[size] += {word} # Add the word to its group

else:
groups[size] = {word} # Add the word to a new group

By removing this extra check we also remove the application of the in operator on a list. We have seen that
testing for membership within a list is more costly than testing for membership within a set. Eliminating
this check removes the potentially costly search for an element within a large list.

11.10 Enumerating the Elements of a Data Structure

The following code prints out the contents of a list named lst, along with the indices of the individual
elements:

11.10. ENUMERATING THE ELEMENTS OF A DATA STRUCTURE 420

for i in range(len(lst)):
print(i, lst[i])

This code requires two function calls in order to manage the indices: one call to len to determine the
highest index and another call to the range constructor to produce each index. The __builtins__ module
provides a function named enumerate that returns an iterable object that produces tuples. Each tuple pairs
an index with its associated element. The following code uses the enumerate function to produce the same
results as the above code:

for i, elem in enumerate(lst):
print(i, elem)

One call to enumerate replaces the two calls from before. In some circumstances code that uses enumerate
can be slightly more efficient than the code that manually manages the integer index.

The enumerate function accepts any type of object that supports iteration. Listing 11.17 (enum.py)
demonstrates the use of enumerate with lists, tuples, dictionaries, sets, and generators:

Listing 11.17: enum.py

lst = [10, 20, 30, 40, 50]
t = 100, 200, 300, 400, 500
d = {“A”: 4, “B”: 18, “C”: 0, “D”: 3}
s = {1000, 2000, 3000, 4000, 5000}
print(lst)
print(t)
print(d)
print(s)
for x in enumerate(lst):

print(x, end=” “)
print()
for x in enumerate(t):

print(x, end=” “)
print()
for x in enumerate(d):

print(x, end=” “)
print()
for x in enumerate(s):

print(x, end=” “)
print()

def gen(n):
“”” Generate n, n – 2, n – 3, …, 0. “””
for i in range(n, -1, -2):

yield i

for x in enumerate(gen(20)):
print(x, end=” “)

print()

# Optionally specify beginning index
for x in enumerate(t, 1):

print(x, end=” “)

11.11. EXERCISES 421

print()

The last call to enumerate in Listing 11.17 (enum.py) uses an optional parameter specifying the beginning
index to use in the enumeration. The default starting index is 0.

Listing 11.17 (enum.py) prints

[10, 20, 30, 40, 50]
(100, 200, 300, 400, 500)
{‘D’: 3, ‘C’: 0, ‘A’: 4, ‘B’: 18}
{5000, 4000, 3000, 2000, 1000}
(0, 10) (1, 20) (2, 30) (3, 40) (4, 50)
(0, 100) (1, 200) (2, 300) (3, 400) (4, 500)
(0, ‘D’) (1, ‘C’) (2, ‘A’) (3, ‘B’)
(0, 5000) (1, 4000) (2, 3000) (3, 2000) (4, 1000)
(0, 20) (1, 18) (2, 16) (3, 14) (4, 12) (5, 10) (6, 8) (7, 6) (8, 4) (9, 2) (10, 0)
(1, 100) (2, 200) (3, 300) (4, 400) (5, 500)

11.11 Exercises

1. How are tuples different from lists?

2. How do tuples support the indexing operation ([]) differently from lists?

3. Are tuples mutable or immutable?

4. Are the elements in tuples ordered or unordered?

5. Rewrite the last assignment statement in the following interactive sequence so that it behaves identi-
cally but uses tuple unpacking instead of tuple slicing.

>>> a = 1, 2, 3, 4, 5, 6, 7, 8
>>> a
(1, 2, 3, 4, 5, 6, 7, 8)
>>> s = a[2:6]
>>> s
(3, 4, 5, 6)

6. Rewrite the last assignment statement in the following interactive sequence so that it behaves identi-
cally but uses tuple slicing instead of tuple unpacking.

>>> a = 1, 2, 3, 4, 5, 6, 7, 8
>>> a
(1, 2, 3, 4, 5, 6, 7, 8)
>>> s = _, _, _, *s, _ = a
>>> s = tuple(s)
>>> s
(4, 5, 6, 7)

7. Consider the tuple tpl defined as

tpl = 7, 10, -3, 18, 6, 10

11.11. EXERCISES 422

Provide one assignment statement that uses tuple unpacking to assign x to the first element and y to
the last element.

8. Write a function named product that computes the product of any number of floating-point argu-
ments; for example, the call product(2.5, 2, 10.0) would evaluate to 50.0. The function should
return 1 (the identity element for multiplication) if the caller passes no arguments.

9. Write a function named zero_sum that accepts any number of integer arguments. The function
should return True if the sum of its arguments is zero; otherwise, it should return False. The call
zero_sum(2, 3, -5), for example, would evaluate to True, since 2 + 3 + −5 = 0. On the other
hand, zero_sum(2, 3, -10, 4) evaluates to False because 2 + 3 + − 10 + 4 = − 1 6= 0.
zero_sum should return True when called with no arguments.

10. Why is a dictionary considered an associative container?

11. What statement assigns an empty dictionary to a variable named d?

12. If d refers to a dictionary, what expression represents the value associated with the key “Fred”?

13. What happens when an executing program attempts to retrieve a value using a key that is not present
in the dictionary?

14. What happens when an executing program attempts to associate a value with a key that is not present
in the dictionary?

15. Are dictionaries mutable or immutable?

16. Given the following dictionary:

d = {3:0, 5:1, 10:1, 8:2, 15:4}

Indicate what each of the following code fragments will print:

(a) print(d)

(b) for x in d:
print(x)

(d) for x in d.values():
print(x)

17. Are the elements in dictionaries ordered or unordered?

18. Modify Listing 9.14 (tkinterlight.py) so that it models a light with a single on/off yellow lamp.

19. Write a graphical, two-player Tic-Tac-Toe game using the tkinter module (see https://en.wikipedia.
org/wiki/Tic-tac-toe for more information about the game). You can use nine separate variables
to track the contents of the game’s squares. You must be able to draw lines and circles in the appro-
priate locations.

20. Explain why the statement

https://en.wikipedia.org/wiki/Tic-tac-toe
https://en.wikipedia.org/wiki/Tic-tac-toe

11.11. EXERCISES 423

A = {}

does not create an empty set.

21. Provide the Python statement that assigns the variable A to the empty set.

22. Are sets mutable or immutable?

23. Given the following initialization statements:

A = {20, 19, 2, 10, 7}
B = {4, 10, 5, 6, 9, 7}
C = {10, 19}

evaluate the following expressions:

(a) A

(b) 20 in A

(d) A & B

(e) A | B

(f) C < A (g) C <= A (h) C <= B (i) A <= A (j) A < A (k) len(A) (l) {x + 2 for x in range(10)} (m) {x - 2 for x in A} (n) {x - 2 for x in A if x < 10} ©2017 Richard L. Halterman Draft date: January 18, 2018 11.11. EXERCISES 424 ©2017 Richard L. Halterman Draft date: January 18, 2018 425 Chapter 12 Handling Exceptions In our programming experience so far we have encountered several kinds of run-time exceptions, such as division by zero, accessing a list with an out-of-range index, and attempting to convert a non-number to an integer. We have seen these and other run-time exceptions immediately terminate a running program. Python provides a standard mechanism called exception handling that allows programmers to deal with these kinds of run-time exceptions and many more. Rather than always terminating the program’s execution, an executing program can detect the problem when it arises and possibly execute code to correct the issue or mitigate it in some way. This chapter explores handling exceptions in Python. 12.1 Motivation Algorithm design can be tricky because the details are crucial. It may be straightforward to write an algo- rithm to solve a problem in the general case, but the designer may have to address a number of special cases within the problem for the algorithm to be correct. Some of these special cases might occur rarely and only under the most extraordinary circumstances. The algorithm must properly handle these exceptional cases to be truly robust; however, adding the necessary details to the algorithm may render it overly complex and difficult to construct correctly. Such an overly complex algorithm would be difficult for others to read and understand, and it would be harder to debug and extend. Ideally, a developer would write the algorithm in its general form including any common special cases. Exceptional situations that should arise rarely, along with a strategy to handle them, could appear elsewhere, perhaps as an annotation to the algorithm. This approach would focus the algorithm on its routine activity and keep its rare behavior tucked out of sight until specifically needed. Python’s exception handling infrastructure allows programmers to cleanly separate the code that imple- ments the focused algorithm from the code that deals with exceptional situations that the algorithm may face. This approach is more modular and encourages the development of code that is cleaner and easier to maintain and debug. An exception is a special object that the executing program can create when it encounters an extraor- dinary situation. Such a situation almost always represents a problem, usually some sort of run-time error. Examples of exceptional situations include: • attempting to read past the end of a file ©2017 Richard L. Halterman Draft date: January 18, 2018 12.2. COMMON STANDARD EXCEPTIONS 426 • evaluating the expression lst[i] where lst is a list, and i ≥ len(lst). • attempting to convert a nonnumeric string to a number, as in int('Fred') • attempting to read a variable that has not been defined • attempting to read data from the network when the connection is lost The algorithm may be able to handle many of these potential problems itself. For example, a program- mer can use an if statement to determine if a list index is within the bounds of a list: if i < len(lst): print(lst[i]) # Safely print lst[i] However, if the code within a function accesses the list in many different places, the large number of conditionals required to ensure the absolute safety of all the list accesses can quickly obscure the overall logic of the function. Fortunately, programmers sometimes can avoid this scenario by checking a list index once for a large number of similar accesses within a block of code or managing the index carefully to ensure it cannot be outside the list’s bounds. Other problems, however, such as the loss of a network connection, may be less straightforward for the algorithm to address directly. Fortunately, specific Python exceptions are available to cover problems such as these. Exceptions represent a standard way to deal with run-time errors. In programming languages that do not support exception handling, programmers must devise their own ways of dealing with exceptional situations. Such ad hoc approaches produce error handling facilities developed by one programmer that can be incompatible with those used by another. Python provides a comprehensive, uniform exception handling framework. Python’s exception framework provides a simple means of communicating errors between functions and short circuiting the normal function return process, effectively bypassing functions up the call chain that are unable to, or have no need to, participate in the error handling activity. The proper use of Python’s exception handling infrastructure leads to code that is logically cleaner and less prone to programming errors. The standard Python library uses exceptions, and programmers can create new exceptions that address issues specific to their particular problems. These exceptions all use a common syntax and are completely compatible with each other. 12.2 Common Standard Exceptions We have encountered a number of Python’s standard exception classes. Table 12.1 lists some of the more common exception classes. The following interactive sequence provides an example of each of the exceptions shown in Table 12.1: >>> from fractions import Fraction
>>> frac = Fraction(1, 2)
>>> print(frac.numerator)
1
>>> print(frac.numertor)
Traceback (most recent call last):

File ““, line 1, in
AttributeError: ‘Fraction’ object has no attribute ‘numertor’
>>> from fraction import Fraction
Traceback (most recent call last):

File ““, line 1, in
ImportError: No module named ‘fraction’

12.2. COMMON STANDARD EXCEPTIONS 427

Table 12.1 Common standard exception classes
Class Meaning

AttributeError Object does not contain the specified instance variable or method
ImportError The import statement fails to find a specified module or name in that module
IndexError A sequence (list, string, tuple) index is out of range
KeyError Specified key does not appear in a dictionary
NameError Specified local or global name does not exist
TypeError Operation or function applied to an inappropriate type
ValueError Operation or function applied to correct type but inappropriate value
ZeroDivisionError Second operand of divison or modulus operation is zero

>>> from fractions import Fractions
Traceback (most recent call last):

File ““, line 1, in
ImportError: cannot import name ‘Fractions’
>>> seq = [2, 5, 11]
>>> print(seq[1])
5
>>> print(seq[3])
Traceback (most recent call last):

File ““, line 1, in
IndexError: list index out of range
>>> d = {}
>>> d[‘Fred’] = 100
>>> print(d[‘Fred’])
100
>>> print(d[‘Freddie’])
Traceback (most recent call last):

File ““, line 1, in
KeyError: ‘Freddie’
>>> print(x)
Traceback (most recent call last):

File ““, line 1, in
NameError: name ‘x’ is not defined
>>> print(seq[‘Fred’])
Traceback (most recent call last):

File ““, line 1, in
TypeError: list indices must be integers, not str
>>> print(int(‘Fred’))
Traceback (most recent call last):

File ““, line 1, in
ValueError: invalid literal for int() with base 10: ‘Fred’
>>> print(1/0)
Traceback (most recent call last):

File ““, line 1, in
ZeroDivisionError: division by zero

Python contains many more standard exception classes than those shown in Table 12.1, and in Section 14.2
we will explore ways to create our own custom exception classes.

12.3. HANDLING EXCEPTIONS 428

12.3 Handling Exceptions

Listing 12.1 (dividenumbers.py) computes the quotient of two integer values supplied by the user.

Listing 12.1: dividenumbers.py

# Get two integers from the user
print(‘Please enter two numbers to divide.’)
num1 = int(input(‘Please enter the dividend: ‘))
num2 = int(input(‘Please enter the divisor: ‘))
print(‘{0} divided by {1} = {2}’.format(num1, num2, num1/num2))

In Listing 12.1 (dividenumbers.py), all is well until the user attempts to divide by zero:

Please enter two numbers to divide.
Please enter the dividend: 4
Please enter the divisor: 0
Traceback (most recent call last):

File “dividenumbers.py”, line 5, in
print(‘{0} divided by {1} = {2}’.format(num1, num2, num1/num2))

ZeroDivisionError: division by zero

This program execution produces a ZeroDivisionError exception.

We can defend against the ZeroDivisionError exception with a conditional statement, as Listing 12.2
(checkforzero.py) shows.

Listing 12.2: checkforzero.py

# Get two integers from the user
print(‘Please enter two numbers to divide.’)
num1 = int(input(‘Please enter the dividend: ‘))
num2 = int(input(‘Please enter the divisor: ‘))
if num2 != 0:

print(‘{0} divided by {1} = {2}’.format(num1, num2, num1/num2))
else:

print(‘Cannot divide by zero’)

The solution expressed by Listing 12.2 (checkforzero.py) illustrates the concept of look before you leap,
usually abbreviated as LBYL in the Python community. This programming idiom checks code that may
misbehave before executing it. The LBYL idiom works well for code like that found in Listing 12.2
(checkforzero.py).

Consider Listing 12.3 (enterinteger.py) that asks the user for a small integer value.

Listing 12.3: enterinteger.py

val = int(input(“Please enter a small positive integer: “))
print(‘You entered’, val)

A typical run of Listing 12.3 (enterinteger.py) looks like

Please enter a small positive integer: 5
You entered 5

12.3. HANDLING EXCEPTIONS 429

A user easily and innocently can thwart the programmer’s original intentions, as the following sample run
illustrates:

Please enter a small positive integer: five
Traceback (most recent call last):

File “enterinteger.py”, line 1, in
val = int(input(“Please enter a small positive integer: “))

ValueError: invalid literal for int() with base 10: ‘five’

For an English-speaking human, the response five should be just as acceptable as 5. The strings acceptable
to the Python int function, however, can contain only numeric characters and an optional leading sign
character (+ or -). The user’s input causes the program to produce a run-time exception. As it stands, the
program reacts to the exception by printing a message and terminating itself. As shown in the exception
error report, the kind of exception that this execution example produces is a ValueError exception.

Unfortunately, any attempt to make Listing 12.3 (enterinteger.py) more robust via the LBYL idiom
is not as easy as it is for Listing 12.2 (checkforzero.py). We basically need to determine if the arbitrary
string the user enters is acceptable to the int conversion function. The string must contain only the digit
characters ‘0’, ‘1’, ‘2’, ‘3’, ‘4’, ‘5’, ‘6’, ‘7’, ‘8’, or ‘9’, and it may contain a leading ‘-‘ or ‘+’
character indicating the number’s sign. Python’s regular expression library is ideal for this purpose, but
it is somewhat complicatied and deserves an entire chapter devoted to its use. Short of using the regular
expression library, the logic to ensure that the string is acceptable to the int function would be relatively
complex.

An alternative to LBYL is EAFP, which stands for easier to ask for forgiveness than permission. The
EAFP approach attempts to execute the potentially problematic code within a try statement. If the code
raises an exception, the program’s execution does not necessarily terminate; instead, the program’s execu-
tion jumps imeidately to a different block within the try statement. Listing 12.4 (enterintexcept.py) wraps
the code from Listing 12.3 (enterinteger.py) within a try statement to successfully defend again bad user
input.

Listing 12.4: enterintexcept.py

try:
val = int(input(“Please enter a small positive integer: “))
print(‘You entered’, val)

except ValueError:
print(‘Input not accepted’)

The two statements between try and except constitute the try block. The statement after the except line
represents an except block. If the user enters a string unacceptable to the int function, the int function
will raise a ValueError exception. At this point the program will not complete the assignment statement
nor will it execute the print statement that follows. Instead the program immediately will begin executing
the code in the except block. This means if the user enters five, the program will print the message Input
not accepted. If the user enters a convertible string like 5, the program will complete the try block and
ignore the code in the except block. Figure 12.1 contrasts the possible program execution flows within a
try/except statement. We say the except block handles the exception raised in the try block. Another
common terminology used to describe the excepting handling process uses the throw/catch metaphor: the
executing program throws an exception that an except block catches.

Listing 12.4 (enterintexcept.py) catches only exceptions of type ValueError. If for some reason the
code within the try block of Listing 12.4 (enterintexcept.py) raises a different type of exception, this try
statement is unable to catch it. In this case the program will behave as if the try/except statement were

12.3. HANDLING EXCEPTIONS 430

Figure 12.1 The possible program execution flows through a try/except statement.

try-block

try:

except ValueError:

except-block

Execute all the

statements with no

exceptions raised

Skip the except

block

try-block

try:

except ValueError:

except-block

Code raises a

ValueError

exception

Execute the

except block

Value
Error

try-block

try:

except ValueError:

except-block

Code raises an

IndexError

exception Uncaught

exception

propagates to

outer context

Index
Error

Skip rest of

try block

Skip rest of

try block

No exceptions Caught exception Uncaught exception

not there. Unless other exception handling code is present in the calling environment, the interpreter simply
will terminate the program with an error message. Listing 12.5 (otherexcept.py) includes a statement that
attempts to assign the value at index 2 of an empty list. Unfortunately, an empty list contains no values, so
any index is outside of its range of indices.

Listing 12.5: otherexcept.py

try:
val = int(input(“Please enter a small positive integer: “))
print(‘You entered’, val)
[][2] = 5 # Try to assign to a nonexistent index of the empty list

except ValueError:
print(‘Input not accepted’)

The expression [] represents the empty list. The expression [][2] represents the element at index 2
within the empty list (there is no such element). Consider the following sample run of Listing 12.5
(otherexcept.py):

Please enter a small positive integer: 5
You entered 5
Traceback (most recent call last):

File “enterintexcept.py”, line 4, in
[][2] = 5 # Try to assign to a nonexistent index of the empty list

IndexError: list assignment index out of range

We see that the except block in Listing 12.5 (otherexcept.py) is unable to catch the IndexError exception.
Figure 12.1 illustrates this possible outcome as well.

12.4. HANDLING MULTIPLE EXCEPTIONS 431

12.4 Handling Multiple Exceptions

A try statement can have multiple except blocks. Each except block must catch a different type of
exception object. Listing 12.6 (multiexcept.py) offers three except blocks. Its try statement specifically
can catch ValueError, IndexError, and ZeroDivisionError exceptions.

Listing 12.6: multiexcept.py

import random

for i in range(10): # Loop 10 times
print(‘Beginning of loop iteration’, i)
try:

r = random.randint(1, 3) # r is pseudorandomly 1, 2, or 3
if r == 1:

print(int(‘Fred’)) # Try to convert a non-integer
elif r == 2:

[][2] = 5 # Try to assign to a nonexistent index of the empty list
else:

print(3/0) # Try to divide by zero
except ValueError:

print(‘Cannot convert integer’)
except IndexError:

print(‘List index is out of range’)
except ZeroDivisionError:

print(‘Division by zero not allowed’)

print(‘End of loop iteration’, i)

Each time through the loop the code within the try block of Listing 12.6 (multiexcept.py) will raise one of
three different exceptions based on the generated pseudorandom number. The program offers three except
blocks. If the code in the try block raises one of the three types of exceptions, the program will execute the
code in the matching except block. Only code in one of the three except blocks will execute as a result of
the exception. The following shows a sample run of Listing 12.6 (multiexcept.py):

Beginning of loop iteration 0
List index is out of range
End of loop iteration 0
Beginning of loop iteration 1
Division by zero not allowed
End of loop iteration 1
Beginning of loop iteration 2
Cannot convert integer
End of loop iteration 2
Beginning of loop iteration 3
List index is out of range
End of loop iteration 3
Beginning of loop iteration 4
Cannot convert integer
End of loop iteration 4
Beginning of loop iteration 5
List index is out of range
End of loop iteration 5
Beginning of loop iteration 6

12.5. THE CATCH-ALL HANDLER 432

Division by zero not allowed
End of loop iteration 6
Beginning of loop iteration 7
List index is out of range
End of loop iteration 7
Beginning of loop iteration 8
List index is out of range
End of loop iteration 8
Beginning of loop iteration 9
Division by zero not allowed
End of loop iteration 9

Observe that only one except block executes each time through the loop.

If we need the exact code to handle more than one exception type, we can associate multiple types with
a single except block by listing each exception type within a tuple. Listing 12.7 (multihandle.py) illustrates.

Listing 12.7: multihandle.py

import random

for i in range(10): # Loop 10 times
print(‘Beginning of loop iteration’, i)
try:

r = random.randint(1, 3) # r is pseudorandomly 1, 2, or 3
if r == 1:

print(int(‘Fred’)) # Try to convert a non-integer
elif r == 2:

[][2] = 5 # Try to assign to a nonexistent index of the empty list
else:

print(3/0) # Try to divide by zero
except (ValueError, ZeroDivisionError):

print(‘Problem with integer detected’)
except IndexError:

print(‘List index is out of range’)

print(‘End of loop iteration’, i)

The first except block in Listing 12.7 (multihandle.py) will catch both ValueError and ZeroDivisionError
exceptions. As shown in Listing 12.7 (multihandle.py), parentheses must enclose a tuple specified in an
except block.

In general it is better to bundle exception handlers rather than duplicating code over multiple handlers.

12.5 The Catch-all Handler

Consider Listing 12.8 (missedexception.py), a slight modification of Listing 12.6 (multiexcept.py).

Listing 12.8: missedexception.py

import random

for i in range(10): # Loop 10 times

12.5. THE CATCH-ALL HANDLER 433

print(‘Beginning of loop iteration’, i)
try:

r = random.randint(1, 4) # r is pseudorandomly 1, 2, 3, or 4
if r == 1:

print(int(‘Fred’)) # Try to convert a non-integer
elif r == 2:

[][2] = 5 # Try to assign to a nonexistent index of the empty list
elif r == 3:

print({}[1]) # Try to use a nonexistent key to get an item from a dictionary
else:

print(3/0) # Try to divide by zero
except ValueError:

print(‘Cannot convert integer’)
except IndexError:

print(‘List index is out of range’)
except ZeroDivisionError:

print(‘Division by zero not allowed’)

print(‘End of loop iteration’, i)

In addition to raising one of the three exceptions from Listing 12.6 (multiexcept.py), Listing 12.8 (missedexception.py)
can raise a KeyError exception. The expression {} represents the empty dictionary, and the expression
{}[1] represents the value associated with the key 1 within the empty dictionary (which, of course, does
not exist). Unfortunately, Listing 12.8 (missedexception.py) has no handler for the KeyError exception.
The following output shows the results for one program run:

Beginning of loop iteration 0
Division by zero not allowed
End of loop iteration 0
Beginning of loop iteration 1
List index is out of range
End of loop iteration 1
Beginning of loop iteration 2
Traceback (most recent call last):

File “missedexception.py”, line 12, in
print({}[1]) # Try to use a nonexistent key to get an item from a dictionary

KeyError: 1

If we want our programs not to crash, we need to handle all possible exceptions that can arise. This is
particularly important when we use libraries that we did not write. A program may execute code that only
under very rare circumstances raises an exception. This situation may be so rare that it evades our thorough
testing and appears only after we deploy the application to users. We need a handler that can catch any
exception.

The type Exception matches any exception type that a programmer would reasonably want to catch.
Listing 12.9 (catchallexcept.py) shows how to use this “catch-all” exception to close the exception hole
found in Listing 12.8 (missedexception.py).

Listing 12.9: catchallexcept.py

import random

for i in range(10): # Loop 10 times
print(‘Beginning of loop iteration’, i)

12.5. THE CATCH-ALL HANDLER 434

try:
r = random.randint(1, 4) # r is pseudorandomly 1, 2, 3, or 4
if r == 1:

print(int(‘Fred’)) # Try to convert a non-integer
elif r == 2:

[][2] = 5 # Try to assign to a nonexistent index of the empty list
elif r == 3:

print({}[1]) # Try to use a nonexistent key to get an item from a dictionary
else:

print(3/0) # Try to divide by zero
except ValueError:

print(‘Cannot convert integer’)
except IndexError:

print(‘List index is out of range’)
except ZeroDivisionError:

print(‘Division by zero not allowed’)
except Exception: # Catch any other type of exception

print(‘This program has encountered a problem’)

print(‘End of loop iteration’, i)

A run of Listing 12.9 (catchallexcept.py) shows that it can run to completion:

List index is out of range
End of loop iteration 0
Beginning of loop iteration 1
Cannot convert integer
End of loop iteration 1
Beginning of loop iteration 2
This program has encountered a problem
End of loop iteration 2
Beginning of loop iteration 3
Cannot convert integer
End of loop iteration 3
Beginning of loop iteration 4
This program has encountered a problem
End of loop iteration 4
Beginning of loop iteration 5
Cannot convert integer
End of loop iteration 5
Beginning of loop iteration 6
Cannot convert integer
End of loop iteration 6
Beginning of loop iteration 7
Cannot convert integer
End of loop iteration 7
Beginning of loop iteration 8
Division by zero not allowed
End of loop iteration 8
Beginning of loop iteration 9
Division by zero not allowed
End of loop iteration 9

12.5. THE CATCH-ALL HANDLER 435

Listing 12.9 (catchallexcept.py) offers four except blocks. The except Exception block at the end rep-
resents the catch-all handler that can catch any exception not caught by an earlier except block within the
try statement. If present, the catch-all except block should be the last except block in the try statement.
Since the Exception type matches any exception type, if it appears before another except block, it will
intercept a specific exception before a later except block has a chance to see it. This is because a program
executes at most one except block when executing a try statement.

There are a few exceptions that the Exception type does not match. These are exceptions that program-
mers usually do not want to handle; for example, the call sys.exit(0) raises an exception and terminates
the executing program. Another example is the keyboard interrupt ( Ctrl C ) entered by the user. The
Exception type does not match either of these types of exceptions. On occasion a program may need to
handle these special exceptions; for example, the program may need to perform some special clean up or
properly close its connection to a remote database before terminating. The try statement allows us to catch
any previously uncaught exception with an untyped except block. Listing 12.10 (reallycatchallexcept.py)
shows how to use this super catch-all handler.

Listing 12.10: reallycatchallexcept.py

import random

for i in range(10): # Loop 10 times
print(‘Beginning of loop iteration’, i)
try:

r = random.randint(1, 4) # r is pseudorandomly 1, 2, 3, or 4
if r == 1:

print(int(‘Fred’)) # Try to convert a non-integer
elif r == 2:

[][2] = 5 # Try to assign to a nonexistent index of the empty list
elif r == 3:

print({}[1]) # Try to use a nonexistent key to get an item from a dictionary
else:

print(3/0) # Try to divide by zero
except ValueError:

print(‘Cannot convert integer’)
except IndexError:

print(‘List index is out of range’)
except ZeroDivisionError:

print(‘Division by zero not allowed’)
except: # Catch absolutely any other type of exception

print(‘This program has encountered a problem’)

print(‘End of loop iteration’, i)

The untyped except block, if present, must be the last except block in the try statement. It is a syntax
error for the untyped except block to appear before a typed except block.

In situations that warrant a catch-all handler, prefer to catch the Exception type; use the untyped catch-
all handler only as a last resort.

Now that we have seen how to write a catch-all exception handler, it is important to note that its use
should be limited. A catch-all handler, if used properly, is appropriate for some situations, but for beginning
programmers it is tempting to provide a catch-all except block all the time, just in case. A good rule of
thumb is this: code should handle specific kinds of exceptions it expects and ignore (that is, do not attempt
to catch) exceptions it does not anticipate. Section 12.7 provides some direction for the proper use the

12.6. CATCHING EXCEPTION OBJECTS 436

catch-all exception handler.

12.6 Catching Exception Objects

The except blocks “catch” exception objects. We can inspect the object that an except block catches if
we specify the object’s name with the as keyword. Listing 12.11 (exceptobject.py) shows how to use the
as keyword to get access to the exception object raised by code in the try block.

Listing 12.11: exceptobject.py

import random

for i in range(10): # Loop 10 times
print(‘Beginning of loop iteration’, i)
try:

r = random.randint(1, 4) # r is pseudorandomly 1, 2, 3, or 4
if r == 1:

print(int(‘Fred’)) # Try to convert a non-integer
elif r == 2:

[][2] = 5 # Try to assign to a nonexistent index of the empty list
elif r == 3:

print({}[1]) # Try to use a nonexistent key to get an item from a dictionary
else:

print(3/0) # Try to divide by zero
except ValueError as e:

print(‘Problem with value ==>’, type(e), e)
except IndexError as e:

print(‘Problem with list ==>’, type(e), e)
except ZeroDivisionError as e:

print(‘Problem with division ==>’, type(e), e)
except Exception as e:

print(‘Problem with something ==>’, type(e), e)

print(‘End of loop iteration’, i)

The following sample program run reveals what the exception objects print when sent to the print function:

Beginning of loop iteration 0
Problem with division ==> division by zero
End of loop iteration 0
Beginning of loop iteration 1
Problem with list ==> list assignment index out of range
End of loop iteration 1
Beginning of loop iteration 2
Problem with division ==> division by zero
End of loop iteration 2
Beginning of loop iteration 3
Problem with division ==> division by zero
End of loop iteration 3
Beginning of loop iteration 4
Problem with division ==> division by zero
End of loop iteration 4
Beginning of loop iteration 5

12.7. EXCEPTION HANDLING SCOPE 437

Problem with list ==> list assignment index out of range
End of loop iteration 5
Beginning of loop iteration 6
Problem with division ==> division by zero
End of loop iteration 6
Beginning of loop iteration 7
Problem with value ==> invalid literal for int() with base 10: ‘Fred’
End of loop iteration 7
Beginning of loop iteration 8
Problem with value ==> invalid literal for int() with base 10: ‘Fred’
End of loop iteration 8
Beginning of loop iteration 9
Problem with division ==> division by zero
End of loop iteration 9

Observe how each exception object (e) prints a message that is meaningful for its particular exception.

12.7 Exception Handling Scope

Python’s exception handling infrastructure is special because it can transcend the usual scoping rules for
functions and objects. The exception handling examples we have seen so far have been simple programs
where all the code is in the main executing module. The origin of the exception is close to the code we can
see. These examples have not demonstrated the true power of Python’s exceptions. To get a better idea of
the scope of exceptions, consider Listing 12.12 (makeintegerlist.py).

Listing 12.12: makeintegerlist.py

def get_int_in_range(low, high):
“”” Obtains an integer value from the user. Acceptable values

must fall within the specified range low…high. “””
val = int(input()) # Can raise a ValueError
while val < low or val > high:

print(‘Value out of range, please try again:’, end=’ ‘)
val = int(input()) # Can raise a ValueError

return val

def create_list(n, min, max):
“”” Allows the user to create a list of n elements consisting

of integers in the range min…max “””
result = []
while n > 0: # Count down to zero

print(‘Enter integer in the range {}…{}:’.format(min, max), end=’ ‘)
result.append(get_int_in_range(min, max))
n -= 1

return result

def main():
“”” Create a list of two elements supplied by the user,

each element in the range 10…20 “””
lst = create_list(2, 10, 20)

12.7. EXCEPTION HANDLING SCOPE 438

Figure 12.2 Function call sequence diagram for Listing 12.12 (makeintegerlist.py) running with the user
providing the input 12 and 14.

main create_list print

P
ro

g
ra

m
E

xe
cu

ti
o

n
(T

im
e

)

str.format get_int_in_range

“Enter integer…”

[12, 14]

Program
block input int list.append

[12, 14]

3, 10, 20

“Enter integer…{}…{}:”, 10, 20

“Enter integer…10…20:”

10, 20

“12”

“12”
12

[], 12

“Enter integer…”

“Enter integer…{}…{}:”, 10, 20

“Enter integer…10…20:”

10, 20

“14”

“14”
14

[12], 14

print(lst)

if __name__ == ‘__main__’:
main() # Invoke main

Listing 12.12 (makeintegerlist.py) provides two handy functions, get_int_in_range and create_list.
The get_int_in_range function expects the user to enter an integer value that falls within the range of
values specified by its parameters. It ensures the integer the user provides is in the correct range, but if the
user enters a non-integer value, the function will raise an exception. The following shows the program’s
interaction with a well-behaved user:

Enter integer in the range 10…20: 12
Enter integer in the range 10…20: 14
[12, 14]

Figure 12.2 diagrams the function call sequences of this sample program execution.

The following shows how the program runs with a more creative user:

Enter integer in the range 10…20: 9+7
Traceback (most recent call last):

File “makeintegerlist.py”, line 27, in
main() # Invoke main

File “makeintegerlist.py”, line 23, in main

12.7. EXCEPTION HANDLING SCOPE 439

lst = create_list(3, 10, 20)
File “makeintegerlist.py”, line 16, in create_list

result.append(get_int_in_range(min, max))
File “makeintegerlist.py”, line 4, in get_int_in_range

val = int(input()) # Can raise a ValueError
ValueError: invalid literal for int() with base 10: ‘9+7’

If the get_int_in_range function used the eval function instead of int, it would avoid this exception, but
that would allow the function to accept floating-point values. Also, using the eval function would not help
for the following input:

Enter integer in the range 10…20: eleven
Traceback (most recent call last):

File “makeintegerlist.py”, line 27, in
main() # Invoke main

File “makeintegerlist.py”, line 23, in main
lst = create_list(3, 10, 20)

File “makeintegerlist.py”, line 16, in create_list
result.append(get_int_in_range(min, max))

File “makeintegerlist.py”, line 4, in get_int_in_range
val = int(input()) # Can raise a ValueError

ValueError: invalid literal for int() with base 10: ‘eleven’

An uncaught exception produces a stack trace. Python uses an area of the computer’s memory known as the
stack to help it control function and method invocations. The stack stores parameters, return values, and the
point in the code where the program’s execution should return when a function completes. An exception
stack trace provides a snapshot of the stack that enables developers to reconstruct the chain of function
and/or method calls that produced the exception.

We can read the stack trace from the top down. We see that the program (referenced in the stack trace
as ) called the main function at line 27 in the source file makeintegerlist.py. In turn, a statement
at line 23 in the main function invoked the create_list function. Code within the create_list function
at line 16 called the get_int_in_range function. Finally, line 4 in the get_int_in_range function raised
a ValueError exception when it called the int function with an invalid string literal (the value ‘eleven’
that the user provided).

We say that a exception “unwinds” the stack, because, if uncaught, an exception will propagate back up
the call chain. The propagation stops when an exception handler catches the exception. If the propagation
progresses all the way back to the program block level and along the way encounters no exception handler
with an except block of its type, the interpreter will terminate the program’s execution.

Figure 12.3 provides the function call sequence diagram for case of Listing 12.12 (makeintegerlist.py)
raising an exception and thereby terminating the program’s execution. In Listing 12.12 (makeintegerlist.py),
get_int_in_range’s call to int function can raise a ValueError exception. To get to this point, the chain
of function calls is

Program block→ main→ create_list→ get_int_in_range→ int

The red arrow in Figure 12.3 shows that the exception rises immediately up the call chain in the reverse
order:

int→ get_int_in_range→ create_list→ main→ Program block

12.7. EXCEPTION HANDLING SCOPE 440

Figure 12.3 Function call sequence diagram for Listing 12.12 (makeintegerlist.py) raising a ValueError
exception when the user enters eleven. The exception interrupts the normal function return control flow an
immediately terminates the program’s execution.

main create_list print

P
ro

g
ra

m
E

xe
cu

ti
o

(T
im

e
)

str.format get_int_in_range

“Enter integer…”

Program
block input int list.append

3, 10, 20

“Enter integer…{}…{}:”, 10, 20

“Enter integer…10…20:”

10, 20

“eleven”

ValueError

Any function in the call chain can catch the exception. In Listing 12.12 (makeintegerlist.py) we know
that int can raise the exception, but which function should catch the exception? Should we handle the
exception close to where it arises or farther up the call chain?

Listing 12.13 (makeintegerlist2.py) adds an exception handler to the create_list function.

Listing 12.13: makeintegerlist2.py

def get_int_in_range(low, high):
“”” Obtains an integer value from the user. Acceptable values

must fall within the specified range low…high. “””
val = int(input()) # Can raise a ValueError
while val < low or val > high:

print(‘Value out of range, please try again:’, end=’ ‘)
val = int(input()) # Can raise a ValueError

return val

def create_list(n, min, max):
“”” Allows the user to create a list of n elements consisting

of integers in the range min…max “””
result = []
try:

while n > 0: # Count down to zero
print(‘Enter integer in the range {}…{}:’.format(min, max), end=’ ‘)
result.append(get_int_in_range(min, max))
n -= 1

except ValueError:
print(‘Disallowed user entry interrupted list creation’)

return result

def main():
“”” Create a list of two elements supplied by the user,

each element in the range 10…20 “””
lst = create_list(2, 10, 20)

12.7. EXCEPTION HANDLING SCOPE 441

Figure 12.4 The execution sequence of a sample run of Listing 12.13 (makeintegerlist2.py) in which
the create list function handles the exception. Observe that the int function does not return to
get int in range as it normally would, but rather int bypasses get int in range on its way to the
nearest exception handler, which it locates in create list.

main create_list print

P
ro

g
ra

m
E

xe
cu

ti
o

n
(T

im
e

)

str.format get_int_in_range

“Enter integer…”

[12]

Program
block input int list.append

[12]

3, 10, 20

“Enter integer…{}…{}:”, 10, 20

“Enter integer…10…20:”

10, 20

“12”

“12”
12

[], 12

“Enter integer…”

“Enter integer…{}…{}:”, 10, 20

“Enter integer…10…20:”

10, 20

“eleven”

“Disallowed…”

print(lst)

if __name__ == ‘__main__’:
main() # Invoke main

The following shows a sample run of Listing 12.13 (makeintegerlist2.py):

Enter integer in the range 10…20: 12
Enter integer in the range 10…20: eleven
Disallowed user entry interrupted list creation
[12]

Figure 12.4 diagrams the behavior of this sample run. When get_int_in_range calls the int conversion
function with the argument ‘eleven’, the int function raises an exception. Since get_int_in_range has
no exception handlers, the ValueError exception propagates back up the call chain to the nearest handler.
The create_list function has a handler that can catch the exception, so it simply does not add any more
elements to the list and returns the list as is to main.

Handling an exception closer to the location that raises it generally gives us more options for corrective
action. Consider the following addition of an exception handler to the get_int_in_range function:

def get_int_in_range(low, high):
“”” Obtains an integer value from the user. Acceptable values

must fall within the specified range low…high. “””

12.7. EXCEPTION HANDLING SCOPE 442

need = True
while need:

try:
val = int(input()) # Can raise a ValueError
if val < low or val > high:

print(‘Value out of range, please try again:’, end=’ ‘)
else:

need = False # No need to continue in loop
except ValueError:

print(‘Value not a valid integer, please try again:’, end=’ ‘)
return val

This version of get_int_in_range forces the user to enter a viable integer value, as we see in the following
sample run:

Enter integer in the range 10…20: 12
Enter integer in the range 10…20: eleven
Value not a valid integer, please try again: eleven
Value not a valid integer, please try again: 11
[12, 11]

The handler is close to the source of the exception, and, therefore, can utilize local information to
address the exception. This new version of get_int_in_range effectively eliminates the need for the
exception handler in create_list.

We could exclude exception handlers from both create_list and get_int_in_range and instead let
the main function handle the exception:

def main():
“”” Create a list of three elements supplied by the user,

each element in the range 10…20 “””
try:

lst = create_list(3, 10, 20)
print(lst)

except Exception:
print(‘Error creating list’)

The main function’s reaction to the exception is more general than that of create_list and get_int_in_range,
since it is farther away from the exception origin. Since create_list contains significant logic, main is
powerless to attempt corrective action. Note that main cannot simply add a loop to allow the user to con-
tinue trying to add numbers each time the code within the try block raises an exception; doing so would
call create_list again, and, since each call to create_list begins with the empty list, calling it again
would lose any values the user entered before the exception appeared. The best main can do is report the
program’s inability to create the list.

Since the main function basically just wraps the call to create_list, we would not gain very much
generality moving up to the program block level:

if __name__ == ‘__main__’:
try:

main() # Invoke main
except Exception:

print(‘Cannot create a list’)

12.7. EXCEPTION HANDLING SCOPE 443

In general, exception handlers located closer to the code originating the exception have access to more
local information that is useful for implementing more focused corrective action. As the exception is
uncaught and propagates up the function-call chain, this local information is lost, and corrective action, if
any, must become less focused and more generic.

In Section 8.11 we considered a program that compared the behavior of a dice simulator to that of a pair
of actual, physical dice. Listing 8.31 (comparerolls.py) included a read_file function, reproduced here:

def read_file(filename, n, val):
“”” Reads n integers from the text file named filename.

Returns the number of times val appears in the file. “””
count, read = 0, 0
with open(filename, ‘r’) as f:

for value in f.readlines():
read += 1
# Have we read enough values in yet?
if read > n:

break
# Convert text integer into an actual integer
if int(value) == val:

count += 1
return count

Notice that we used read_file in Listing 8.31 (comparerolls.py) to read data from the results of a dice
rolling experiment, but read_file is not really dice-specific. The function simply reads n integers from
any compatible text file, counting how many times the value val appears in the file. Given the string name
of a text file, read_file is to open the text file and read its contents consisting of integer data.

What are some things that could go wrong with the read_file function? Consider the following
possibilities:

• a file by the given name does not exist, at least not in the location expected by the program

• a file by the given name exists, but the program (or more precisely, the user running the program) is
not authorized to read the file

• the device where the file resides is not ready for reading; for example, a DVD is not present in the
drive

• the program encountered bad sectors on the disk while reading the file

• the data in the file is not of the proper format; for example, the data consists of arbitrary strings rather
than text convertible to integers

• some other file error exists

As you can see, there are many ways the program can fail. The caller could misspell the file’s name, or the
file may reside in a different folder on the disk. A file of that name may exist in the right place but contain
non-integer text. It seems the program’s failure is a strong possibility.

Listing 12.14 (comparerollsrobust.py) takes advantage of our new knowledge to better manage the ex-
cepions that can Listing 8.31 (comparerolls.py) raise.

Listing 12.14: comparerollsrobust.py

12.7. EXCEPTION HANDLING SCOPE 444

from random import randint
from functools import partial

def read_file(filename, n, val):
“”” Reads n integers from the text file named filename.

Returns the number of times val appears in the file. “””
count, read = 0, 0
with open(filename, ‘r’) as f:

for value in f.readlines():
read += 1
# Have we read enough values in yet?
if read > n:

break
# Convert text integer into an actual integer
if int(value) == val:

count += 1
return count

def roll(n, val):
“”” Simulates the roll of a pair of dice n times.

Returns the number of times a roll resulted in val. “””
count = 0
for i in range(n):

roll = randint(1, 6) + randint(1, 6)
if roll == val:

count += 1
return count

def run_trials(f, n):
“”” Performs n experiments using function f as the source of

outcomes. Counts the number of occurrences of each possible
outcome. “””

for value in range(2, 13):
print(“{:>3}:{:>5}”.format(value, f(n, value)))

def main():
“”” Compare the actual experiments to the simulation “””
number_of_trials = 100
print(‘— Pseudorandom number rolls —‘)
run_trials(roll, number_of_trials)
print(‘— Actual experimental data —‘)
try:

run_trials(partial(read_file, ‘dicedata.data’), number_of_trials)
except FileNotFoundError:

print(‘Cannot open the file “dicedata.data”‘)
except PermissionError:

print(‘You do not have access to the file “dicedata.data”‘)
except OSError:

print(‘Cannot read the file “dicedata.data”‘)
except ValueError:

12.7. EXCEPTION HANDLING SCOPE 445

print(‘Data formatting error in “dicedata.data”‘)

if __name__ == ‘__main__’:
main()

In Listing 12.14 (comparerollsrobust.py) the try statement wraps the single statement that calls read_file,
since the rest of the code should execute safely. The operating system will raise a FileNotFoundError ex-
ception on an attempt to open a file that does not exist in the current folder. If the OS can find the file
but the user does not have permission to access the file, the OS will raise a PermissionError excep-
tion. The OSError covers all file related errors, such as attempting to process a corrupted file. In fact,
just as Exception is the type that matches all routine exception types, the OSError type covers both the
FileNotFoundError and PermissionError exceptions, as well as other file problems. We include the
more specific exceptions to provide more helpful messages to the user. Also note that because OSError
is more general than FileNotFoundError and PermissionError its except blcok must appear after the
except blocks of both FileNotFoundError and PermissionError. If OSError’s except block appears in
the source earlier, it will catch the file not found and permission error exceptions before the more specific
handlers get a chance. The OSError exception type is good to use if you need to defend against all file
processing errors but do not need the finer-grained control offered by the more specific file exception types.

The read_file function will raise a ValueError if it extracts a line of text from the file that it cannot
convert to an integer.

The following is a sample run of Listing 12.14 (comparerollsrobust.py) with a missing data file:

— Pseudorandom number rolls —
2: 5
3: 3
4: 9
5: 11
6: 13
7: 8
8: 16
9: 14

10: 8
11: 5
12: 4
— Actual experimental data —
Cannot open the file “dicedata.data”

The following shows a sample run in which the letter R replaces one of the integers in the data file:

— Pseudorandom number rolls —
2: 2
3: 5
4: 9
5: 8
6: 14
7: 13
8: 15
9: 13

10: 11
11: 11
12: 4

12.8. RAISING EXCEPTIONS 446

— Actual experimental data —
Data formatting error in “dicedata.data”

It is important to note the absence of a catch-all handler, introduced in Section 12.5. Any type of
exception other than those specified by the except blocks will terminate the program with an error message.
We could have added a catch-all exception handler that prints a message such as Some other error occurred,
but such a message is no more helper to the user than a cryptic stack trace. To the developers, however, the
stack trace printed by the uncaught exception is invaluable for precisely locating the source of the problem
so they can address it.

As mentioned in Section 12.5, you should limit your use of catch-all exception handlers. Catch-all
handlers have the potential to “swallow” exceptions; that is, code within a function will catch an exception
it did not expect and perhaps attempt some generic remedial action. The caught exception then will not
propagate up to its caller, and so the caller (and its callers further up the call chain) will be cut off from the
notification of the problem.

What is an appropriate use of a catch-all exception handler? A called function may need to do some
sort of local damage control if it encounters any kind of exception, expected or not. Perhaps the function
simply needs to log the unexpected error in its own error file. In this case the function can use the catch-all
exception handler. The last action in the catch-all exception handler should be re-raising the exception. This
allows one or more of its callers up the call chain to deal with the exception. In situations that warrant a
catch-all handler, prefer to catch the Exception type; use the untyped catch-all handler only as a last resort.

12.8 Raising Exceptions

We have seen how to write code that reacts to exceptions. We know that certain functions, like open and
int can raise exceptions. Also, statements that attempt to divide by zero or print an undefined variable will
raise exceptions. The following statement raises a ValueError exception:

x = int(‘x’)

The following statement is a more direct way to raise a ValueError exception:

raise ValueError()

The raise keyword raises an exception. Its argument, if present, must be an exception object. The class
constructor for most exception objects accepts a string parameter that provides additional information to
handlers:

raise ValueError(’45’)

In the interactive shell:

>>> raise ValueError()
Traceback (most recent call last):

File ““, line 1, in
ValueError
>>> raise ValueError(’45’)
Traceback (most recent call last):

File ““, line 1, in
ValueError: 45
>>> raise ValueError(‘This is a value error’)
Traceback (most recent call last):

12.8. RAISING EXCEPTIONS 447

File ““, line 1, in
ValueError: This is a value error

This means we can write a custom version of the int function that behaves similar to the built-in int
function, as Listing 12.15 (nonnegconvert.py) illustrates.

Listing 12.15: nonnegconvert.py

def non_neg_int(n):
result = int(n)
if result < 0: raise ValueError(result) return result while True: x = non_neg_int(input('Please enter a nonnegative integer:')) if x == 999: # Secret number exits loop break print('You entered', x) The following shows a sample run of Listing 12.15 (nonnegconvert.py): Please enter a nonnegative integer:3 You entered 3 Please enter a nonnegative integer:-3 Traceback (most recent call last): File "nonnegconvert.py", line 8, in
x = nonnegint(input(‘Please enter a nonnegative integer:’))

File “nonnegconvert.py”, line 4, in nonnegint
raise ValueError(result)

ValueError: -3

The built-in int function accepts well-formed negative integers with no problem, but our non_neg_int
function is more selective. It does not accept valid negative integers; hence, it raises a value error. List-
ing 12.16 (nonnegexcept.py) catches the exception so the program does not crash.

Listing 12.16: nonnegexcept.py

def non_neg_int(n):
“”” Converts argument n into a nonnegative integer, if possible.

Raises a ValueError if the argument is not convertible
to a nonnegative integer. “””

result = int(n)
if result < 0: raise ValueError(result) return result while True: try: x = non_neg_int(input('Please enter a nonnegative integer:')) if x == 999: # Secret number exits loop break ©2017 Richard L. Halterman Draft date: January 18, 2018 12.8. RAISING EXCEPTIONS 448 print('You entered', x) except ValueError: print('The value you entered is not acceptable') The following shows a sample run of Listing 12.16 (nonnegexcept.py): Please enter a nonnegative integer:3 You entered 3 Please enter a nonnegative integer:-3 The value you entered is not acceptable Please enter a nonnegative integer:5 You entered 5 Please enter a nonnegative integer:999 If one of Python’s built-in exception types is not appropriate to describe the exception you need to raise, you can use the generic Exception class and provide a descriptive message to its constructor, as in raise Exception('Cannot add non-integer to restricted list') If raised and uncaught, the interpreter will print the following line at the end of the stack trace: Exception: Cannot add non-integer to restricted list In Section 14.2 we will see a better way to customize exceptions by designing our own custom exception classes that integrate seamlessly with Python’s exception handling infrastructure. Sometimes it is appropriate for a function (or method) to catch an exception, take some action appro- priate to its local context, and then re-raise the same exception so that the function’s caller can take further action if necessary. In essence, the function that catches the exception first administers “first aid” and then passes the exception up the call chain for more advanced, application-specific treatment and care. In List- ing 12.17 (reraise.py), the count_elements function accepts a list, lst, presumed to contain only integers, and a Boolean function predicate. The predicate function parameter accepts a single argument and returns true or false based on whether or not its argument parameter has a certain property. The program defines two such predicate functions: is_prime and non_neg. The is_prime function determines if its integer argument is prime, and the non_neg function determines if its argument is a nonnegative integer. Both is_prime and non_neg can raise a TypeError exception if the caller passes a non-integer argument. Neither the is_prime nor the non_neg function attempts to handle the TypeError exception itself. List- ing 12.17 (reraise.py) exercises count_elements with the is_prime and non_neg functions. Listing 12.17: reraise.py def is_prime(n): """ Returns True if nonnegative integer n is prime; otherwise, returns false. Raises a TypeError exception if n is not an integer. """ from math import sqrt if n == 2: # 2 is the only even prime number return True if n < 2 or n % 2 == 0: # Handle simple cases immediately return False # Raises a TypeError if n is not an integer trial_factor = 3 root = sqrt(n) + 1 while trial_factor <= root: ©2017 Richard L. Halterman Draft date: January 18, 2018 12.8. RAISING EXCEPTIONS 449 if n % trial_factor == 0: # Is trial factor a factor? return False # Yes, return right away trial_factor += 2 # Next potential factor, skip evens return True # Tried them all, must be prime def non_neg(n): """ Determines if n is nonnegative. Raises a TypeError if n is not an integer. """ return n > 0

def count_elements(lst, predicate):
“”” Counts the number of integers in list lst that are

acceptable to a given predicate (Boolean function).
Prints an error message and raises a type error if
the list contains an element incompatible with
the predicate. “””

count = 0
for x in lst:

try:
if predicate(x):

count += 1
except TypeError:

print(x, ‘is a not an acceptable element’)
raise # Re-raise the caught exception

return count

def main():
print(count_elements([3, -71, 22, -19, 2, 9], non_neg))
print(count_elements([2, 3, 4, 5, 6, 8, 9], is_prime))
print(count_elements([2, 4, ‘6’, 8, ‘x’, 7], is_prime))

if __name__ == ‘__main__’:
main()

The count_elements function uses a try statement to defend against the possible exceptions raised by
is_prime and non_neg. If it catches a TypeError exception, it prints a diagnostic message alerting the
user that it found an element in the list that is not compatible with the predicate’s expected parameter type.

Listing 12.17 (reraise.py) prints the following:

4
3
6 is a not an acceptable element
Traceback (most recent call last):

File “reraise.py”, line 48, in
main()

File “reraise.py”, line 44, in main
print(count_elements([2, 4, ‘6’, 8, ‘x’, 7], is_prime))

File “reraise.py”, line 33, in count_elements
if predicate(x):

12.8. RAISING EXCEPTIONS 450

File “reraise.py”, line 9, in is_prime
if n < 2 or n % 2 == 0: # Handle simple cases immediately TypeError: unorderable types: str() < int() As we can see, the program prints the error message from the except block in count_elements, and then terminates due to handler’s re-raising of the exception it caught. The printed stack trace preserves all the information about where the exception originated. After catching the TypeError exception and reporting the problem, the count_elements function re- raises the same exception for the benefit of its caller via the statement raise # Re-raises the same exception it caught Notice that this is different from the statement raise TypeError() # Raise a NEW TypeError exception This latter statement creates a new exception object with its own stack trace that is different from the caught exception object. Raising the new exception results in a more complicated stack trace, as the following shows: 4 3 6 is a not an acceptable element Traceback (most recent call last): File "reraise.py", line 33, in count_elements if predicate(x): File "reraise.py", line 9, in is_prime if n < 2 or n % 2 == 0: # Handle simple cases immediately TypeError: unorderable types: str() < int() During handling of the above exception, another exception occurred: Traceback (most recent call last): File "reraise.py", line 48, in

main()
File “reraise.py”, line 44, in main

print(count_elements([2, 4, ‘6’, 8, ‘x’, 7], is_prime))
File “reraise.py”, line 37, in count_elements

raise TypeError() #e # Re-raise the exception
TypeError

You also use the unadorned raise statement to re-raise an exception caught by an untyped except
handler. This is because the raise keyword appearing by itself within an except block will re-raise the
same exception object that the block caught.

If we wrap the calling code of Listing 12.17 (reraise.py) with a try, as in

# Wrap the calling code in a try/except statement
def main():

try:
print(count_elements([3, -71, 22, -19, 2, 9], non_neg))
print(count_elements([2, 3, 4, 5, 6, 8, 9], is_prime))
print(count_elements([2, 4, ‘6’, 8, ‘x’, 7], is_prime))

except TypeError:
print(‘Error in count_elements’)

12.9. THE TRY STATEMENT’S OPTIONAL ELSE BLOCK 451

the calling code’s except block produces simpler output:

4
3
6 is a not an acceptable element
Error in count_elements

What is the reason for re-raising an exception? After all, the count_elements function could just print
the message and continue. If it does so, however, the count that it eventually returns would be meaningless,
and its caller would not know that count_elements had a problem. Re-raising the exception enables
count_elements’s caller to be informed of the failure so the caller can react to the exception in its own
way.

In general, suppose some function A calls function B that calls function C. The call chain thus looks like

A→ B→ C

If C raises an exception, functions A and B both may need to know about it to take appropriate action.
Function B is closer to C in the call chain. B can catch the exception raised by C, remedy the situation as best
it can, and then ensure that its caller (A) receives the same exception. A then can take action appropriate to
its own context.

The idea is that B is the caller in the call chain closest the exception origin (C), and B has information
unique to its context that its caller (A) would not have. B should handle any exceptions it expects and can
handle in some way. If the exception is such that B can repair the situation, continue its execution, and in
the end correctly fulfill A’s expectations, then there is no reason for B to re-raise the exceptions it caught
from C. On the other hand, if C’s exception renders B unable to meet A’s expectations, B can do local damage
control but must also raise an exception that A can process. Often this means re-raising the same exception,
but it can mean raising a different exception that is more B-specific.

What if C raises an exception type that B does not expect? This means B has no except block to handle
that type of exception. In this case, the exception propagates naturally back up to A, and it then becomes A
responsibility to deal with it.

This technique represents a good rule of thumb for managing exceptions. A function (or method) should
catch any exceptions it expects, ignore exceptions it does not expect (or cannot handle in some way), and
avoid a catch-all exception handler. Figure 12.5 illustrates this basic exception handling strategy.

12.9 The try Statement’s Optional else Block

The Python try statement supports an optional else block. Its behavior is remimiscent of the while
statement’s else block (see Section 5.6). If the code within the try block does not produce an exception,
no except blocks trigger, and the program’s execution continues with code in the else block. Figure 12.6
contrasts the possible program execution flows within a try/else statement. The else block, if present,
must appear after all of the except blocks.

Since the code in the else block executes only if the code in the try block does not raise an exception,
why not just append the code in the else block to the end of the code within the try block and eliminate
the else block altogether? The code restructured in this way may not behave identically to the original
code. Consider Listing 12.18 (trynoelse.py) which demonstrates the different behavior.

Listing 12.18: trynoelse.py

12.9. THE TRY STATEMENT’S OPTIONAL ELSE BLOCK 452

Figure 12.5 A flowchart of the execution of a function named f as it encounters exceptions. Function f
handles exceptions it expects, potentially repairing what it can and sending an exception to its caller if it
cannot. Function f ignores exceptions it does not expect or cannot handle.

Function f receives exception e Function f completes its task and
returns normally to its caller

Function f expects exception e

Function f can recover and continue
with correct behavior from its caller’s

perspective

Function f exits prematurely, naturally
propagating exception e back to

function f’s caller

Function f takes corrective action and
continues

Function f takes corrective action as
possible and then exits prematurely by

re-raising exception e or raising a
different exception object

Yes

Figure 12.6 The possible program execution flows through a try/else statement.

try-block

try:

except :

else:

except-block

Execute all the

statements with no

exceptions raised

Skip the except

block

Uncaught

exception

propagates to

outer context

No exceptions Caught exception Uncaught exception

exception-type

else-block

try-block

try:

except :

else:

except-block
Execute the

except block

exception-type

else-block

Code raises a

catchable

exception

Execute the

else block

Skip the

else block

try-block

try:

except :

else:

except-block

exception-type

else-block

Code raises an

uncatchable

exception

12.10. FINALLY BLOCK 453

def fun1():
try:

print(‘try code’)
except:

print(‘exception handling code’)
else:

print(‘no exception raised code’)
x = int(‘a’) # Raises an exception

def fun2():
try:

print(‘try code’)
print(‘no exception raised code’)
x = int(‘a’) # Raises an exception

except:
print(‘exception handling code’)

print(‘Calling fun2’)
fun2()
print(‘————-‘)
print(‘Calling fun1’)
fun1()

The fun1 function in Listing 12.18 (trynoelse.py) uses an else block, and fun2 moves the else code up
into the try block. The program’s output is

Calling fun2
try code
no exception raised code
exception handling code
————-
Calling fun1
try code
no exception raised code
Traceback (most recent call last):

File “trynoelse.py”, line 22, in
fun1()

File “trynoelse.py”, line 8, in fun1
x = int(‘a’) # Raises an exception

ValueError: invalid literal for int() with base 10: ‘a’

If the code in the original else block can raise an exception, moving it up into the try block means that
one of the try statement’s except blocks could catch that exception. Leaving the code in the else block
means that any exception it might raise cannot be caught by one of that try statement’s except blocks.

12.10 finally block

A try statement may include an optional finally block. Code within a finally block always executes
whether the try block raises an exception or not. A finally block usually contains “clean-up code” that

12.10. FINALLY BLOCK 454

Figure 12.7 The possible program execution flows through a try/except/finally statement.

try-block

try:

except :

finally:

except-block

Execute all the

statements with no

exceptions raised

Skip the except

block

Uncaught

exception

propagates to

outer context

No exceptions Caught exception Uncaught exception

exception-type

finally-block

try-block

try:

except :

finally:

except-block
Execute the

except block

exception-type

finally-block

Code raises a

catchable

exception

Execute the

finally block

try-block

try:

except :

finally:

except-block

exception-type

finally-block

Code raises an

uncatchable

exception

Execute the

finally block

Execute the

finally block

must execute due to activity initiated in the try block. Figure 12.7 contrasts the possible program execution
flows within a try/except/finally statement.

Consider Listing 12.19 (riskyread.py) which opens a file and reads its contents.

Listing 12.19: riskyread.py

# Sum the values in a text file containing integer values
sum = 0
f = open(‘mydata.dat’)
for line in f:

sum += int(line)
f.close() # Close the file
print(sum)

Listing 12.19 (riskyread.py) does not use a with/as statement as recommended in Section 9.3, and so it
will have a problem should an exception arise before the program executes the f.close() statement. The
file could be corrupted and one or more of the lines could contain text that is not convertible to a number.
Either of these problems would raise an exception before the f.close method executes.

Listing 12.20 (tryfileread.py) rectifies the problems with Listing 12.19 (riskyread.py) by adding excep-
tion handling with nested try statements.

Listing 12.20: tryfileread.py

# Sum the values in a text file containing integer values
try:

f = open(‘mydata.dat’)

12.10. FINALLY BLOCK 455

except OSError:
print(‘Could not open file’)

else: # File opened properly
sum = 0
try:

for line in f:
sum += int(line)

f.close() # Close the file if no exception
except Exception as er:

print(er) # Show the problem
f.close() # Close the file if exception

print(‘sum =’, sum)

Listing 12.20 (tryfileread.py) uses two try statements. The first try statement defends against an OSError
exception. The operating system will prompt the open function to raise such an exception if it cannot satisfy
the request; for example, the file may not exist in the current directory or the user may not have sufficient
permissions to access the file. The program does not proceed if it cannot open the file for reading.

The code in the outer try statement’s else block contains the interesting part. Once the file is open,
more exceptions are possible. In particular, the text file may contain a string that is does not evaluate to a
number. The inner try statement includes a catch-all except block to handle any exception that may arise.

If the file mydata.dat contains the following:

5.5
2.0
6.1

Listing 12.20 (tryfileread.py) will print

sum = 13.6

If the file instead contains the following:

5.5
2.0
five
6.1

Listing 12.20 (tryfileread.py) will print

name ‘five’ is not defined
sum = 7.5

Finally, if no file named mydata.dat exists in the current directory, Listing 12.20 (tryfileread.py) will print

Could not open file

Observe that Listing 12.20 (tryfileread.py) contains two identical statements to close the file:

• If the execution makes it all the way to the end of the inner try block, it needs to close the file.

• If an exception arises in the inner try block, the exception handler must close the file.

12.10. FINALLY BLOCK 456

This code duplication is undesirable, so we can use a finally block to consolidate the code, as shown in
Listing 12.21 (filereadfinally.py).

Listing 12.21: filereadfinally.py

# Sum the values in a text file containing integers
try:

f = open(‘mydata.dat’)
except OSError:

print(‘Could not open file’)
else:

sum = 0
try:

for line in f:
sum += int(line)

except Exception as er:
print(er) # Show the problem

finally:
f.close() # Close the file

print(‘sum =’, sum)

Listing 12.21 (filereadfinally.py) behaves exactly like Listing 12.20 (tryfileread.py) contains.

Because of the design of the file class, the with/as statement takes care of the details of properly
closing a file should an exception arise. The with/as statement, however, will not automatically handle
any exceptions. We can remedy this with with another pair of nested try statements, as Listing 12.22
(betterfileread.py) shows.

Listing 12.22: betterfileread.py

# Sum the values in a text file containing integers
try:

with open(‘mydata.dat’) as f:
sum = 0
try:

for line in f:
sum += int(line)

except Exception as er:
print(er) # Show the problem

print(‘sum =’, sum)
except OSError:

print(‘Could not open file’)

Since Listing 12.22 (betterfileread.py) uses the with/as statement, the program does not explicitly call the
file object’s close method. The omission of the f.close() statement eliminates the need of the finally
block.

The try keyword cannot appear without at least one of except or finally. This means the except
blocks are optional. In fact, the following code fragment:

with open(‘data.dat’) as f: # f is a file object
for line in f: # Read each line as text

print(line.strip()) # Remove trailing newline character

is roughly equivalent to

12.11. USING EXCEPTIONS WISELY 457

Figure 12.8 The possible program execution flows through a try/finally statement.

try-block

try:

finally:

Execute all the

statements with no

exceptions raised

Uncaught

exception

propagates to

outer context

No exceptions Exception

finally-block

Execute the

finally block

try-block

Code raises an

exception

try:

finally:

finally-block

Execute the

finally block

f = None # No file object by default
try:

f = open(‘data.dat’) # f is a file object
else:

for line in f: # Read each line as text
print(line.strip()) # Remove trailing newline character

finally:
if f:

f.close() # Close the file, if open

Figure 12.8 compares the possible program execution flows within a try/finally statement.

The except and finally blocks may not appear without an associated try block. An else block must
be used in the context of a try statement (or if, while, or for statement).

As a final note about finally: the finally block, if present, must appear after all except blocks and
after the else block.

12.11 Using Exceptions Wisely

Exceptions should be reserved for uncommon errors. For example, the following code adds up all the
elements in a list of numbers named lst:

sum = 0
for elem in lst:

sum += elem
print(“Sum =”, sum)

This loop is fairly typical. Another, much poorer, approach uses an exception:

12.12. EXERCISES 458

sum = 0
int i = 0
try:

while True:
sum += lst[i]
i += 1

except IndexError:
pass

print(“Sum =”, sum)

Here, an IndexError exception interrupts the loop when the list access is out of bounds. The exception
interrupts the statement

sum += lst[i]

in midstream, before it fully evaluates the expression on the right side of the += operator. This prevents the
program’s execution from incorrectly incrementing sum’s value.

Both approaches compute the same result. However, the second approach always raises and handles
an exception. The exception definitely is not an uncommon occurrence. You should not use exceptions
to dictate normal logical flow. While very useful for its intended purpose, the exception mechanism adds
some overhead to program execution, especially when an exception is raised. This overhead is reasonable
when exceptions are rare but not when exceptions are part of the program’s normal execution.

Exceptions are valuable aids for careless or novice programmers. A careful programmer ensures that
code accessing a list does not exceed the list’s bounds. Another programmer’s code may accidentally
attempt to access a[len(a)]. A novice may believe a[len(a)] is a valid element. Since no programmer
is perfect, exceptions provide a nice safety net.

As you develop more sophisticated programs you will find exceptions more compelling. You should
analyze your code carefully to determine its limitations. Exceptions can be valuable for covering these
limitations. The Python standard library uses exceptions extensively, so programs that make use of library
functions and classes should properly handle the exceptions they can raise.

12.12 Exercises

1. What does LBYL stand for in Python programming? What does it mean?

2. What does EAFP stand for in Python programming? What does it mean?

3. What is the maximum number of try blocks in a try statement?

4. What is the minimum number of try blocks in a try statement?

5. What is the maximum number of except blocks in a try statement?

6. What is the minimum number of except blocks in a try statement?

7. What is the maximum number of else blocks in a try statement?

8. What is the minimum number of else blocks in a try statement?

9. What is the maximum number of finally blocks in a try statement?

12.12. EXERCISES 459

10. What is the minimum number of finally blocks in a try statement?

11. Wrap the following code in a try statement to defend against any exceptions it can raise. Do not use
a catch-all handler.

lst = [0, 0, 0, 0]
with open(‘data.txt’, ‘r’) as f:

count = 0
for line in f.readlines():

lst[count] = int(line)
count += 1

12. For the next set of questions show what each program will print when the user supplies the indicated
input text.

Write *EXCEPTION* if and when the execution will generate an exception stack trace for an un-
caught exception.

(a) print(‘Begin’)
x = int(input())
print(x)
print(‘End’)

i. User enters 22
ii. User enters ZZ

(b) print(‘Begin’)
try:

x = int(input())
print(x)

except ValueError:
print(‘Wrong!’)

print(‘End’)

i. User enters 22
ii. User enters ZZ

x = int(input())
print(x)

except IndexError:
print(‘Wrong!’)

print(‘End’)

i. User enters 22
ii. User enters ZZ

(d) print(‘Begin’)
try:

x = int(input())
print(x)

except Exception:
print(‘Wrong!’)

print(‘End’)

12.12. EXERCISES 460

i. User enters 22
ii. User enters ZZ

(e) print(‘Begin’)
try:

x = int(input())
print(x)

except ValueError:
print(‘Wrong!’)

else:
print(‘Wow’)

print(‘End’)

i. User enters 22
ii. User enters ZZ

(f) print(‘Begin’)
try:

x = int(input())
print(x)

except ValueError:
print(‘Wrong!’)

finally:
print(‘Done’)

print(‘End’)

i. User enters 22
ii. User enters ZZ

(g) print(‘Begin’)
try:

x = int(input())
print(x)

except ValueError:
print(‘Wrong!’)

else:
print(‘Wow’)

finally:
print(‘Done’)

print(‘End’)

i. User enters 22
ii. User enters ZZ

13. What is the problem with the following code?

try:
f() # Function f can raise an exception

except Exception:
print(1)

except ValueError:
print(2)

12.12. EXERCISES 461

14. What is the problem with the following code?

try:
f() # Function f can raise an exception

except OSError:
print(1)

except FileNotFoundError:
print(2)

12.12. EXERCISES 462

463

Chapter 13

Custom Types

We have examined many of Python’s built-in types. Some, like, integers, floating-point numbers, and
Booleans are relatively simple, while others such as lists, tuples, dictionaries, sets, and exceptions are more
complex. Python’s rich collection of built-in types enable us to write a wide variety of programs in diverse
problem domains. Python also provides the ability for programmers to design their own custom types by
which developers can craft data types that more closely model the problem at hand. This better alignment
of software assets with the problem domain can expedite the development process.

13.1 Circle Objects

A software object generally bundles together data (instance variables) and functionality (methods). The
instance variables and methods of an object comprise its members. The class of an object defines the
object’s basic structure and capabilities. As a simple concrete example, consider the familiar geometric
circle, shown in Figure 13.1. Given a circle’s radius (r in Figure 13.1), we can compute the circle’s area and
circumference. The circle’s center, (x,y), establishes the circle’s position. We will define a custom Circle
class in Python from which we can create Circle instances (objects). The Circle class specifies what circle
objects can do and how clients (that is, code outside of the Circle class needing the services that a Circle
object can provide) can interact with them. A center and radius may be good enough for mathematicians,
but in a graphical computer program circle objects may need other attributes like a fill color, fill style, edge
thickness, etc. We will keep things simple for now and stick to the abstract mathematical concept of a circle.

What data must each Circle object maintain? Since circles can appear in various places, each circle
must keep track of its own position. Just like in mathematics, we can specify the location of a Circle object
by its (x,y) center. Also, since some circles are larger or smaller than others, each Circle should have its
own radius. It is natural, then, for our Circle object to have a center instance variable and a radius
instance variable.

Should our circle objects have an area instance variable and/or a circumference instance variable?
Both area and circumference depend solely on a circle’s radius, so if we include a radius instance variable,
both area and circumference would be redundant information. Besides, we easily can compute them as
needed with simple formulas. We will implement area and circumference as methods in our Circle
class.

As we finalize the design for our Circle class, we will add a few interesting points:

13.1. CIRCLE OBJECTS 464

Figure 13.1 A circle with radius r centered at (x,y). A represents the circle’s area, and C is its circumference

(x, y)

A = πr
2

C = 2πr

• Clients should be able to create a Circle object with a specified center point (a tuple of two numbers)
and radius.

• An attempt to create a circle with a negative radius should produce a ValueError exception.

• Clients can determine a Circle object’s radius via a get_radius method.

• Clients can determine a Circle object’s center via a get_center method.

• Clients can reposition the circle via a move method.

• Clients can increase the circle’s radius by one unit via a grow method.

• Clients can decrease the circle’s radius by one unit via a shrink method. At no time should the
circle’s radius fall below zero.

Our intention is to discourage clients from changing the instance variables (center and radius) of Circle
objects directly; thus, we offer the move, grow, and shrink methods.

Based on our criteria, we will need the following methods in our Circle class:

• __init__: The special name of all constructors in Python classes is __init__. Our __init__
method must create and initialize the center and radius instance variables, and it must detect an
attempt to make a Circle object with a negative radius. The client code must supply a center (a tuple
consisting of two numbers) and a radius.

• get_radius: This method simply returns the value of the radius instance variable. This method
accepts no parameters.

• get_center: This method simply returns the value of the center instance variable. This method
accepts no parameters.

• get_area: This method computes and returns the circle object’s area. This method accepts no pa-
rameters.

• get_circumference: This method computes and returns the circumference. This method accepts no
parameters.

13.1. CIRCLE OBJECTS 465

• move: This method repositions the Circle object’s center. The client must provide a tuple consisting
of two numbers. This tuple represents the new coordinates of the object’s center.

• grow: This method increases the Circle object’s radius by one unit. This method accepts no param-
eters.

• shrink: If the Circle object’s radius is greater than zero, this method decreases its radius by one
unit. This method does not change the radius if the radius is zero before the call. This method accepts
no parameters.

Armed with this more detailed specification, we are ready to define our Circle class. Listing 13.1 (circle.py)
contains the complete definition for Circle.

Listing 13.1: circle.py

class Circle:
“”” Represents a geometric circle object “””
def __init__(self, center, radius):

“”” Initalize the center’s center and radius “””
# Disallow a negative radius
if radius < 0: raise ValueError('Negative radius') self.center = center self.radius = radius def get_radius(self): """ Return the radius of the circle """ return self.radius def get_center(self): """ Return the coordinatess of the center """ return self.center def get_area(self): """ Compute and return the area of the circle """ from math import pi return pi*self.radius*self.radius def get_circumference(self): """ Compute and return the circumference of the circle """ from math import pi return 2*pi*self.radius def move(self, pt): """ Moves the enter of the circle to point pt """ self.center = pt def grow(self): """ Increases the radius of the circle """ self.radius += 1 def shrink(self): """ Decreases the radius of the circle; does not affect a circle with radius zero """ if self.radius > 0:

13.1. CIRCLE OBJECTS 466

Figure 13.2 General form of a class definition

block

class :name

self.radius -= 1

We see in Listing 13.1 (circle.py) that a class definition begins with the reserved word class followed by
the name of the class and a colon (:) at the end of the line. Figure 13.2 shows the general form of a class
definition. As in function definitions, the body of the class is indented within a block of code. The code in
this block looks like a series of function definitions; however, since the definitions appear within the block
of a class definition they are method definitions. As with functions, we can (and should) document classes
and methods with docstrings.

Notice that each method definition has self for its first parameter. The language does not require the
first parameter’s name to be self (it could be x, obj, or any valid identifier), but the universal convention in
the Python programming world is to use the name self. During a method’s execution, the self parameter
references the object on whose behalf the method is being invoked. In Turtle graphics, for example, the
Turtle class definition contains a forward method definition that begins

def forward(self, distance):
# Details omitted . . .

If t is a reference to a Turtle object, we can move the turtle forward 100 pixels with the call

t.forward(100)

This method invocation assigns the actual parameter t to the formal parameter self and the actual param-
eter 100 to the formal parameter distance. In fact, we can rewrite the call as

Turtle.forward(t, 100)

The call expressed this way clearly shows that t corresponds to self and 100 corresponds to distance.

In the case of our Circle class, if circ refers to a Circle object, the call

circ.grow()

is equivalent to

Circle.grow(circ)

In the Circle class definition, the __init__ method initializes a Circle object. A client might write
the statement

circ = Circle((10, 3.4), 5)

13.1. CIRCLE OBJECTS 467

Figure 13.3 A conceptual illustration of a circle object. Each instance of the Circle class has its own
center and radius instance variables.

circ

circ = Circle((2.5, 6), 5)

(2.5, 6)

center

radius

This statement creates a new Circle object with a center at (10,3.4) and radius 5. It implicitly invokes the
__init__ method to do the initialization work. The statement then assigns the variable circ to this newly
created Circle object. The constructor first ensures that the radius parameter is nonnegative. An attempt
to make a circle with a negative radius produces an exception. Next, the constructor initializes the center
and radius instance variables of the objects it is in the process of creating. Within method definitions (like
__init__), we prefix instance variable names with self. Any variables not prefixed with self are treated
as normal local or global variables. In the following two statements in the constructor:

self.center = center
self.radius = radius

The expression self.center refers to the center instance variable of the object under construction, and
center on the right side of the assignment operator refers to the formal parameter. Similarly, self.radius
refers to the radius instance variable of the object, and radius on the right side is the parameter.

The methods get_center and get_radius are sometimes called accessor methods, or getters, as they
give clients access to see the state of an object. In this case, clients can obtain a Circle object’s center and
radius via these methods. In contrast, the methods move, grow, and shrink are known as mutator methods,
or setters, because they allow clients to modify the state of an object. Note that grow and shrink do not
allow arbitrary changes; they allow clients to adjust a circle’s radius only by one-unit increments.

The methods get_area and get_circumference are neither accessors not mutators. They do not
provide direct access to the data in a Circle object but rather provide indirect access via a computation
(you could reverse engineer the result of either method to deduce the radius, but the get_radius method
provides direct access).

Figure 13.3 provides a conceptual view of a Circle object. Note that each Circle object needs only
store a reference to its instance variables. All Circle instances share the code for their methods. In the
following code:

c1 = Circle((2, 4), 5)
c2 = Circle((0, 0), 1)

The objects refered by c1 and c2 have their own center and radius instance variables. The call

print(c1.get_radius())

13.1. CIRCLE OBJECTS 468

passes a reference to c1’s object as the first (self) parameter to the method get_radius, while

print(c2.get_radius())

passes a reference to c2’s object as the first (self) parameter to the get_radius method. As you can see,
there is no need for each object to have its own copy of the method code; however, every distinct object
must maintain its own instance variables.

Listing 13.2 (circlemaker.py) exercises our new Circle class. It uses Turtle graphics (Section 9.5) to
render Circle objects in a graphical window.

Listing 13.2: circlemaker.py

from turtle import Turtle, Screen, mainloop, delay, clear
from circle import Circle

t = Turtle() # Global turtle
circ = Circle((0, 0), 100) # Global circle object

def draw_circle(t, circle):
x, y = circle.get_center() # Unpack center’s coordinates
radius = circle.get_radius()
t.penup() # Lift pen
t.setposition(x, y) # Move pen to (x,y)
t.pendown() # Place pen
t.dot() # Draw a dot at the circle’s center
t.penup() # Lift pen
t.setposition(x, y – radius) # Position pen to draw rim of circle
t.pendown() # Place pen to draw
t.circle(radius) # Draw the circle
t.penup() # Lift pen

def do_click(x, y):
circ.move((x, y)) # Move the circle to a new location
redraw()

def do_up():
circ.grow() # Make the circle bigger
redraw()

def do_down():
circ.shrink() # Make the circle smaller
redraw()

def redraw():
t.clear() # Clear the drawing screen
draw_circle(t, circ) # Draw the circle object

def main():
delay(0) # Do not slowly trace drawing
t.speed(0) # Make turtle’s actions as fast as possible

13.1. CIRCLE OBJECTS 469

t.hideturtle() # Make the turtle invisible
screen = Screen() # Create Screen object to receive user input
screen.listen() # Set focus for keystrokes
screen.onclick(do_click) # Set mouse press handler
screen.onkey(do_up, ‘Up’) # Set “up” cursor key handler
screen.onkey(do_down, ‘Down’) # Set “down” cursor key handler
mainloop()

if __name__ == ‘__main__’:
main()

Listing 13.2 (circlemaker.py) is an interactive program that allows the user to place the image of a Circle
object in the window via a mouse click. Subsequent mouse clicks move the circle to the mouse position.
Users can use the up ↑ and down ↓ cursor keys to enlarge and reduce the size of the circle.

The turtle module provides the Screen class. In Listing 13.2 (circlemaker.py), the screen variable
references a Screen object. Screen objects accept user input from the pointing device and keyboard. The
statement

screen = Screen()

creates the Screen object and assigns it to the variable screen. The statement

screen.listen()

enables the graphical window to receive keystrokes from the user. The statement

screen.onclick(do_click)

calls the onclick method of the Screen class. Like functions (see Section 8.5), methods can accept func-
tions and other methods as parameters. The onclick method accepts a function as a parameter. The turtle
module provides the Screen.onclick method, and we must provide the function we send to it. The only
restriction on the function we send to onclick is that the function must accept two integer parameters. In
this case we pass it our do_click function. The purpose of the onclick function is to register a callback
function with the Turtle graphics framework. The framework will “call back” the function when a certain
event occurs. If the user clicks the mouse when the pointer is over the graphics window, the framework will
call the function registered with onclick (in this case do_click) and pass to it the x and y coordinates of
the mouse pointer at the time of the click. That is why this callback function requires a function that expects
the two integer parameters. Note that our do_click function packs up into a tuple the x and y coordinates
it receives and passes this tuple on to the global Circle object circ’s move method. We must use a global
variable in the do_click function because we cannot pass in the circ object—remember, we do not call
do_click, the framework does, and the framework only passes in the mouse pointer coordinates.

Similarly, the statements

screen.onkey(do_up, ‘Up’)
screen.onkey(do_down, ‘Down’)

assign callback functions to invoke when the user presses the up ↑ and down ↓ cursor keys. The
callback functions accepted by the Screen.onkey method take no parameters. Consequently, neither do_up
nor do_down accept parameters. The second parameter to the onkey method specifies which key event to
associate with the given callback function. The Turtle graphics framework defines the strings ‘Up’ and
‘Down’, as well as many others, for use with the Screen object’s onkey method.

13.1. CIRCLE OBJECTS 470

Figure 13.4 Using the custom Circle class in a graphical application

Note that the do_click, do_up, and do_down functions modify the global Circle object circ’s state,
but the draw_circle method simply uses the Circle object’s get_center and get_radius methods to
be able to draw the circle using the Turtle object’s circle method. The Turtle.circle method draws
a circle starting from the turtle’s current position—three o’clock on the circle—and it draws a counter-
clockwise curve around the circle.

Figure 13.4 shows a sample run of Listing 13.2 (circlemaker.py).

Listing 13.2 (circlemaker.py) uses global variables to give multiple functions access to the same Turtle
and Circle object. Section 8.1 exposed some of the disadvantages of using global variables. Object-
oriented techniques allow us to confine globals to classes. Listing 13.3 (circlemakerobject.py) is a rewrite of
Listing 13.2 (circlemaker.py) that moves the previously global Turtle and Circle objects inside of a new
object of type GraphicalCircle.

Listing 13.3: circlemakerobject.py

from turtle import Turtle, Screen
from circle import Circle

class GraphicalCircle:
“”” Wraps a Circle object with a primitive graphical interface.

Each GraphicalCircle object maintains its own Circle
object and Turtle graphics Turtle object. “””

def __init__(self, center, radius):
“”” Initializes a graphical circle object. The circle is

centered at the position specified by the center
parameter. The circle’s radius is set to the radius
parameter. “””

# Make a turtle graphics object to do the drawing. Assign it
# to an instance variable so other methods can access it.
self.turtle = Turtle()
self.turtle.speed(0) # Make turtle’s actions as fast as possible
self.turtle.hideturtle() # Make the turtle invisible

13.1. CIRCLE OBJECTS 471

# Create a local Screen object to receive user input.
screen = Screen()
screen.delay(0) # Do not slowly trace drawing
screen.listen() # Set focus for keystrokes
# Mouse click repositions the circle
screen.onclick(self.move) # Set mouse press handler
# Up cursor key calls the increase method to expand the circle
screen.onkey(self.increase, ‘Up’) # Set “up” cursor key handler
# Down cursor key calls the decrease method to contract the circle
screen.onkey(self.decrease, ‘Down’) # Set “down” cursor key handler

# Make a circle object. Assign it to an instance variable so other methods
# can access it.
self.circle = Circle(center, radius)

# Start the graphics environment. The local screen object
# will exist until the user quits the program.
screen.mainloop()

def draw(self):
“”” Draws the circle in the graphical window. “””
x, y = self.circle.get_center() # Unpack center’s coordinates
radius = self.circle.get_radius()
self.turtle.penup() # Lift pen
self.turtle.setposition(x, y) # Move pen to (x,y)
self.turtle.pendown() # Place pen
self.turtle.dot() # Draw a dot at the circle’s center
self.turtle.penup() # Lift pen
self.turtle.setposition(x, y – radius) # Position pen to draw rim of circle
self.turtle.pendown() # Place pen to draw
self.turtle.circle(radius) # Draw the circle
self.turtle.penup() # Lift pen

def move(self, x, y):
“”” Moves the circle’s center to the specified (x, y) location .

Delegates the work to the contained Circle object. “””
self.circle.move((x, y)) # Move the circle to a new location
self.redraw()

def increase(self):
“”” Increases the circle’s radius by one, then redraws the circle.

Delegates the work to the contained Circle object. “””
self.circle.grow() # Make the circle bigger
self.redraw() # Redraw the circle object

def decrease(self):
“”” Reduces the circle’s radius by one, then redraws the circle.

Delegates the work to the contained Circle object. “””
self.circle.shrink() # Make the circle smaller
self.redraw()

def redraw(self):
“”” Clears the graphical window, then draws the circle. “””
self.turtle.clear() # Clear the drawing screen

13.1. CIRCLE OBJECTS 472

self.draw() # Redraw the circle object

def main():
“”” Allows the user to manipulate a graphical circle object. “””
circle = GraphicalCircle((0, 0), 100) # Make a graphical circle object
print(“Program done”)

if __name__ == ‘__main__’:
main()

Listing 13.3 (circlemakerobject.py) defines the GraphicalCircle class. Each GraphicalCircle object
contains two instance variables:

• the turtle instance variable is a turtle.Turtle object, and

• the Circle instance variable is a circle.Circle object.

Observe that one object (a GraphicalCircle instance) is composed of two other objects (a Turtle instance
and a Circle instance). This concept of objects containing other objects is known as object composition.

The instance variables of an object essentially behave like global variables within their containing ob-
ject. A method within the class has unfettered access to any instance variable within an object of that class
via the self parameter. This means that each of the methods in the GraphicalCircle class can access the
turtle and circle instance variables of a GraphicalCircle object.

As an aside, the turtle.TurtleScreen object named screen is not an instance variable; instead, it is
a local variable within the GraphicalCircle.__init__ method. Observe that none of the other methods
within the GraphicalCircle class need to access screen. We know that local variables disappear when the
function in which they are used returns. Does this mean that the screen object may be garbage collected
(see Section 9.9) before the user is finished running the program?

The last statement in the constructor:

screen.mainloop()

starts the Turtle graphics environment. This function call ensures the GraphicalCircle.__init__ func-
tion will not return to main until the user quits the program; thus, we do not need to worry about the local
screen variable disappearing while the program executes.

As with regular functions, the methods within Python classes can accept default arguments, an arbitrary
number of arguments (specified via *, as in Section 11.2), and keyword arguments (specified via **, as in
Section 11.7). The illustrate default arguments, we can rewrite the Circle constructor as

class Circle:
“”” Represents a geometric circle object “””
def __init__(self, center, radius=1):

“”” Initalize the center’s center and radius “””
# Disallow a negative radius
if radius < 0: raise ValueError('Negative radius') self.center = center self.radius = radius ©2017 Richard L. Halterman Draft date: January 18, 2018 13.2. RESTRICTING ACCESS TO MEMBERS 473 # Other details of the Circle class omitted . . . Under this new definition both of the following statements are valid: c1 = Circle((3, 17), 4) # Radius specified to be 4 units c2 = Circle((22, 8)) # Radius defaults to 1 unit Many of the classes in the tkinter package have methods that accept keyword arguments. 13.2 Restricting Access to Members The developers of the Circle class intend that clients should not directly manipulate a Circle object’s center and radius instance variables. The constructor (__init__), move, grow, and shrink are the only methods that can influence the state of a Circle object; however, nothing prevents client code from access- ing the instance variables directly via the dot (.) operator. The following interactive sequence illustrates: >>> from circle import *
>>> c = Circle((0, 0), 4)
>>> c.get_radius()
4
>>> c.radius = 10
>>> c.get_radius()
10

As we can see, clients can alter the radius of a circle outside the facilities provided by the grow and shrink
methods.

The convention in Python is to use a leading underscore to name instance variables not meant for general
access by clients:

class MyClass:
def __init__(self, num):

self.public_var = num
self._private_var = num

Here, clients are encouraged to access the public_var instance variable of MyClass objects directly:

mc = MyClass(10)
mc.public_var = 12 # Acceptable access

but code like the following is discouraged:

mc = MyClass(10)
mc._private_var = 12 # Modifying an instance variable not meant for public access

The statement that modifies the intended private instance variable is not illegal. It is understood that a
programmer doing so assumes all the risk of any problems that may arise from the action.

Python does support a naming scheme that makes it more difficult to access an instance variable or
method, in effect rendering it private to code inside the class. Python does not permit normal access with the
dot (.) to members of an object with names that begin with two underscores. (The Python community often
tersely refers to the double underscore prefix as dunder.) The following interactive sequence illustrates:

13.3. RATIONAL NUMBERS 474

>>> class MyType:
… def __init__(self):
… self.__id = 2
…
>>> m = MyType()
>>> m.__id
Traceback (most recent call last):

File ““, line 1, in
AttributeError: ‘MyType’ object has no attribute ‘__id’
>>> m._MyType__id
2

As you can see, internally Python changes the name of a class member with a name that begins with double
underscores by prefixing it with a single underscore followed by the class name. Python thus does not
provide a way to truly protect object members from the outside world. This sets Python apart from most
other mainstream object-oriented languages like C++, Java, and C# which provide language features that
can protect the internal details of an object.

13.3 Rational Numbers

The concept of mathematical rational numbers is accessible even to elementary school students, so it
presents an ideal platform for further exploration into custom class design in Python. We will define our
own simple rational number class. Note that if you are developing an application that requires the use of
rational numbers, you ought to use Python’s standard Fraction class that we saw in Section 9.4. We build
our own class here because our goal in this section is simply to gain more experience developing custom
classes in Python.

A rational number is the ratio of two integers. There is a restriction, however—the number on the
bottom of a fraction cannot be zero. The number on the top of the fraction is called the numerator, and
the bottom number is known as the denominator. Consider the following beginnings of a simple Rational
class:

class Rational:
def __init__(self, num, den):

self.numerator, self.denominator = num, den

There is nothing in this class definition that prevents a client from making a rational number like the fol-
lowing:

fract = Rational(1, 0)

In this case the variable fract represents an undefined integer. We can help matters with a different con-
structor:

class Rational:
def __init__(self, num, den):

self.numerator = num
if den != 0:

self.denominator = den
else:

raise ValueError(“Attempt to make an illegal rational number”)

13.3. RATIONAL NUMBERS 475

While this new constructor will prevent illegal initialization by raising a run-time exception, clients still can
subvert our Rational objects:

fract = RationalNum(1, 2) # This is OK
fract.denominator = 0 # This is bad!

At best, the programmer made an honest mistake introducing an error into the program. Perhaps it was a
careless “copy and paste” error. On the other hand, a clever programmer may be fully aware of how the
program works in the larger context and intentionally write such bad code to exploit a weakness in the
system that compromises its functionality or security.

We can use the Python’s dunder notation to better protect our denominator instance variable, as shown
in Listing 13.4 (rational.py). Note that this form of protection defends against a conscientious but careless
programmer but not a malicious one.

Listing 13.4: rational.py

class Rational:
“””
Represents a rational number (fraction)
“””
def __init__(self, num, den):

self.__numerator = num
if den != 0:

self.__denominator = den
else:

raise ValueError(“Attempt to make an illegal rational number”)

def get_numerator(self):
“”” Returns the numerator of the fraction. “””
return self.__numerator

def get_denominator(self):
“”” Returns the denominator of the fraction. “””
return self.__denominator

def set_numerator(self, n):
“”” Sets the numerator of the fraction to n. “””
self.__numerator = n

def set_denominator(self, d):
“””
Sets the denominator of the fraction to d,
unless d is zero. If d is zero, the method
terminates the program with an error meesage.
“””
if d != 0:

self.__denominator = d
else:

raise ValueError(“Error: zero denominator!”)

def __mul__(self, other):
“””
Returns the product of this rational number object with
the other rational object.

13.3. RATIONAL NUMBERS 476

“””
return Rational(self.__numerator * other.__numerator,

self.__denominator * other.__denominator)

def __add__(self, other):
“””
Returns the sum of this rational number object with
the other rational object.
“””
pass # Not yet implemented

def __str__(self):
“””
Make a string representation of a Rational object
“””
return str(self.get_numerator()) + “/” + str(self.get_denominator())

# Client code that uses Rational objects
def main():

fract1 = Rational(1, 2)
fract2 = Rational(2, 3)
print(“fract1 =”, fract1)
print(“fract2 =”, fract2)
fract1.set_numerator(3)
fract1.set_denominator(4)
fract2.set_numerator(1)
fract2.set_denominator(10)
print(“fract1 =”, fract1)
print(“fract2 =”, fract2)
fract3 = Rational(1, 2)
fract4 = Rational(3, 5)
print(fract3, “*”, fract4, “=”, fract3 * fract4)
frac5 = Rational(4, 0)

main()

When run, Listing 13.4 (rational.py) prints

fract1 = 1/2
fract2 = 2/3
fract1 = 3/4
fract2 = 1/10
1/2 * 3/5 = 3/10
Traceback (most recent call last):

File “rational.py”, line 74, in
main()

File “rational.py”, line 71, in main
frac5 = Rational(4, 0)

File “rational.py”, line 10, in __init__
raise ValueError(“Attempt to make an illegal rational number”)

ValueError: Attempt to make an illegal rational number

The anticipated exception from the next-to-last statement in the main function prevents the function from
completing successfully.

13.3. RATIONAL NUMBERS 477

Notice in Listing 13.4 (rational.py) in the Rational class that the field names begin with __. This means
that client code like

fract = Rational(1, 2)
print(fract.__numerator) # Error, not possible

will not work. Clients no longer have direct access to the __numerator and __denominator instance
variables of Rational objects.

Clients may appear to change a protected field as

fract = Rational(1, 2)
fract.__denominator = 0 # Legal, but what does it do?
print(fract.get_denominator()) # Prints 2, not 0
print(fract.__denominator) # Prints 0, not 2

Surprisingly, the second statement (assignment of fract.__denominator) does not affect the __denominator
field used by the methods in the Rational class; it instead adds a new, unprotected field named __denominator.
The client cannot get to the protected field by merely using the dot (.) operator. To avoid such confusion, a
client should not attempt to use instance variables of an object with names that begin with two underscores.

We may define a __str__ method for any class. It is one of the special methods like __add__, __sub__,
__eq__, etc. introduced in Section 9.4 that provide syntactic sugar to the language. The interpreter calls
an object’s __str__ method when executing code that requires a string representation of an object; for
example, the print function converts an object into a string so it can display textual output. The str string
constructor function also uses the __str__ method of an object behind the scenes. The following simple
program demonstrates how this works:

# Define class X
class X:

def __str__(self):
return “abcdef”

# Make some X objects
a = X()
b = X()
c = X()
# Print them
print(a, b, c)
print(“————–“)
message = str(b)
print(message)

This code prints

abcdef abcdef abcdef
————–
abcdef

Our Rational.__mul__ method allows us to multiply two Rational objects using the convenient *
syntax:

fract3 = Rational(1, 2)
fract4 = Rational(3, 5)
print(fract3, “*”, fract4, “=”, fract3*fract4)

13.3. RATIONAL NUMBERS 478

The expression fract3 * fract4 is syntactic sugar for fract3.__mul__(fract4). We leave the imple-
mentation of the Rational.__add__ method to the reader; it is a bit more complicated, as rational number
addition involves finding a common denominator and making adjustments to the numerators to make them
compatible for adding together.

As a review of how objects and methods work in Python, consider the main function of Listing 13.4
(rational.py) which contains code that uses Rational objects. The statement

fract1.set_numerator(2)

calls the set_numerator method of the Rational class on behalf of the object fract1. During the call,
from the perspective of the code in the method self is assigned fract1, and n is assigned 2. Recall that
this statement is syntactic sugar for the more verbose

Rational.set_numerator(fract1, 2)

This means the code within set_numerator sees self as fract1 and n as the integer object 2. Dur-
ing this particular execution of the set_numerator method the expression self.__numerator within the
method’s definition refers to the fract1 object’s __numerator field. The method, therefore, reassigns the
__numerator member of fract1.

In comparison, consider the call

fract2.set_numerator(1)

This statement calls the set_numerator method of the Rational class on behalf of the object fract2.
Within the method’s execution in this case the expression self.__numerator refers to fract2’s numerator.
The method invocation in this case will assign 1 to the __numerator field of the fract2 object.

In OO-speak, we say the statement

fract1.set_numerator(2)

represents the client sending a set_numerator message to object fract1. In this message, it provides the
value 2. In this case frac1 is the message receiver. In the statement

fract2.set_numerator(1)

object fract2 receives the set_numerator message with the value 1.

In the Rational class in Listing 13.4 (rational.py) clients can see the values of the instance variables via
methods get_numerator and get_denominator. These methods do not change the state of a Rational
object. Recalling the terminology from Section 13.1, these methods are often called getter methods be-
cause they can get the values of instance variables but cannot change the instance variables. In contrast,
set_numerator and set_denominator are mutator methods because they can change the values of in-
stance variables.

When the values of one or more instance variables in an object change, we say the object changes its
state; for example, if we use an object to model the behavior of a traffic light, the object likely will contain
an instance variable that represents its current color: red, yellow, or green. When that field changes, the
traffic light’s color changes. In the green to yellow transition, we can say the light goes from the state of
being green to the state of being yellow.

13.4. BANK ACCOUNT OBJECTS 479

13.4 Bank Account Objects

Consider the task of writing a program that manages accounts for a bank. Real bank accounts must store a
large amount of information: the account owner’s name, address, social security number, account number,
etc. To streamline our example, we will model bank accounts that maintain just three attributes:

• Every account has a unique identifier, the account number.

• Each account’s owner has a name.

• Each account has a current balance.

We can define a class of bank account objects. Each account object would have an account number
instance variable (integer), a name instance variable (string), and a balance instance variable (integer num-
ber of cents—we will use integers to avoid floating-point imprecision). The bank account management
application could store the accounts in a list and move the contents of the list to a file for persistent storage.

Listing 13.5 (bankaccounts.py) uses a BankAccount class to implement a simple database of customer
bank accounts.

Listing 13.5: bankaccounts.py

class BankAccount:
“”” Models a bank account “””
def __init__(self, number, name, balance):

“”” Initialize the instance variables of a bank account object.
Disallows a negative initial balance. “””

if balance < 0: raise ValueError('Negative initial balance') self.__account_number = number # Account number self.__name = name # Customer name self.__balance = balance # Funds available in the account def id(self): """ Returns the account number of this bank account object. """ return self.__account_number def deposit(self, amount): """ Add funds to the account. There is no limit to the size of the deposit. """ self.__balance += amount def withdraw(self, amount): """ Remove funds from the account, if possible. Only completes the withdrawal successfully if there are enough funds in the account to fulfill the withdrawal. Return true if successful, false otherwise """ result = False # Unsuccessful by default if self.__balance - amount >= 0:

self.__balance -= amount
result = True # Success

return result

def __str__(self):

13.4. BANK ACCOUNT OBJECTS 480

“”” Returns the string representation for this object “””
return ‘[{:>5} {:<10} {:>7} ]’.format(self.__account_number,

self.__name, self.__balance)

# —————————————————————–
# Global functions that use BankAccount objects

def open_database(filename, db):
“”” Read account information from a given file and store it

in the given list. “””
with open(filename) as lines: # Open file to read

for line in lines:
line.strip()
number, name, balance = line.split(“,”)
db.append(BankAccount(int(number), name, int(balance)))

def print_database(db):
“”” Display the contents of the database “””
for acct in db:

print(acct) # Calls the __str__ method of acct

def get_account(db, account_number):
“”” Retrieve an account object with a given account number. “””
for acct in db:

if acct.id() == account_number:
return acct

def main():
# Simple bank account “database”
database = []

try:
# Open the database of accounts
open_database(‘accountdata.text’, database)
print_database(database)
print(“——————–“)
customer = get_account(database, 129)
if customer:

print(“Account 129 before deposit of $100: “, end=””)
print(customer)
customer.deposit(100)
print(“Account 129 after deposit of $100: “, end=””)
print(customer)
print(“——————–“)
print(“Account 129 before withdraw of $500: “, end=””)
print(customer)
customer.withdraw(500)
print(“Account 129 after withdraw of $500: “, end=””)
print(customer)
print(“——————–“)
print(“Account 129 before withdraw of $80000: “, end=””)
print(customer)

13.4. BANK ACCOUNT OBJECTS 481

customer.withdraw(80000)
print(“Account 129 after withdraw of $80000: “, end=””)
print(customer)

except Exception:
print(‘Error in account database’)
raise

main()

Given a text file named accountdata.text containing the data

324, ‘Fred’, 34523
371, ‘Ella’, 1263210
129, ‘Zoe’, 78934
120, ‘Owen’, 247702
412, ‘Lily’, 12000
420, ‘Bert’, 10354

1038, ‘George’, 6733498
966, ‘Jan’, 9923912

1210, ‘Judy’, 83497
1300, ‘Sam’, 50315

the program Listing 13.5 (bankaccounts.py) would produce the output

[ 324 Fred 34523 ]
[ 371 Ella 1263210 ]
[ 129 Zoe 78934 ]
[ 120 Owen 247702 ]
[ 412 Lily 12000 ]
[ 420 Bert 10354 ]
[ 1038 George 6733498 ]
[ 966 Jan 9923912 ]
[ 1210 Judy 83497 ]
[ 1300 Sam 50315 ]
——————–
Account 129 before deposit of $100: [ 129 Zoe 78934 ]
Account 129 after deposit of $100: [ 129 Zoe 79034 ]
——————–
Account 129 before withdraw of $500: [ 129 Zoe 79034 ]
Account 129 after withdraw of $500: [ 129 Zoe 78534 ]
——————–
Account 129 before withdraw of $80000: [ 129 Zoe 78534 ]
Account 129 after withdraw of $80000: [ 129 Zoe 78534 ]

Clients interact with these bank account objects via the methods. The intention is that clients should not
access a bank account object’s instance variables directly to alter the object’s state.

In the BankAccount methods

• The constructor (__init__) initializes the instance variables of a BankAccount object, but it disal-
lows the creation of an object with a negative account balance.

13.4. BANK ACCOUNT OBJECTS 482

• Clients may add funds via the deposit method. The deposit method does limit the amount of a
deposit.

• The withdraw method prevents a client from withdrawing more money than is in the account. An
overdraft attempt will not change the account’s balance.

The following code will not work:

acct = BankAccount(31243, ‘Joe’, 1000)
acct.deposit(100)
acct.__balance -= 100 # Illegal

Clients instead should use the withdraw method. The withdraw method prevents actions such as

# New bank account object with $1,000.00 balance
acct = BankAccount(31243, ‘Joe’, 1000)
acct.withdraw(2000.00); # Method should disallow this operation

Notice that the operations of depositing and withdrawing funds are the responsibility of the object itself,
not the client code. The attempt to withdraw the $2,000 dollars will not alter the state of the object.

Consider a non-programming example. If I deposit $1,000.00 dollars into a bank, the bank then has
custody of my money. It is still my money, so I theoretically can reclaim it at any time. The bank stores
money in its safe, and my money is in the safe as well. Suppose I wish to withdraw $100 dollars from my
account. Since I have $1,000 total in my account, the transaction should be no problem. What is wrong
with the following scenario:

1. Enter the bank.

2. Walk past the teller into a back room that provides access to the safe.

3. The door to the safe is open, so enter the safe and remove $100 from a stack of $20 bills.

4. Exit the safe and inform a teller that you got $100 out of your account.

5. Leave the bank.

This is not the process a normal bank uses to handle withdrawals. In a perfect world where everyone is
honest and makes no mistakes, all is well. In reality, many customers might be dishonest and intentionally
take more money than they report. Even though I faithfully counted out my funds, perhaps some of the bills
were stuck to each other and I made an honest mistake by picking up six $20 bills instead of five. If I place
the bills in my wallet with other money that is there already, I may never detect the error. Clearly a bank
needs a more controlled procedure for customer withdrawals.

When working with programming objects, in many situations it is advantageous to discourage client
access to the internals of an object. Client code should not be able to easily modify directly bank account
instance variables for various reasons, including:

• A withdrawal should not exceed the account balance.

• Federal laws dictate that deposits above a certain amount should be reported to the Internal Revenue
Service, so a bank would not want customers to be able to add funds to an account in a way to
circumvent this process. We could add this functionality to our deposit method.

• An account number should never change for a given account for the life of that account.

13.5. STOPWATCH OBJECTS 483

We know that naming the instance variables with a dunder prefix provides only mild security (Section 13.2).
One check we can perform is to search client code for dunders. Behaving client code should be dunder-free
with regard to bank account instance variables.

13.5 Stopwatch Objects

In 6.5 we saw how to use the clock function to measure elapsed time during a program’s execution. The
following skeleton code fragment

seconds = clock() # Record starting time
#
# Do something here that you wish to time
#
other = clock() # Record ending time
print(other – seconds, “seconds”)

can be adapted to any program, but we can make it more convenient if we wrap the functionality into an
object. We can wrap all the messy details of the timing code into a convenient package. Consider the
following client code that uses an object to keep track of the time:

timer = Stopwatch() # Declare a stopwatch object

timer.start() # Start timing

#
# Do something here that you wish to time
#

timer.stop() # Stop the clock
print(timer.elapsed(), ” seconds”)

This code using a Stopwatch object is simpler. A programmer writes code using a Stopwatch in a similar
way to using an actual stopwatch: push a button to start the clock (call the start method), push a button
to stop the clock (call the stop method), and then read the elapsed time (use the result of the elapsed
method). Programmers using a Stopwatch object in their code are much less likely to make a mistake
because the details that make it work are hidden and inaccessible.

Given our experience designing our own types though Python classes, we now are adequately equipped
to implement such a Stopwatch class. Listing 13.6 (stopwatch.py) defines the structure and capabilities of
our Stopwatch objects.

Listing 13.6: stopwatch.py

from time import clock

class Stopwatch:
“”” Provides stopwatch objects that that programmers

can use to time the execution time of portions of
a program. “””

def __init__(self):
“”” Makes a new stopwatch ready for timing. “””
self.reset()

13.5. STOPWATCH OBJECTS 484

def start(self):
“”” Starts the stopwatch, unless it is already running.

This method does not affect any time that may have
already accumulated on the stopwatch. “””

if not self._running:
self._start_time = clock() – self._elapsed
self._running = True # Clock now running

def stop(self):
“”” Stops the stopwatch, unless it is not running.

Updates the accumulated elapsed time. “””
if self._running:

self._elapsed = clock() – self._start_time
self._running = False # Clock stopped

def reset(self):
“”” Resets stopwatch to zero. “””
self._start_time = self._elapsed = 0
self._running = False

def elapsed(self):
“”” Reveals the stopwatch running time since it

was last reset. “””
if not self._running:

return self._elapsed
else:

return clock() – self._start_time

Four methods are available to clients: start, stop, reset, and elapsed. A client does not have to
worry about the “messy” detail of the arithmetic to compute the elapsed time.

Note that our design allows clients to read the elapsed time on a Stopwatch object via the elapsed
method without needing to call the stop method first. Also, this implementation allows a user to stop the
stopwatch and resume the timing later without resetting the time in between.

Listing 13.7 (newtimeprimes.py) is a rewrite of Listing 10.25 (timeprimes.py) that uses a Stopwatch
object to compare the execution speed of two different prime number algorithms.

Listing 13.7: newtimeprimes.py

“”” Count the number of prime numbers less than
two million and time how long it takes
Compares the performance of two different
algorithms. “””

from stopwatch import Stopwatch
from math import sqrt

def count_primes(n):
“””
Generates all the prime numbers from 2 to n – 1.
n – 1 is the largest potential prime considered.
“””
timer = Stopwatch()

13.5. STOPWATCH OBJECTS 485

timer.start() # Record start time

count = 0
for val in range(2, n):

root = round(sqrt(val)) + 1
# Try all potential factors from 2 to the square root of n
for trial_factor in range(2, root):

if val % trial_factor == 0: # Is it a factor?
break # Found a factor

else:
count += 1 # No factors found

timer.stop() # Stop the clock
print(“Count =”, count, “Elapsed time:”, timer.elapsed(), “seconds”)

def sieve(n):
“””
Generates all the prime numbers from 2 to n – 1.
n – 1 is the largest potential prime considered.
Algorithm originally developed by Eratosthenes.
“””

timer = Stopwatch()
timer.start() # Record start time

count = 0

# First prime number is 2; 0 and 1 are not prime
nonprimes[0] = nonprimes[1] = True

# Start at the first prime number, 2.
for i in range(2, n):

# See if i is prime
if not nonprimes[i]:

count += 1
# It is prime, so eliminate all of its
# multiples that cannot be prime
for j in range(2*i, n, i):

nonprimes[j] = True
# Print the elapsed time
timer.stop()
print(“Count =”, count, “Elapsed time:”, timer.elapsed(), “seconds”)

def main():
count_primes(2000000)
sieve(2000000)

13.6. TRAFFIC LIGHT OBJECTS 486

main()

The code managing the execution timing in this new, object-oriented version is simpler and more readable
than our earlier version.

13.6 Traffic Light Objects

Section 9.6 introduced the Tk graphical user interface toolkit. Listing 9.14 (tkinterlight.py) provides a pro-
gram that draws three circular lamps of various colors and a rectangular frame. It supports user interaction
and simulates a standard traffic light. What if we wish to build a more sophisticated application that graphi-
cally models an intersection containing four traffic lights? We could follow the same approach, writing code
to draw four rectangular frames and 12 circular lamps. Making sure all the rectangular frames and circular
lamps are in the correct locations would be tedious work. Next consider an expansion of the application
that is to model the scores of intersections and hundreds of traffic lights within a community. Coding all
the parts of the lights in their correct positions within the graphics window would be beyond tedious.

We really are not interested in drawing rectangles and circles in our more sophisticated application; we
actually need to be able to draw traffic lights. Further, such traffic lights ought to know their current color
and automatically be able to become a different color when told to do so. In fact, a traffic light’s normal
operating procedure should be to change from red to green, green to yellow, and yellow to red. Other
transitions, such as green to red or red to yellow should not be supported. A single program must be able to
use multiple traffic lights with each light maintaining its own independent operation.

By now you probably have thought of the solution. We need a TrafficLight class that enables us to
create TrafficLight objects. Each TrafficLight object should contain instance variables that represents
the light’s position and current color. The class constructor could set the light’s position and initial color. A
change method could transition the light’s current color to its new color, ensuring no out-of-sequence color
changes.

Recall the Tk program in Listing 9.14 (tkinterlight.py) that allows the user to cycle through the colors
of a graphical traffic light by pressing a button. We will use that code as a starting point in designing our
traffic light class. We want clients to be able to specify the position and size of traffic light objects within
the graphics window. Clients also should be able to specify the light’s initial color. To simplify things for
this example, we will not provide to clients the ability to reposition or resize a light after its creation. After
creating a traffic light object, a clients can cycle through its color states via a change method.

Listing 13.8 (trafficlight.py) provides the class definition for traffic light objects.

Listing 13.8: trafficlight.py

from tkinter import Canvas

class TrafficLight:
“”” Models a traffic light. “””

def __init__(self, x, y, width, canvas, initial_color=”red”):
“”” Makes a new traffic light object. The light’s

left-top corner is anchored at the point (x, y).
The is width pixels wide.
The light will render on the canvas drawing surface.

13.6. TRAFFIC LIGHT OBJECTS 487

The light’s initial color is initial_color. “””

# Check to see if the supplied color is valid
if initial_color not in (“red”, “yellow”, “green”):

raise ValueError(initial_color + ” is not a valid color”)

# Initialize instance variables
self.canvas = canvas
self.color = initial_color

# Set the individual lamps initial fill colors
red_fill = “red” if initial_color == “red” else “black”
yellow_fill = “yellow” if initial_color == “yellow” else “black”
green_fill = “green” if initial_color == “green” else “black”

# 1/5 of the width will the be the basic unit for computing the height of
# the traffic light and positioning the individual lamps.
unit = width//5 # Ensure integer division

# Traffic light frame
canvas.create_rectangle(x, y, x + width, y + 13*unit, fill=’gray’)

x = x + unit
y = y + unit
diameter = 3*unit # Diameter (bounding box width) of each lamp

# Red lamp, currently on
self.red_lamp = canvas.create_oval(x, y, x + diameter, y + diameter, fill=red_fill)
y += 4*unit
# Yellow lamp, currently off
self.yellow_lamp = canvas.create_oval(x, y, x + diameter, y + diameter, fill=yellow_fill)
y += 4*unit
# Green lamp, currently off
self.green_lamp = canvas.create_oval(x, y, x + diameter, y + diameter, fill=green_fill)

def change(self):
“”” Changes the traffic light’s color to the next color in

the sequence. “””
if self.color == ‘red’:

self.color = ‘green’
self.canvas.itemconfigure(self.red_lamp, fill=’black’) # Turn red off
self.canvas.itemconfigure(self.green_lamp, fill=’green’) # Turn green on

elif self.color == ‘green’:
self.color = ‘yellow’
self.canvas.itemconfigure(self.green_lamp, fill=’black’) # Turn green off
self.canvas.itemconfigure(self.yellow_lamp, fill=’yellow’) # Turn yellow on

elif self.color == ‘yellow’:
self.color = ‘red’
self.canvas.itemconfigure(self.yellow_lamp, fill=’black’) # Turn yellow off
self.canvas.itemconfigure(self.red_lamp, fill=’red’) # Turn red on

The following are some important points from Listing 13.8 (trafficlight.py):

• Listing 13.8 (trafficlight.py) is not an executable Python program; it is module meant to be imported

13.6. TRAFFIC LIGHT OBJECTS 488

by other modules.

• The TrafficLight constructor accepts an (x,y) position and width for the graphical traffic light. The
constructor calculates the light’s height and the size and placement of its three lamps from these three
parameters. The constructor also accepts a Tk canvas reference from the client. This means the client
is responsible for setting up the Tk graphics environment before creating a TrafficLight object.
Finally, the constructor can accept an initial color from the client. The color is one of the following
strings: “red”, “yellow”, or “green”. The constructor throws a ValueError exception if the client
attempts to pass an object as the last argument that is not one of these strings. If the client omits this
parameter, the color defaults to “red”.

The constructor establishes five instance variables: canvas, color, red_lamp, yellow_lamp, and
green_lamp. The following indicates their purpose:

– canvas: After object construction methods must have access to the canvas object in order to
recolor the lamps as necessary. This means each TrafficLight object must store the caller’s
canvas object.

– color: This instance variable keeps track of the light’s current color.
– red_lamp, yellow_lamp, and green_lamp: These instance variables allow methods to access

the circle shapes the constructor created via calls to create_oval. The change method needs
access to these shapes to be able change the lamps’ colors.

The mathematics within the constructor ensures that all the shapes that make up a visual traffic light
will appear in their correct positions regardless of a light’s location and size.

• The change method in the TrafficLight class updates the color instance variable to the next color
in the light’s sequence of signals and modifies the fill colors of the two lamps affected by the change.

Given the module specified by Listing 13.8 (trafficlight.py), Listing 13.9 (trafficlightobject.py) behaves
exactly like Listing 9.14 (tkinterlight.py), but the code is completely reorganized into classes.

Listing 13.9: trafficlightobject.py

from tkinter import Tk, Canvas
from tkinter.ttk import Button, Frame

from trafficlight import TrafficLight

class TrafficLightWindow:
“”” Graphical window that displays a traffic light and change button. “””

def __init__(self):
root = Tk() # Create the main window
root.title(“Traffic Light”) # Set title bar text
# Create widget container
frame = Frame(root)
frame.pack()
# Create a graphical button and ensure it calls the do_button_press
# method when the user presses it
button = Button(frame, text=’Change’, command=self.do_button_press)
# Create and add a drawing surface within the window
canvas = Canvas(frame, width=200, height=300)
# Make a traffic light object instance variable

13.6. TRAFFIC LIGHT OBJECTS 489

self.light = TrafficLight(50, 20, 100, canvas)
# Position button and canvas objects
button.grid(row=0, column=0)
canvas.grid(row=0, column=1)
# Start the GUI event loop
root.mainloop()

def do_button_press(self):
“”” The window manager calls this function when the user

presses the graphical button. “””
self.light.change()

# Main program ———————————————————————

# Create and execute a traffic light window
TrafficLightWindow()

The following are some important points from Listing 13.9 (trafficlightobject.py):

• Listing 13.9 (trafficlightobject.py) imports the Listing 13.8 (trafficlight.py) module. This gives it access
to our TrafficLight class.

• The TrafficLightWindow class is responsible for setting up the Tk graphical infrastructure. Its
constructor creates a Canvas object and uses that to create a TrafficLight object. The constructor
also creates a tkinter.ttk Button object, and wires it into the do_button_press method.

• The do_button_press method simply delegates its work to the change method of its TrafficLight
instance variable.

• The event handling code in Listing 13.9 (trafficlightobject.py) does not access any global variables. In
fact, global variables are absent from both the Listing 13.8 (trafficlight.py) and Listing 13.9 (trafficlightobject.py)
modules. This is an important distinction from the code in Listing 9.14 (tkinterlight.py) which required
global variables to achieve the necessary communication with the function that changed the light’s
color. The instance variables within TrafficLight objects assume the roles formerly played by
global variables in Listing 9.14 (tkinterlight.py).

Instance variables are like global variables confined to an particular object; any method within that
class can access that object’s instance variables via its self parameter.

Listing 13.10 (multisizelightwindow.py) demonstrates the flexibility of our TrafficLight class by cre-
ating traffic light objects of various sizes.

Listing 13.10: multisizelightwindow.py

from tkinter import * #Tk, Canvas
from tkinter.ttk import Button, Frame
from random import choice, randrange

from functools import partial

from trafficlight import TrafficLight

class MultisizeLightWindow:

13.6. TRAFFIC LIGHT OBJECTS 490

Figure 13.5 The initial display of Listing 13.10 (multisizelightwindow.py). The user can press buttons to
change the color of their associated traffic light images.

“”” Graphical window that displays multiple traffic lights
of different sizes. “””

def do_button_press(self, idx):
“”” The window manager calls this function when the user

presses the graphical button. “””
self.lights[idx].change()

def __init__(self):
root = Tk() # Create the main window
root.title(“Multiple Traffic Lights”) # Set title bar text
self.lights = []
# The outer frame holds the nine inner frames that each contain
# a canvas and a button.
outer_frame = Frame(root)
outer_frame.pack()
# Create nine drawing surfaces within the window
for i in range(1, 10):

f = Frame(outer_frame, borderwidth=2, relief=GROOVE)
f.grid(row=0, column=i)
c = Canvas(f, width=20*i, height=250)
c.grid(row=0, column=0)
self.lights.append(TrafficLight(5*i, 10, 10*i, c))
#b = Button(f, text=”Change”, command=lambda x=i: lights[x – 1].change())
b = Button(f, text=”Change”, command=partial(self.do_button_press, i – 1))
b.grid(row=1, column=0)

# Start the GUI event loop
root.mainloop()

# Main program ———————————————————————

# Create and execute a traffic light window
MultisizeLightWindow()

Figure 13.5 shows a sample run of Listing 13.10 (multisizelightwindow.py). Listing 13.10 (multisizelightwindow.py):
The following are some important points from Listing 13.10 (multisizelightwindow.py):

13.6. TRAFFIC LIGHT OBJECTS 491

• In the constructor builds a list of traffic light objects. Note that the loop variable determines the exact
location and size of each light it creates.

• The constructor uses Tk ttk.Frame widgets. Their purpose is to organize the place of other widgets;
in this case each Frame widget contains exactly one traffic light object and one button object.

• The widget grid method positions a widget within a grid of rows and columns within its parent. The
root widget is the parent of all nine frame widgets. The grid method places every frame widget in
row 0 (the first row), but its column depends on i, the loop variable. Within each frame, the grid
method places each canvas widget at row 0, column 0 and each button widget at row 1, column 0.

• You can verify that each traffic light maintains its own color by pressing a button below a light. Each
button press affects only the light appearing above itself.

• Note the application of the functools.partial function (see Section 8.11). The command keyword
argument in the tkinter.ttk.Button class constructor must be paired with a function or method that
expects no parameters. The do_button_press method expects two parameters—self and idx (for
index). How do we make these two parameters “go away?” In the expression partial(self.do_button_press, i – 1)
the self. prefix for do_button_press takes care of the self parameter. That leaves the idx param-
eter. The expression partial(self.do_button_press, i – 1) makes a new function with the
idx parameter hardwired in to be i – 1. The first time through the loop registers a callback to
self.do_button_press with the argument 0, the second time through the loop the argument is 1,
and so forth. Each call to partial creates a new, independent function, and each function created
during a loop iterator becomes the callback of the button object created during that iteration. The net
effect is our do_button_press method can flexibly call the change method of the proper traffic light
object.

An alternative to the statement

b = Button(f, text=”Change”, command=partial(self.do_button_press, i – 1))

b = Button(f, text=”Change”, command=lambda x=i: lights[x – 1].change())

Here we use a lambda function (see Section 8.7) with a default argument of the current loop variable’s
value. As in the partial function application, this approach creates nine separate independent func-
tions, each associated with a particular button. This approach makes the do_button_press method
superfluous; if we use the lambda functions, we can remove the do_button_press method from the
class.

Listing 13.11 (randomlights.py) further demonstrates the flexibility of our TrafficLight class by cre-
ating 50 traffic light objects at random positions with random sizes. The program even selects the initial
color of each light at random.

Listing 13.11: randomlights.py

from tkinter import Tk, Canvas
from tkinter.ttk import Button, Frame
from random import choice, randrange

from trafficlight import TrafficLight

class RandomLightsWindow:
“”” Graphical window that displays multiple traffic lights

13.7. AUTOMATED TESTING 492

of different sizes. “””

def __init__(self):
root = Tk() # Create the main window
root.title(“Multiple Traffic Lights”) # Set title bar text
f = Frame(root)
f.pack()
# Create a drawing surface within the window
canvas = Canvas(f, width=800, height=600)
# Make a list of random traffic light objects
color_list = [“red”, “yellow”, “green”]
self.light_list = []
for i in range(50):

self.light_list.append(TrafficLight(randrange(2, 700),
randrange(2, 400),
randrange(5, 120),
canvas,
choice(color_list)))

# Create a graphical button and ensure it calls the do_button_press
# function when the user presses it
button = Button(f, text=’Change’, command=self.do_button_press)
# Position button and canvas objects
button.grid(row=0, column=0)
canvas.grid(row=0, column=1)
# Start the GUI event loop
root.mainloop()

def do_button_press(self):
“”” The window manager calls this function when the user

presses the graphical button. “””
for light in self.light_list:

light.change()

# Main program ———————————————————————

# Create and execute a traffic light window
RandomLightsWindow()

Figure 13.6 shows a sample run of Listing 13.11 (randomlights.py). When the user presses the Change
button, all the lights change to their next valid state.

13.7 Automated Testing

We know that just because a program runs to completion without a run-time error it does not imply that the
program works correctly. We can detect logic errors in our code as we interact with the executing program.
The process of exercising code to reveal errors or demonstrate the lack thereof is called testing. The informal
testing that we have done up to this point has been adequate, but serious software development demands a
more formal approach. Good testing requires the same skills and creativity as programming itself.

Until relatively recently in the software development world, testing was often an afterthought. Testing
was not perceived to be as glamorous as designing and coding. Poor testing led to buggy programs that

13.7. AUTOMATED TESTING 493

Figure 13.6 A sample execution of Listing 13.11 (randomlights.py) that creates 50 traffic light objects at
random positions, with random sizes, and with random initial colors.

13.7. AUTOMATED TESTING 494

frustrated users. Also, tests were written largely after the program’s design and coding were complete.
The problem with this approach is major design flaws may not be revealed until late in the development
cycle. Changes late in the development process are invariably more expensive and difficult to deal with than
changes earlier in the process.

Weaknesses in the standard approach to testing led to a new strategy: test-driven development. In
test-driven development the testing is automated, and the design and implementation of good tests is just
as important as the design and development of the actual program. In pure test-driven development, test
engineers develop tests based on the problem’s requirements before developers write any application code.
Testers then can subject all new application code to the pre-existing tests as soon as the code becomes
available.

Listing 13.12 (functiontester.py) defines the structure of a rudimentary object that we can use to test
functions.

Listing 13.12: functiontester.py

class FunctionTester:
“”” Provides support for testing simple Python functions. “””

def __init__(self):
“”” Creates a FunctionTester object. Resets the counts to zero. “””
self.__error_count = self.__total_count = 0
print(“+—————————————“)
print(“| Testing “)
print(“+—————————————“)

def check(self, msg, expected, func, *args):
“”” Clients pass a human-readable message (msg) to uniquely

identify the test case, the expected value that a
correct test would produce (expected), the function to
test (func), and any arguments that the function under
test requires (*args).
Provides immediate printed feedback about the test’s
success or failure and adjusts error count accordingly.
Returns True if the function passed the test;
otherwise, returns False. “””

result = True # Test passed unless we determine otherwise
print(” “, msg, ” “, end=” “)
self.__total_count += 1 # Count this test
try:

actual = func(*args) # Apply function to arguments
if expected == actual:

print(“OK”)
else:

self.__error_count += 1 # Count this failed test
print(“*** Failed! Expected:”, expected,

“actual:”, actual)
result = False # Test failed

except Exception as e:
self.__error_count += 1 # Count this failed test
print(“****** Exception”, e)
result = False # Test failed

return result # Notify client of test result

13.7. AUTOMATED TESTING 495

def report_results(self):
“”” Prints the testing statistics. “””
print(“+————————————–“)
print(“|”, self.__total_count, “tests run”)
print(“|”, self.__total_count – self.__error_count, ” passed”)
print(“|”, self.__error_count, ” failed”)
print(“+————————————–“)

Listing 13.12 (functiontester.py) provides the class of simple test objects that enables a client to exercise
one or more functions to see if they produce expected results. A test object keeps track of the number of
tests performed and the number of failures.

The FunctionTester.__init__ method establishes the __total_count and __error_count instance
variables to handle the accounting. Clients use the FunctionTester.check method to test a function;
callers pass up to four arguments:

• a string that uniquely identifies the test (so the tester can determine which test failed),

• the predicted return value of a correctly implemented function,

• the function to test, and

• the parameters to pass to the function, if any.

During its execution, the FunctionTester.check method calls the function it receives with the specified
parameters and compares the actual result to the expected result. The method will indicate the test’s success
or failure and track the number of failed tests. Clients call the report_results method after performing
all the tests. The report_results method provides the error statistics for all the tests performed.

Listing 13.13 (testliststuff.py) uses our FunctionTester class to test a few simple functions.

Listing 13.13: testliststuff.py

from functiontester import FunctionTester

def max_of_three_bad(x, y, z):
“”” Attempts to determine and return the maximum of three

numeric values. “””
result = x
if y > result:

result = y
elif z > result:

result = z
return result

def max_of_three_good(x, y, z):
“”” Computes and returns the maximum of three numeric values. “””
result = x
if y > result:

result = y
if z > result:

result = z
return result

13.7. AUTOMATED TESTING 496

def sum(lst):
“”” Attempts to compute and return the sum of all the elements in

a list of integers. “””
total = 0
for i in range(1, len(lst)):

total += lst[i]
return total

# maximum has a bug (it has yet to be written!)
def maximum(lst):

“”” Computes the maximum element in a list of integers. “””
return 0 # maximum not yet implemented

def main():
t = FunctionTester() # Make a test object

# Some test cases to test max_of_three_bad
t.check(“max_of_three_bad test #1”, 4, max_of_three_bad, 2, 3, 4)
t.check(“max_of_three_bad test #2”, 4, max_of_three_bad, 4, 3, 2)
t.check(“max_of_three_bad test #3”, 4, max_of_three_bad, 3, 2, 4)

# Some test cases to test max_of_three_good
t.check(“max_of_three_good test #1”, 4, max_of_three_good, 2, 3, 4)
t.check(“max_of_three_good test #2”, 4, max_of_three_good, 4, 3, 2)
t.check(“max_of_three_good test #3”, 4, max_of_three_good, 3, 2, 4)

# Some test cases to test maximum
t.check(“maximum test #1”, 4, maximum, [2, 3, 4, 1])
t.check(“maximum test #2”, 4, maximum, [4, 3, 2, 1])
t.check(“maximum test #3”, 0, maximum, [-2, -3, 0, -21])

# Some test cases to test sum
t.check(“sum test #1”, 7, sum, [0, 3, 4])
t.check(“sum test #2”, 2, sum, [-3, 0, 5])

t.report_results()

main()

The program’s output is

+—————————————
| Testing
+—————————————

max_of_three_bad test #1 *** Failed! Expected: 4 actual: 3
max_of_three_bad test #2 OK
max_of_three_bad test #3 OK
max_of_three_good test #1 OK
max_of_three_good test #2 OK
max_of_three_good test #3 OK

13.8. PLOTTING DATA 497

maximum test #1 *** Failed! Expected: 4 actual: 0
maximum test #2 *** Failed! Expected: 4 actual: 0
maximum test #3 OK
sum test #1 OK
sum test #2 *** Failed! Expected: 2 actual: 5

+————————————–
| 11 tests run
| 7 passed
| 4 failed
+————————————–

In the max_of_three_bad and max_of_three_good functions the test program clearly demonstrates
the different between sequential if statements and multi-way if/elif/else statements.

In the sum function, the programmer was careless and used 1 as the beginning index for the list. Notice
that the first test does not catch the error, since the element in the zeroth position (zero) does not affect the
outcome. A tester must be creative and even devious to try and force the code under test to demonstrate its
errors.

Notice that even though we have yet to implement the maximum function, we can test it anyway. This is
true test-driven development—design the tests first, then write the code. The maximum function here is an
example of a stub. A stub is a function or method that does not provide the expected functionality but may
be executed without causing a run-time error. A stub ordinarily ignores all parameters passed to it and, if
necessary, returns a default value of the type expected by its caller. The yet-to-be implemented maximum
function simply returns zero—notice that it accidentally passes one of the tests. We can define a square root
function stub as

def sqrt(x):
“”” Computes the square root of x. “””
return 0.0 # TODO implement the square root function

Stubs are invaluable during the development process because they serve as placeholders for incomplete
functionality or missing features in a fully executable and testable program. Stubs allow programmers
to develop and test the overall logic and structure of a program while many of the details remain to be
determined or implemented.

A FunctionTester object robustly handles any exceptions a function under test may raise. It records
an exception as a failed test, and continues on with any remaining tests.

The FunctionTester class from Listing 13.12 (functiontester.py) has some limitations; for example,
testers cannot use it to check the correctness of a function that sorts a list in place. The FunctionTester.check
method determines only if a function returns the expected result. It also cannot test that a function does
not modify a mutable parameter; for example, in the course of their execution the sum and maximum func-
tions in Listing 13.13 (testliststuff.py) should not modify the list passed by a caller. We could enhance the
FunctionTester class to check that functions handle mutable parameters properly.

Our FunctionTester class is limited in its testing abilities. In Section 14.5 we will examine a better
way to test our code using the unittest module in the Python standard library.

13.8 Plotting Data

Listing 8.17 (plotter.py) uses Turtle graphics to plot mathematical functions. We can use a class to wrap the
details of Turtle graphics and design a plotter object that is more convenient for programmers. At the same

13.8. PLOTTING DATA 498

time we can add some enhancements that enable plotting of data obtained experimentally.

Listing 13.14 (plotobj.py) defines a class named Plotter. The class contains the following methods:

• __init__: The constructor initializes the Turtle graphics window. It accepts parameters that define
the window’s physical size and ranges of x and y axes.

• __del__: The interpreter calls this method, also known as destructor, when the object is no longer
bound to a reference with in the executing program. Among other times, this happens when the
program’s execution terminates.

• draw_axes: Draws the x and y axes on the plot. An option Boolean parameter controls the presence
of accessory reference lines that divide the plot into 20 equal sections.

• draw_grid: Draws horizontal and vertical accessory reference coordinate lines on the plot. Parame-
ters control the frequency of the reference lines.

• draw_arrow: Draws a line segment with an attached arrow head. Expects four numeric parameters
representing the (x1,y1) tail end point and (x2,y2) head end point of the arrow.

• plot_function: Plots the curve of a given function with a specified color. An optional Boolean
parameter determines if the function renders immediately or requires the client to call the update
method after a series of plots (defaults to True).

• plot_data: Plots the curve formed by the (x, y) points contained in a list of data. A parameter speci-
fies the curve’s color. An optional Boolean parameter determines if the function renders immediately
or requires the client to call the update method after a series of plots (defaults to True).

• setcolor: Sets the current drawing color.

• onclick: Assigns a callback function that the frame should call when the user clicks the mouse
button when the pointer is over the plotter window.

• interact: Sets the plotter to interactive mode, enabling the user to provide mouse and keyboard
input.

Listing 13.14: plotobj.py

“”” Provides the Plotter class that clients can use to
draw graphs of a mathematical functions on a Cartesian
coordinate plane. “””

from turtle import Pen, Screen
from math import atan2, pi

class Plotter:
“”” A plotter object provides a graphical window for

plotting data and mathematical functions. “””

def __init__(self, width, height, min_x, max_x, min_y, max_y):
“”” Initializes the plotter with a window that is

width wide and height high. Its x-axis ranges from
min_x to max_x, and its y-axis ranges from
min_y to max_y. Establishes the global beginning and ending

13.8. PLOTTING DATA 499

x values for the plot and the x_increment value.
Draws the x- and y-axes. “””

self.pen = Pen() # The plotter object’s pen
self.screen = Screen() # The plotter object’s screen

self.pen.speed(0) # Speed up rendering
self.screen.tracer(0, 0) # Do not draw pen while drawing
# Establish global x and y ranges
self.min_x, self.max_x = min_x, max_x
self.min_y, self.max_y = min_y, max_y
# Set up window size, in pixels
self.screen.setup(width=width, height=height)
# Set up screen size, in pixels
self.screen.screensize(width, height)
self.screen.setworldcoordinates(min_x, min_y, max_x, max_y)

# x-axis distance that corresponds to one pixel in window distance
self.x_increment = (max_x – min_x)/width
self.draw_grid(20)
self.draw_axes()
self.screen.title(“Plot”)
self.screen.update()

def __del__(self):
“”” Called when the client no longer uses the plotter

object. “””
print(“Done plotting”)

def draw_axes(self, grid=False):
“”” Draws the x and y axes within the plotting window.

The grid parameter controls the drawing of accessory
horizontal and vertical lines. “””

if grid:
self.draw_grid(20)

self.pen.hideturtle() # Make pen invisible
prev_width = self.pen.width()
self.pen.width(2)
# Draw x axis
self.pen.color(‘black’)
self.draw_arrow(self.min_x, 0, self.max_x, 0)
# Draw y axis
self.draw_arrow(0, self.min_y, 0, self.max_y)
self.pen.width(prev_width)

def draw_grid(self, n):
“”” Draws horizontal and vertical accessory reference

coordinate lines on the plot. Parameter n controls
the frequency of the reference lines. “””

self.pen.up()
#self.pen.setposition(self.min_x, self.min_y)
inc = (self.max_x – self.min_x)/n
self.pen.color(“lightblue”)
x = self.min_x
while x <= self.max_x: ©2017 Richard L. Halterman Draft date: January 18, 2018 13.8. PLOTTING DATA 500 self.pen.setposition(x, self.min_y) self.pen.down() self.pen.setposition(x, self.max_y) self.pen.up() x += inc # Next x inc = (self.max_y - self.min_y)/n y = self.min_y while y <= self.max_y: self.pen.setposition(self.min_x, y) self.pen.down() self.pen.setposition(self.max_x, y) self.pen.up() y += inc # Next y def draw_arrow(self, x1, y1, x2, y2): """ Draws an arrow starting at (x1, y1) and ending at (x2, y2). """ # Draw arrow shaft self.pen.up() self.pen.setposition(x1, y1) # Move the pen starting point self.pen.down() # Draw line bottom to top self.pen.setposition(x2, y2) # Move the pen starting point # Draw arrow head dy = y2 - y1 dx = x2 - x1 angle = atan2(dy, dx) *180/pi self.pen.setheading(angle) self.pen.stamp() def plot_function(self, f, color, update=True): """ Plots function f on the Cartesian coordinate plane established by initialize_plotter. Plots (x, f(x)), for all x in the range min_x <= x < max_x. The color parameter dictates the curve's color. """ # Move pen to starting position self.pen.up() self.pen.setposition(self.min_x, f(self.min_x)) self.pen.color(color) self.pen.down() # Iterate over the range of x values for min_x <= x < max_x x = self.min_x while x < self.max_x: self.pen.setposition(x, f(x)) x += self.x_increment # Next x if update: self.screen.update() def plot_data(self, data, color, update=True): """ Plots the (x, y) pairs of values in the data list. The curve's color is specified by the color parameter. """ # Move pen to starting position self.pen.up() self.pen.setposition(data[0][0], data[0][1]) ©2017 Richard L. Halterman Draft date: January 18, 2018 13.8. PLOTTING DATA 501 self.pen.color(color) self.pen.down() # Plot the points in the data set for x, y in data: self.pen.setposition(x, y) if update: self.screen.update() def update(self): """ Draws any pending plotting actions to the screen. """ self.screen.update() def setcolor(self, color): """ Sets the current drawing color. """ self.pen.color(color) def onclick(self, fun): """ This method assigns a function to call when the user clicks the mouse over the plotting window. The function must accept two integer parameters that represent the (x, y) location of the mouse when the click occurred. """ self.screen.onclick(fun) def interact(self): """ Places the plotting object in interactive mode so the user can provide input via the mouse or keyboard. """ self.screen.mainloop() Listing 13.15 (testplotter.py) exercises the plotobj module, demonstrating its use within a program. Listing 13.15: testplotter.py from plotobj import Plotter from math import sin def quad(x): """ Quadratic function (parabola) """ return 1/2 * x**2 + 3 def arrow_wheel(plotter, x, y, len, angle, color): """ Draws a collection of arrows extending radially from an (x, y) center point. The arrows all are len long, the angle parameter specifes the angle between each adjacent arrow, and color specifies their color. """ from math import cos, sin, radians COS_theta = cos(radians(angle)) SIN_theta = sin(radians(angle)) plotter.setcolor(color) xe, ye = len, 0.0 for i in range(360//angle): xe, ye = xe*COS_theta - ye*SIN_theta, xe*SIN_theta + ye*COS_theta plotter.draw_arrow(x, y, xe + x, ye + y) ©2017 Richard L. Halterman Draft date: January 18, 2018 13.9. DYNAMIC CONTENT 502 def main(): """ Provides a simple test of the plotting object. """ from math import sin def run_test(x, y): """ Generate an arrow wheel centered at (x, y) with random size and color. """ #test_arrow(plt) from random import randrange colors = ["red", "green", "blue", "black"] arrow_wheel(plt, x, y, randrange(10) + 1, 10, colors[randrange(4)]) # Create a plotter object plt = Plotter(600, 600, -10, 10, -10, 10) # Plot f(x) = 1/2*x + 3, for -10 <= x < 100 plt.plot_function(quad, 'red') # Plot f(x) = x, for -10 <= x < 100 plt.plot_function(lambda x: x, 'blue') # Plot f(x) = 3 sin x, for -10 <= x < 100 plt.plot_function(lambda x: 3*sin(x), 'green') # Execute the run_test function when the user clicks the mouse plt.onclick(run_test) #test_arrow(plt) plt.interact() if __name__ == '__main__': main() Listing 13.15 (testplotter.py) first draws some mathematical curves and then allows the user to place cir- cles of radiating arrows of random colors and sizes. Figure 13.7 shows the initial plot of Listing 13.15 (testplotter.py) before the user clicks the mouse over the window. Figure 13.8 shows a subsequent display of Listing 13.15 (testplotter.py) after the user creates several arrow wheels. The arrow circles give the vague appearance of exploding fireworks. 13.9 Dynamic Content Section 13.1 showed how we can set up the instance variables of an object in the __init__ method of its class. This technique ensures every object of that class will contain those instance variables. Python allows programmers to add instance variables dynamically to individual objects. Consider the following very simple class: class Widget: pass The following code creates a Widget object and adds some instance variables: w = Widget() ©2017 Richard L. Halterman Draft date: January 18, 2018 13.9. DYNAMIC CONTENT 503 Figure 13.7 The initial plot of Listing 13.15 (testplotter.py) before the user clicks the mouse over the window. Figure 13.8 A subsequent display of Listing 13.15 (testplotter.py) after the user creates several arrow wheels by clicking the mouse over various parts of the window. ©2017 Richard L. Halterman Draft date: January 18, 2018 13.9. DYNAMIC CONTENT 504 w.a = 16 w.t = 100 print(w.a, w.t) The code prints 16 100 This ability to dynamically add instance variables to objects sets Python apart from other mainstream object- oriented programming languages like C++, Java, and C#. A C++ class, for example, establishes the structure (instance variables) of an object, and that structure is the same for all objects of that type. Furthermore, programmers cannot add instance variables to an object without editing the source code for its class. Python’s instance variables are flexible because each object stores its instance variables in a dictionary (see Section 11.3 for a review of dictionaries). The dictionary is located in an instance variable named __dict__ that is common to all objects. The following experiment with the interactive interpreter demon- strates the __dict__ instance variable in action: >>> class Widget:
… def __init__(self):
… self.a = 10
…
>>> w = Widget()
>>> w.__dict__
{‘a’: 10}
>>> class Gadget:
… pass
…
>>> g = Gadget()
>>> g.__dict__
{}
>>> g.x = 20
>>> g.y = 30
>>> g.__dict__
{‘x’: 20, ‘y’: 30}

Notice that whether the constructor assigns the instance variable or a statement outside the class assigns the
instance variable, the variable appears in the object’s dictionary.

Programmers ordinarily do not need to dynamically add instance variables to an object. The ability to
add instance variables on the fly is convenient for some algorithms; for example, when traversing a list of
objects a program could add an instance variable named visited to mark the object as being processed.

The del statement removes an instance variable:

del g.x # Removes the x instance variable from object g

We can express the statement

g.x = 5

setattr(g, “x”, 5)

Similarly, we can rewrite

13.9. DYNAMIC CONTENT 505

print(g.x)

print(getattr(g, “x”))

The setattr function stands for set attribute, and getattr stands for get attribute. The term attribute
is another name for instance variable. Note that in the calls to the functions setattr and getattr the
instance variable name x is expressed as the string “x”. If the name x did not appear in quotes, it would
refer to a variable named x; such a variable may or may not exist, but, more importantly, it would not refer
to the instance variable named x in the g object.

The ability to specify an instance variable name via a string enables users to create instance variable
names at run time. Listing 13.16 (dynamicfield.py) demonstrates such code. id to an object.

Listing 13.16: dynamicfield.py

class Widget:
def __init__(self):

self.a = 5 # Provide a preexisting attribute

w = Widget()
print(w.__dict__)
print(“w.a =”, getattr(w, “a”))
setattr(w, “a”, 10)
print(“w.a =”, getattr(w, “a”))
field_name = input(“Enter instance variable name: “)
setattr(w, field_name, 15)
print(getattr(w, field_name))
setattr(w, field_name, 20)
print(getattr(w, field_name))
print(w.__dict__)

In the following sample run of Listing 13.16 (dynamicfield.py), the user adds the instance variable named
my_field:

{‘a’: 5}
w.a = 5
w.a = 10
Enter instance variable name: my_field
15
20
{‘a’: 10, ‘my_field’: 20}

The setattr and getattr functions are almost perfect alternatives to the dot (.) notation. The following
session in the interactive interpreter reveals an interesting difference:

>>> class Widget:
… pass
…
>>> w = Widget()
>>> w.__dict__
{}
>>> setattr(w, “a”, 1)
>>> w.__dict__

13.10. CLASS VARIABLES 506

{‘a’: 1}
>>> getattr(w, “a”)
1
>>> w.a
1
>>> setattr(w, “#@&”, 2)
>>> w.__dict__
{‘#@&’: 2, ‘a’: 1}
>>> getattr(w, “#@&”)
2
>>> w.#@&

File ““, line 1
w.#@&

ˆ
SyntaxError: invalid syntax
>>> setattr(w, “”, 3)
>>> w.__dict__
{”: 3, ‘#@&’: 2, ‘a’: 1}
>>> getattr(w, “”)
3

We may use the dot notation only for instance variable names that obey the usual identifier rules (see
Section 2.3 for identifier naming rules). The instance variable names established by setattr have no such
restrictions. Even the empty string (“”) is a valid instance variable name for setattr and getattr!

13.10 Class Variables

In Python a class is not simply a pattern for a type of object; a class is an object itself. Consider the
following interactive session:

>>> class X:
… pass # An empty class
…
>>> x_obj = X() # Make an instance
>>> type(x_obj)

>>> type(X)

We see the type of a class is type. Every object has a __class__ field that reveals the same information as
the type function:

>>> x_obj.__class__

>>> X.__class__

We can obtain the name of any class via its __name__ field:

>>> X.__name__
‘X’
>>> x_obj.__class__.__name__

13.11. EXERCISES 507

‘X’
>>> X.__class__.__name__
‘type’

Each individual instance of a class maintains its own instance variables. Since a class is an instance
of type, a class can have its own variables. We reserve the term instance variable for variables within
instances of classes; we denote variables stored in a class object as class variables.

A variable defined within a class but outside of all methods of that class is a class variable. Listing 13.17
(widgetfactory.py) uses a class variable to manage serial numbers of widget objects it manufactures. It is
important that manufactured products have unique serial numbers, and the Widget constructor ensures the
serial number of each widget object is different from any other widget object.

Listing 13.17: widgetfactory.py

class Widget:
“”” Models a manufactured item. “””
serial_number_source = 0 # Class variable
def __init__(self):

“”” Make a widget with a unique serial number. “””
self.serial_number = Widget.serial_number_source
Widget.serial_number_source += 1

def get_serial_number(self):
“”” Return the widget’s serial number. “””
return self.serial_number

if __name__ == ‘__main__’:
widget_list = []
for i in range(10):

widget_list.append(Widget())
for w in widget_list:

print(w.serial_number, end=’ ‘)
print()

In Listing 13.17 (widgetfactory.py) the statement

serial_number_source = 0 # Class variable

appears in class body of Widget but outside the body of any method in the class. This makes serial_number_source
a class variable. Observe that every use of the class variable within a method prefixes the name with the
Widget class qualifier.

13.11 Exercises

CAUTION! SECTION UNDER CONSTRUCTION

1. Given the definition of the geometric Point class, complete the function named distance:

def distance(r1, r2):
# Details go here

that returns the distance between the two points passed as parameters.

13.11. EXERCISES 508

2. Given the definition of the Rational number class, complete the following function named reduce:

def reduce(r):
# Details go here

that returns the rational number that represents the parameter reduced to lowest terms; for example,
the fraction 10/20 would be reduced to 1/2.

3. What is the purpose of the __init__ method in a class?

4. What is the parameter named self that appears as the first parameter of a method?

5. Given the definition of the Rational number class, complete the following method named reduce:

class Rational:
# Other details omitted here …

# Returns an object of the same value reduced
# to lowest terms
def reduce(self):

# Details go here

that returns the rational number that represents the object reduced to lowest terms; for example, the
fraction 10/20 would be reduced to 1/2.

6. Given the definition of the Rational number class, complete the following method named reduce:

class Rational:
# Other details omitted here …

# Reduces the object to lowest terms
def reduce(self):

# Details go here

that reduces the object on whose behalf the method is called to lowest terms; for example, the fraction
10/20 would be reduced to 1/2.

7. Given the definition of the geometric Point class, add a method named distance:

class Point:
# Other details omitted

# Returns the distance from this point to the
# parameter p
double distance(self, p):

# Details go here

that returns the distance between the point on whose behalf the method is called and the parameter p.

8. Consider the following Python code:

class Rectangle:
“”” Represents a geometrical rectangle at a specific location and with a

specific width and height. “””

def __init__(self, point, width, height):

13.11. EXERCISES 509

“”” Establishes the rectangle’s lower-left corner, width, and height.
point: a tuple representing the (x, y) location of the rectangle’s lower-left corner
width: an integer representing the rectangle’s width
height: an integer representing the rectangle’s height “””

# Ensure the lower-left corner’s x and y coordinates fall in the range -100…100
x, y = point
x = -100 if x < -100 else 100 if x > 100 else x
y = -100 if y < -100 else 100 if y > 100 else y
self.corner = x, y # Pack the x and y values into a tuple
# Ensure the rectangle’s width and height are both nonnegative
self.width = 0 if width < 0 else width self.height = 0 if height < 0 else height def get_perimeter(self): """ Computes the perimeter of the rectangle. """ return 2*self.width + 2*self.height def get_area(self): """ Computes the perimeter of the rectangle. """ return self.width * self.height def get_width(self): """ Returns the width of the rectangle. """ return self.width def get_height(self): """ Returns the height of the rectangle. """ return self.height def grow(self, n): """ Increases the dimensions of the rectangle. Both width and height increase by one. """ self.width += 1 self.height += 1 def move(self, x, y): """ Moves the rectangle's lower-left corner to the specified (x, y) location. """ self.corner = x, y def intersect(self, other_rec): """ Returns true if rectangle other_rec overlaps this rectangle object; otherwise, returns false. """ # Details omitted pass def diagonal(self): """ Returns the length of a diagonal rounded to the nearest integer. """ # Details omitted ©2017 Richard L. Halterman Draft date: January 18, 2018 13.11. EXERCISES 510 pass def center(self): """ Returns the geometric center of the rectangle with the (x,y) coordinates rounded to the nearest integer. """ # Details omitted pass def is_inside(self, pt): """ Returns true if the tuple pt represents a point within the bounds of the rectangle; otherwise, returns false. As in soccer and tennis, "on the line" is "in." """ # Details omitted pass def main(): rect1 = Rectangle((2, 3), 5, 7) rect2 = Rectangle((5, 13), 1, 3) rect3 = Rectangle((20, 40), -5, 45) rect4 = Rectangle((-510, -220), 5, -4) print(rect1.get_width()) print(rect1.get_height()) print(rect2.get_width()) print(rect2.get_height()) print(rect3.get_width()) print(rect3.get_height()) print(rect4.get_width()) print(rect4.get_height()) print(rect1.get_perimeter()) print(rect1.get_area()) print(rect2.get_perimeter()) print(rect2.get_area()) print(rect3.get_perimeter()) print(rect3.get_area()) print(rect4.get_perimeter()) print(rect4.get_area()) if __name__ == '__main__': main() (a) What does the program print? (b) With regard to a Rectangle object’s lower-left corner, what are the minimum and maximum values allowed for the x coordinate? What are the minimum and maximum values allowed for the y coordinate? (c) What is a Rectangle object’s minimum and maximum width? (d) What is a Rectangle object’s minimum and maximum height? (e) What happens when a client attempts to create a Rectangle object with parameters that are outside the acceptable ranges? ©2017 Richard L. Halterman Draft date: January 18, 2018 13.11. EXERCISES 511 (f) Implement the intersect method. The method should not modify the rectangle. (g) Implement the diagonal method. The method should not modify the rectangle. (h) Implement the center method. The method should not modify the rectangle. (i) Implement the intersect method. The method should not modify the rectangle. (j) Implement the is_inside method. The method should not modify the rectangle. (k) Complete the following function named corner that returns the lower-left corner of the Rectangle object r passed to it: def corner(rect) """ Returns a tuple representing the lower-left corner of Rectangle object rect. """ pass # Replace with your code You may not modify the Rectangle class. (l) 9. Develop a Circle class that, like the Rectangle class above, provides methods to compute perimeter and area. The Rectangle instance variables are not appropriate for circles; specifically, circles do not have corners, and there is no need to specify a width and height. A center point and a radius more naturally describe a circle. Build your Circle class appropriately. 10. Given the Rectangle and Circle classes from questions above, write the following encloses func- tion: bool encloses(rect, circ) # Returns true if rectangle rect is large enough to # completely enclose circle circ regardless of the positions of the # two objects; otherwise, returns false. pass # Replace with your code The function returns true if circle circ’s dimensions would allow it to fit completely within rectangle rect. If circ is too big, the function returns false. The positions of rect and circ do not influence the result. 11. Consider the following Python code: class Widget: def __init__(self, v = 40): if v >= 40:
self.value = v

else:
self.value = 0

def get(self):
return self.value

def bump(self):
if self.value < 50: self.value += 1 def main(): ©2017 Richard L. Halterman Draft date: January 18, 2018 13.11. EXERCISES 512 w1 = Widget() w2 = Widget(5) print(w1.get()) print(w2.get()) w1.bump() w2.bump() print(w1.get()) print(w2.get()) for i in range(20): w1.bump() w2.bump() print(w1.get()) print(w2.get()) if __name__ == '__main__': main() (a) What does the program print? (b) If wid is a Widget object, what is the minimum value the expression wid.get() can return? (c) If wid is a Widget object, what is the maximum value the expression wid.get() can return? ©2017 Richard L. Halterman Draft date: January 18, 2018 513 Chapter 14 Class Design: Composition and Inheritance In object-oriented programming class design is key. In most cases developers do not start empty handed but build new classes from one or more existing classes. The goal is for the new class to provide capabilities unavailable in the existing classes. This chapter explores two key techniques for reuse in class design: composition and inheritance. 14.1 Composition CAUTION! SECTION UNDER CONSTRUCTION The typical Python class contains instance variables, usually established by the class constructor. These instance variables refer to other objects. If these instance variables are essential to the intrinsic meaning of the class, we say objects of the class are composed of other, more fundamental objects. This relationship represents an object-oriented design technique known as composition. Examples of composition abound in the classes we have designed so far: • Listing 13.1 (circle.py): Each Circle object is composed of a center tuple object and a radius numeric object. Removing either of these instance variables would disqualify our Circle objects from modeling mathematical circles. • Listing 13.3 (circlemakerobject.py): A GraphicalCircle object contains a Turtle object and a Circle object. Removing the Turtle object removes the graphical nature of our GraphicalCircle objects, and removing the Circle component eliminates the desired circle concept. • Listing 13.4 (rational.py): Rational objects hold numeric numerator and denominator objects. Every rational number must have both a numerator and a denominator. • Listing 13.5 (bankaccounts.py): BankAccount objects contain numeric (__account_number and __balance) and string (__account_number) objects. All of these instance variables are essential in every bank account. ©2017 Richard L. Halterman Draft date: January 18, 2018 14.1. COMPOSITION 514 • Listing 13.6 (stopwatch.py): Stopwatch objects hold four other numeric objects: _start_time, _running, and _elapsed. These components are necessary to control a stopwatch object in the manner demonstrated. • Listing 13.8 (trafficlight.py): TrafficLight objects are composed of a string object (color), a Tk object (canvas), and three integer objects (red_lamp, yellow_lamp, and green_lamp—these are integers returned by the Canvas.create_oval method; a canvas object keeps track of its shapes via integer indices known as tags. • Listing 13.9 (trafficlightobject.py): TrafficLightWindow objects contain TrafficLight objects. With- out TrafficLight objects, the graphical window would have no traffic light image to display. • Listing 13.12 (functiontester.py): Each FunctionTester object holds two integer objects (__error_count and __total_count). • Listing 13.14 (plotobj.py): Plotter objects are composed of a couple of Turtle objects (Pen and Screen) and four numeric objects (min_y, max_x, min_y, max_y). We can deduce the composite nature of our classes by examining the instance variables used within their methods. Any expression of within a method of the form self.something, where something refers to an object defined outside of the class itself indicates a dependence on an external object and is evidence of composition. Unless it was superfluous or unused, removing the reference to that external object will reduce the functionality of the class or possibly make the class completely inoperable. Some of the objects involved in Listing 13.10 (multisizelightwindow.py) form a similar but slightly dif- ferent relationship. Each MultisizeLightWindow object contains a list of nine TrafficLight and Button objects. The quantity nine is arbitrary—we could have had five or 20 lights of different sizes, and the MultisizeLightWindow object would not behave in a fundamentally different manner. In this case we cannot claim that MultisizeLightWindow objects of composed of multiple traffic light objects, but rather we say that MultisizeLightWindow objects contain an aggregate of traffic light objects. This concept is called aggregation. In some cases the line between composition and aggregation is not so clear cut and can be open to interpretation. Both aggregation and composition model the has a relationship between objects, but the composition model models a stronger relationship, the needs a relationship. Composition is sometimes called a part-whole relationship. We can illustrate the concept of composition using higher-level objects. Listing 14.1 (comptrafficlight.py) redesigns the traffic light class with more explicit composition in mind. Listing 14.1: comptrafficlight.py import tkinter as tk import tkinter.ttk as ttk class CompLamp: """ Serves as one lamp within a traffic light object. """ def __init__(self, parent, width, order, color="red", *args, **kwargs): """ Creates a new lamp to be used in a traffic light object. parent: The traffic light owning this lamp width: The width of the case of the circular lamp order: Distance of this lamp from the top of the traffic light color: The lamp's initial color (defaults to "red") *args: Additional arguments to pass to the ttk.Frame ©2017 Richard L. Halterman Draft date: January 18, 2018 14.1. COMPOSITION 515 superclass constructor **kwargs: Additional keyword arguments to pass to the ttk.Frame superclass constructor """ self.frame = ttk.Frame(parent.frame, *args, **kwargs) self.canvas = tk.Canvas(self.frame, width=width, height=width, bg="gray", highlightthickness=0) self.canvas.pack() self.color = color offset = width//8 self.lamp = self.canvas.create_oval(offset, offset, 7*offset, 7*offset, fill='black') # Place the lamp in its proper place in the traffic light self.frame.grid(row=order, column=0) self.state = "off" def turn_on(self): """ Illuminates the lamp """ self.state = "on" self.canvas.itemconfigure(self.lamp, fill=self.color) def turn_off(self): """ Turns off the lamp """ self.state = "off" self.canvas.itemconfigure(self.lamp, fill='black') def resize(self, width): self.canvas.config(width=width, height=width) offset = width//8 self.canvas.coords(self.lamp, offset, offset, 7*offset, 7*offset) class CompTrafficLight: """ Models a simple traffic light widget """ def __init__(self, root, wd, initial_color="red", *args, **kwargs): """ Makes a new traffic light object. root is the parent widget. wd is the pixels width. The light's initial color is initial_color. Clients may pass additional arguments to the constructor of the light's frame via *args and **kwargs. """ # Check to see if the supplied color is valid if initial_color not in ("red", "yellow", "green"): raise ValueError(initial_color + " is not a valid color") # Create the widget frame for the light self.frame = ttk.Frame(root, width=wd, *args, **kwargs) self.frame.grid(row=0, column=0) # Only widget in a 1x1 grid # Set initial color self.color = initial_color ©2017 Richard L. Halterman Draft date: January 18, 2018 14.1. COMPOSITION 516 # Make lamp objects and store them a dictionary keyed by # their color self.lamps = dict(zip(('red', 'yellow', 'green'), (CompLamp(self, wd, 0, 'red'), CompLamp(self, wd, 1, 'yellow'), CompLamp(self, wd, 2, 'green')))) # Turn on lamp for initial color self.lamps[self.color].turn_on() def change(self): """ Changes the traffic light's color to the next color in the sequence. """ # First, determine which color should be next if self.color == 'red': new_color = 'green' elif self.color == 'green': new_color = 'yellow' elif self.color == 'yellow': new_color = 'red' # Next, activate and deactivate the appropriate lamps self.lamps[self.color].turn_off() self.color = new_color self.lamps[self.color].turn_on() def resize(self, width): """ Changes the traffic light's frame width according to the parameter passed by the caller. """ for lamp in self.lamps.values(): lamp.resize(width) # Resize each lamp in the dictionary of lamps In Listing 14.1 (comptrafficlight.py), objects of the class CompLamp class form the building blocks for traffic lights. The CompTrafficLight class stores three of these lamp objects in a dictionary. This may appear to be aggregation, but for a traffic signal of this kind the quantity three is neither arbitrary nor variable, so in this case we safely can classify the lamps to traffic light relationship as composition. The constructor in the CompLamp class accepts four required arguments (self, parent, width, and order), one named default argument (color), and additional optional arguments (*args) and keyword arguments (**kwargs). The first five parameters are meant for the CompLamp class itself, and the *args and **kwargs arguments are meant for the ttk.Frame instance variable on which a CompLamp object relies to handle the graphics. The constructor makes these extra parameters available just in case a client requires special control over the style of the frame object. A CompLamp object basically is a rectangular Tk frame that contains a Tk canvas widget that draws a circular shape. A lamp has an “on” color and its “off” color is black. The turn_on and turn_off methods adjust the lamp’s color accordingly. The resize method allows clients to change the size of a lamp after its creation. The CompTrafficLight class specifies traffic light objects. Conceptually, a traffic light object is com- posed of lamp objects. The CompTrafficLight constructor accepts the optional *args and **kwargs to give clients additional control over the underlying Tk widgets that display the traffic light. The statement self.lamps = dict(zip(('red', 'yellow', 'green'), (CompLamp(self.frame, wd, 0, 'red'), CompLamp(self.frame, wd, 1, 'yellow'), ©2017 Richard L. Halterman Draft date: January 18, 2018 14.1. COMPOSITION 517 CompLamp(self.frame, wd, 2, 'green')))) uses a technique introduced in Section 11.3 to build a dictionary with keys selected, in order, from the first tuple paired with values selected, in order, from the second tuple. Each traffic light object maintains its own color state, and clients can change a light’s color via the change method. The resize method increases or decreases the size of the light by adjusting the sizes of the individual lamps. The dimensions of the frame of the traffic light will conform to the sizes of the lamps it holds—the Tk widgets take care of such details. Listing 14.2 (comptrafficlightapp.py) uses the comptrafficlight module’s CompTrafficLight class in yet another version of Listing 9.14 (tkinterlight.py) and Listing 13.9 (trafficlightobject.py). Listing 14.2: comptrafficlightapp.py import tkinter as tk import tkinter.ttk as ttk from comptrafficlight import CompTrafficLight class CompTrafficLightApp: """ Graphical window that displays a traffic light and change button. """ def __init__(self): root = tk.Tk() # Create the main window root.title("Traffic Light") # Set title bar text # Create widget container frame = ttk.Frame(root) frame.pack() # Create a graphical button and ensure it calls the do_button_press # method when the user presses it button = ttk.Button(frame, text='Change', command=self.do_button_press) # Make a traffic light object instance variable self.light = CompTrafficLight(frame, 100, padding=25) # Position button and canvas objects button.grid(row=0, column=0) self.light.frame.grid(row=0, column=1) # Start the GUI event loop root.mainloop() def do_button_press(self): """ The window manager calls this function when the user presses the graphical button. """ self.light.change() # Main program --------------------------------------------------------------------- # Create and execute a traffic light window CompTrafficLightApp() Note the following statement from the constructor: self.light = CompTrafficLight(frame, 100, padding=25) ©2017 Richard L. Halterman Draft date: January 18, 2018 14.2. CLASS INHERITANCE 518 This creates a CompTrafficLight object and takes advantage of the **kwargs parameter to add a padding of 25 pixels around the border of the light. This puts some additional space between the button and the traffic light image. Listing 14.1 (comptrafficlight.py) uses Tk widgets to produce the graphical images and deal with user interaction. These widgets are themselves Python objects. Our custom lamp and traffic light objects use Tk objects, but our custom objects and the Tk objects live in two different worlds. We developed our custom classes, and someone else developed the Tk classes. We must write extra code to allow our custom objects and Tk objects to interoperate correctly to achieve the effects we desire. This extra code is the price we pay for using a library that we did not write and, therefore, have no control over its contents. Our traffic light object must have an associated Tk frame object because we want to be able to do things with Tk frames. What if we could design a custom traffic light class that itself was a Tk Frame class? That could simplify our code considerably. Section 14.2 introduces the concept of inheritance which makes this possible. [Move below elsewhere] Section 13.6 presented the problem of graphically modeling the traffic lights in an intersection. Now we are ready to design the necessary classes and assemble an Intersection class using composition. [Move above elsewhere] 14.2 Class Inheritance CAUTION! SECTION UNDER CONSTRUCTION We can base a new class on an existing class using a technique known as inheritance. Recall our Stopwatch class we defined in Listing 13.6 (stopwatch.py). Clients can start and stop Stopwatch objects as often as necessary without resetting the time. Suppose we need a stopwatch object that records the number of times the watch has been started until it is reset. We can build our enhanced Stopwatch class from scratch, but it would more efficient to begin with our existing unadorned Stopwatch class and some- how add on the features we need. We will not merely copy the source code from our existing Stopwatch class and then add code to it. The inheritance mechanism does not touch the source code of our original Stopwatch class, and, at the same time, it allows us to write as little new code as possible. Listing 14.3 (countingstopwatch.py) provides an example of inheritance, defining the new class of our enhanced stop- watch objects. Listing 14.3: countingstopwatch.py from stopwatch import Stopwatch class CountingStopwatch(Stopwatch): def __init__(self): # Allow base class to do its initialization of the # inherited instance variables super().__init__() # Set number of starts to zero self._count = 0 def start(self): # Count this start message unless the watch already is running if not self._running: self._count += 1 # Let base class do its start code ©2017 Richard L. Halterman Draft date: January 18, 2018 14.2. CLASS INHERITANCE 519 super().start() def reset(self): # Let base class reset the inherited instance variables super().reset() # Reset new instance variable that the base class method does not know about self._count = 0 def count(self): return self._count The line from stopwatch import Stopwatch indicates the code in this module will somehow use the Stopwatch class from Listing 13.6 (stopwatch.py). The line class CountingStopwatch(Stopwatch): defines a new class named CountingStopwatch, but this new class is based on the existing class Stopwatch. This single line enables the CountingStopwatch class to inherit characteristics from the Stopwatch class. CountingStopwatch objects automatically will have start, stop, reset, and elapsed methods because the Stopwatch class has them. When only one class name appears within the parentheses, the kind of inheritance is called single inheritance. This section focuses on single inheritance, the most commonly used form of inheritance. Section 14.4 briefly examines multiple inheritance. We say Stopwatch is the superclass of CountingStopwatch. Another term for superclass is base class. CountingStopwatch is a subclass of Stopwatch, or, said another way, CountingStopwatch is a derived class of Stopwatch. Even though a subclass inherits all the methods of its superclass, a subclass may add new methods and provide new code for an inherited method. The new CountingStopwatch class has a constructor definition, as usual named __init__. When a class has exactly one superclass, the statement super().__init__() within its constructor definition invokes the constructor of its superclass. The expression super() thus refers to code in the superclass. The superclass constructor calls the reset method which establishes the _start_time, _elapsed, and _running instance variables. After executing the superclass constructor code, the subclass constructor defines and initializes a new instance variable named _count. What happens if you do not provide a constructor (__init__ method) for the subclass? In this case when creating an instance of the subclass the interpreter automatically will invoke the superclass construc- tor. If you do provide an __init__ constructor in a subclass, the interpreter will not call the superclass constructor—you must call the superclass constructor via the super function to ensure the initialization responsibilities of the superclass occur. Observe that the super() expression appears also in the start and reset methods in CountingStopwatch; in these methods super() similarly invokes the services of their namesake counterparts in the superclass. The count method is a brand new method not found in the superclass. Note the definitions of the start and reset methods. Because these methods have the same names as methods found in the superclass, we say that they override the inherited methods of the same name. A good ©2017 Richard L. Halterman Draft date: January 18, 2018 14.2. CLASS INHERITANCE 520 rule of thumb is this: you generally should invoke the super() version of the method within a method you are overriding. The super invocation within a method of a class that has exactly one superclass allows the superclass to manage the details known to the superclass. The subclass can take care of the details specific to the subclass via the rest of the code in the overridden method. Notice that the CountingStopwatch class has no apparent stop method. In fact, it does have a stop method because it inherits the stop method as is from the Stopwatch class. The start and reset methods in CountingStopwatch must work with the new __count instance variable and thus must be overridden, but the stop method needs no enhancement at all. Since stop needs no changes or additions, we omit its definition within the CountingStopwatch class. A derived class may inherit a method as is from its base class, or it may override the method. An overridden method may invoke the services of the base class version via super and add some additional functionality, or, less commonly, it may not use the base class version of the method at all and do something completely different. Listing 14.4 (usecountingsw.py) provides some sample client code that uses the CountingStopwatch class. Listing 14.4: usecountingsw.py from countingstopwatch import CountingStopwatch from time import sleep timer = CountingStopwatch() timer.start() sleep(10) # Pause program for 10 seconds timer.stop() print("Time:", timer.elapsed(), " Number:", timer.count()) timer.start() sleep(5) # Pause program for 5 seconds timer.stop() print("Time:", timer.elapsed(), " Number:", timer.count()) timer.start() sleep(20) # Pause program for 20 seconds timer.stop() print("Time:", timer.elapsed(), " Number:", timer.count()) Listing 14.4 (usecountingsw.py) produces Time: 10.010378278632945 Number: 1 Time: 15.016618866378108 Number: 2 Time: 35.02881993198008 Number: 3 For a more interactive, graphical example, consider Listing 14.5 (stopwatchplay.py). Listing 14.5: stopwatchplay.py import turtle as t from countingstopwatch import CountingStopwatch timer = CountingStopwatch() def draw_watch(sw): ©2017 Richard L. Halterman Draft date: January 18, 2018 14.2. CLASS INHERITANCE 521 """ Renders the stopwatch object sw in a digital hr:min:sec formmat. """ # Compute time in hours, minutes, and seconds seconds = round(sw.elapsed()) time = "" hours = seconds // 3600 # Compute total hours seconds %= 3600 # Update seconds remaining minutes = seconds // 60 # Compute minutes seconds %= 60 # Update seconds remaining # Each digit occupies two spaces; pad with leading zeros, if necessary time = "{0:0>2}:{1:0>2}:{2:0>2}”.format(hours, minutes, seconds)

# Draw graphical string
t.clear()
t.penup()
t.setposition(-200, 0)
t.pendown()
t.write(time, font=(“Arial”, 64, “normal”))
t.penup()
t.setposition(-50, -50)
t.pendown()
t.write(sw.count(), font=(“Arial”, 24, “normal”))

def quit():
“”” Quits the program. “””
t.bye()

def update():
“”” Updates the program’s view of the global stopwatch object. “””
draw_watch(timer) # Draw the digital display
t.ontimer(update, 500) # Call the update function again after one-half second

t.title(“Stopwatch Test”) # Set window’s titlebar text
t.onkey(timer.start, “s”) # Call start method of timer if user presses s
t.onkey(timer.stop, “t”) # Call stop method of timer if user presses t
t.onkey(timer.reset, “r”) # Call reset method of timer if user presses r
t.onkey(quit, “q”) # Call quit function if user presses r
t.listen() # Ensure window receives keyboard events
t.delay(0) # Draw as fast as possible
t.speed(0) # Fastest turtle actions
t.ontimer(update, 500) # Call update function every one-half second
t.hideturtle() # Do not show the pen when drawing
t.mainloop() # Start the show

Figure 14.1 shows a screenshot of Listing 14.5 (stopwatchplay.py) in the middle of a sample run. The
smaller number below the digital readout represents the number of times the user has started the stopwatch
from a nonrunning state. Pressing the S key starts the clock running. The T key stops the clock, and
the R resets the clock back to 00:00:00. Attempts to start the stopwatch when it already is running will
not increment the count.

Section 2.1 introduced Python’s type function. The type function returns the exact type of an object.
A related function named isinstance returns True or False revealing whether or not its first argument (an
expression) is an instance of the type specified by its second argument. The following interactive sequence

14.2. CLASS INHERITANCE 522

Figure 14.1 The program in Listing 14.5 (stopwatchplay.py) in the middle of a sample run. The smaller
number below the digital readout represents the number of times the stopwatch as been started.

14.2. CLASS INHERITANCE 523

illustrates (the Stopwatch type used in the sequence is from Listing 13.6 (stopwatch.py)):

>>> type(5)

>>> isinstance(5, int)
True
>>> isinstance(5, float)
False
>>> isinstance(5, str)
False
>>> x = 2
>>> isinstance(x, int)
True
>>> type(x + 4.5)

>>> isinstance(x + 4.5, int)
False
>>> isinstance(x + 4.5, float)
True
>>> from stopwatch import Stopwatch
>>> sw = Stopwatch()
>>> isinstance(sw, Stopwatch)
True
>>> isinstance(sw, int)
False
>>> isinstance(sw, str)
False

This all appears to be in order. Now we will see how inheritance makes things more interesting. Consider
the following new interactive session (the Stopwatch type is from Listing 13.6 (stopwatch.py), and the
CountingStopwatch type is from Listing 14.3 (countingstopwatch.py)):

>>> from stopwatch import Stopwatch
>>> from countingstopwatch import CountingStopwatch
>>> sw = Stopwatch()
>>> csw = CountingStopwatch()
>>> type(sw)

>>> type(csw)

>>> isinstance(sw, Stopwatch)
True
>>> isinstance(csw, CountingStopwatch)
True
>>> isinstance(sw, CountingStopwatch)
False
>>> isinstance(csw, Stopwatch)
True

The type function reveals that the sw variable refers to an object of type Stopwatch and csw refers to an
object of type CountingStopwatch. It follows that the isinstance function indicates that sw refers to an
object that is an instance of Stopwatch. Similarly, csw’s object is an instance of CountingStopwatch. Not
surprisingly, isinstance indicates that sw is not an instance of CountingStopwatch. Perhaps surprisingly,
however, we see that csw is an instance of both the CountingStopwatch class and Stopwatch class!

14.2. CLASS INHERITANCE 524

Inheritance establishes a special relationship between two classes. An instance of a derived class is also
an instance of the base class. In object-oriented software terminology this known as the is a relationship.
The major benefit of this is a relationship is this: an instance of a derived class may safely be used in any
context meant to work with an instance of its base class. Suppose we write a function for timing a particular
process:

def time_process(timer):
# Details omitted . . .

The parameter is supposed to be a reference to a Stopwatch object. As such the time_process function
can exercise any methods that a Stopwatch object provides: start, stop, and reset. Any class derived
from Stopwatch will automatically inherit these methods and may or may not override their behavior.
Regardless, the code within the time_process function legitimately may call the start, stop, or reset
method on a timer object if its actual type is Stopwatch or CountingStopwatch (or any other class we
may derive from Stopwatch).

Suppose we wish to use counting stopwatch objects that limit the number of times the clock can be
stopped and restarted. Listing 14.6 (restrictedstopwatch.py) provides the RestrictedStopwatch class def-
inition that leverages the capabilities of the CountingStopwatch object via inheritance:

Listing 14.6: restrictedstopwatch.py

from countingstopwatch import CountingStopwatch

class RestrictedStopwatch(CountingStopwatch):
def __init__(self, n):

“”” Restrict the number stopwatch starts to n times. “””
# Allow superclass to do its initialization of the
# inherited instance variables
super().__init__()
self._limit = n

def start(self):
“”” If the count exceeds the limit, terminate the program’s

execution. “””
if self._count < self._limit: super().start() # Let superclass do its start code else: import sys print("Limit exceeded") sys.exit(1) # Limit exceeded, terminate the program Listing 14.7 (testrestrictedsw.py) exercises the RestrictedStopwatch class. Listing 14.7: testrestrictedsw.py from restrictedstopwatch import RestrictedStopwatch sw = RestrictedStopwatch(3) print("Starting 1") sw.start() print("Stopping 1") sw.stop() print("Starting 2") ©2017 Richard L. Halterman Draft date: January 18, 2018 14.2. CLASS INHERITANCE 525 sw.start() print("Stopping 2") sw.stop() print("Starting 3") sw.start() print("Stopping 3") sw.stop() print("Starting 4") sw.start() print("Stopping 4") sw.stop() print("Done") The following shows the program’s output: Starting 1 Stopping 1 Starting 2 Stopping 2 Starting 3 Stopping 3 Starting 4 Limit exceeded The attempt to restart the clock past its limit of three attempts terminates the program. Listing 14.6 (restrictedstopwatch.py) derives RestrictedStopwatch from CountingStopwatch. The CountingStopwatch class has Stopwatch as its base class. We say that CountingStopwatch is a direct base class of RestrictedStopwatch and Stopwatch is an indirect base class of RestrictedStopwatch. The inheritance is transitive: since RestrictedStopwatch inherits from CountingStopwatch and CountingStopwatch inherits from Stopwatch, it is the case that RestrictedStopwatch inherits from Stopwatch as well. We can demonstrate this transitivity in the interactive interpreter: >>> from stopwatch import Stopwatch
>>> from countingstopwatch import CountingStopwatch
>>> from restrictedstopwatch import RestrictedStopwatch
>>> rsw = RestrictedStopwatch(3)
>>> isinstance(rsw, RestrictedStopwatch)
True
>>> isinstance(rsw, CountingStopwatch)
True
>>> isinstance(rsw, Stopwatch)
True

As we can see, the rsw variable refers to an object that simultaneously is a RestrictedStopwatch,
CountingStopwatch, and plain Stopwatch.

When we say simply “class A is a base class of B,” A could be either a direct or indirect base class of B.
Similarly, when we say “B inherits from A,” the inheritance could be direct or indirect. Generally speaking,
however, when we omit the qualifier direct or indirect in this context, we usually mean direct.

In Python, the built-in class object serves as the direct or indirect base class for all other types. All
types (except object) inherit from object. The following demonstrates:

>>> from stopwatch import Stopwatch

14.2. CLASS INHERITANCE 526

>>> from countingstopwatch import CountingStopwatch
>>> from restrictedstopwatch import RestrictedStopwatch
>>> sw = Stopwatch()
>>> csw = CountingStopwatch()
>>> rsw = RestrictedStopwatch(3)
>>> isinstance(rsw, object)
True
>>> isinstance(sw, object)
True
>>> isinstance(4, object)
True
>>> isinstance(4.5, object)
True
>>> isinstance(“Wow”, object)
True
>>> obj = object()
>>> isinstance(obj, object)
True

The following class definition:

class Widget:
pass

is an abbreviation for the following:

class Widget(object):
pass

This means object is the implied direct base class for any class that does not specify an explicit base class.

Suppose we derive another class from Stopwatch, one with a new method that returns a string con-
taining the digital representation of the time, similar to the way the graphical program in Listing 14.5
(stopwatchplay.py) displays the elapsed time. Listing 14.8 (digitalstopwatch.py) provides such a class.

Listing 14.8: digitalstopwatch.py

from stopwatch import Stopwatch

class DigitalStopwatch(Stopwatch):
def digital_time(self):

“”” Returns a string representation of the elapsed time
in hours : minutes : seconds. “””

# Compute time in hours, minutes, and seconds
seconds = round(self.elapsed())
hours = seconds // 3600 # Compute total hours
seconds %= 3600 # Update seconds remaining
minutes = seconds // 60 # Compute minutes
seconds %= 60 # Update seconds remaining
# Each digit occupies two spaces; pad with leading zeros, if necessary
return “{0:0>2}:{1:0>2}:{2:0>2}”.format(hours, minutes, seconds)

Listing 14.9 (testdigitalsw.py) exercises the DigitalStopwatch class.

Listing 14.9: testdigitalsw.py

14.2. CLASS INHERITANCE 527

Figure 14.2 A Unified Modeling Language diagram representing the Stopwatch class hierarchy. A rectan-
gle represents a class, and an arrow points from a derived class to its base class. As shown here, the object
class is the ultimate superclass of all Python classes.

CountingStopwatch

RestrictedStopwatch

DigitalStopwatch

Stopwatch

object

from digitalstopwatch import DigitalStopwatch
from time import sleep

dsw = DigitalStopwatch()
dsw.start() # Start the timer
sleep(140) # Do noting for 2:20
dsw.stop() # Stop the timer
print(dsw.digital_time()) # Print elapsed time in digital format

The DigitalStopwatch class does not add any new instance variables and does not modify how existing
methods work; it simply adds a new method. When executed, the program appears to do nothing for 140
seconds (two minutes and 20 seconds) and then prints

00:02:20

At this point we have several classes derived from Stopwatch. A collection of classes related through
inheritance is called a class hierarchy, or inheritance hierarchy. Figure 14.2 illustrates the Stopwatch
hierarchy using a standard graphical notation known as the Unified Modeling Language, or UML (see
http://www.uml.org). In the UML, a rectangle represents a class, and an arrow with a hollow arrowhead
points from a derived class to its immediate base class. A UML class diagram such as the one in Figure 14.2
communicates to developers the relationships amongst the classes more quickly than the textual Python

http://www.uml.org

14.2. CLASS INHERITANCE 528

source code potentially spread out over multiple files.

Section 14.1 alluded to the conceptual mismatch between the custom classes from Listing 14.1 (comptrafficlight.py)
and the standard Tk widget classes on which the custom classes depend. Inheritance provides a way to unify
these two distinct sets of classes. We can build custom Tk widgets from existing Tk widget classes using
inheritance. Listing 14.10 (trafficsignal.py) uses both composition and inheritance in the design of a new
traffic light class called TrafficSignal.

Listing 14.10: trafficsignal.py

import tkinter as tk
import tkinter.ttk as ttk

class SignalLamp(ttk.Frame):
“”” Serves as one lamp within a traffic light object. “””

def __init__(self, parent, width, color=”red”, *args, **kwargs):
“”” Creates a new lamp to be used in a traffic light object.

parent: The parent widget
width: The width of the case of the circular lamp
color: The lamp’s initial color (defaults to “red”)
*args: Additional arguments to pass to the ttk.Frame

superclass constructor
**kwargs: Additional keyword arguments to pass to the

ttk.Frame superclass constructor “””
super().__init__(parent, *args, **kwargs)
self.canvas = tk.Canvas(self, width=width, height=width, bg=”gray”,

highlightthickness=0)
self.canvas.pack()
self.color = color
offset = width//8
self.lamp = self.canvas.create_oval(offset, offset,

7*offset,
7*offset,
fill=’black’)

self.state = “off”

def turn_on(self):
“”” Illuminates the lamp “””
self.state = “on”
self.canvas.itemconfigure(self.lamp, fill=self.color)

def turn_off(self):
“”” Turns off the lamp “””
self.state = “off”
self.canvas.itemconfigure(self.lamp, fill=’black’)

def resize(self, width):
“”” Adjusts the width of the lamp’s frame “””
self.canvas.config(width=width, height=width)
offset = width//8
self.canvas.coords(self.lamp, offset, offset, 7*offset, 7*offset)

14.2. CLASS INHERITANCE 529

class TrafficSignal(ttk.Frame):
“”” Models a simple traffic light widget “””

def __init__(self, parent, wd, initial_color=”red”, *args, **kwargs):
“”” Makes a new traffic light object.

parent is the parent widget.
wd is the pixels width.
The light’s initial color is initial_color. “””

super().__init__(parent, width=wd, *args, **kwargs)

# Check to see if the supplied color is valid
if initial_color not in (“red”, “yellow”, “green”):

raise ValueError(initial_color + ” is not a valid color”)

self.grid(row=0, column=0) # Only widget in a 1×1 grid
# Initialize instance variables
self.color = initial_color

# Make lamp objects and store them a dictionary keyed by
# their color
self.lamps = dict(zip((‘red’, ‘yellow’, ‘green’),

(SignalLamp(self, wd, ‘red’),
SignalLamp(self, wd, ‘yellow’),
SignalLamp(self, wd, ‘green’))))

# Add the lamps to the frame
self.lamps[‘red’].grid(row=0, column=0)
self.lamps[‘yellow’].grid(row=1, column=0)
self.lamps[‘green’].grid(row=2, column=0)

# Turn on lamp for initial color
self.lamps[self.color].turn_on()

def change(self):
“”” Changes the traffic light’s color to the next color in

the sequence. “””
if self.color == ‘red’:

new_color = ‘green’
elif self.color == ‘green’:

new_color = ‘yellow’
elif self.color == ‘yellow’:

new_color = ‘red’
self.lamps[self.color].turn_off()
self.color = new_color
self.lamps[self.color].turn_on()

def resize(self, width):
“”” Changes the traffic light’s frame width according to the

parameter passed by the caller. “””
for lamp in self.lamps.values():

lamp.resize(width)

Before, a traffic light lamp object had a Tk frame object; now, a traffic light lamp object is a Tk frame
object. Similarly, a traffic light object is a Tk frame object. Listing 14.11 (newtrafficlightapp.py) is our final

14.2. CLASS INHERITANCE 530

installment of the button-controlled traffic light image found in Listing 9.14 (tkinterlight.py), Listing 13.9
(trafficlightobject.py), and Listing 14.2 (comptrafficlightapp.py).

Listing 14.11: newtrafficlightapp.py

import tkinter as tk
import tkinter.ttk as ttk

from trafficsignal import TrafficSignal

class NewTrafficLightApp:
“”” Graphical window that displays a traffic light and change button. “””

def __init__(self):
root = tk.Tk() # Create the main window
root.title(“Traffic Light”) # Set title bar text
# Create widget container
frame = ttk.Frame(root)
frame.pack()
# Create a graphical button and ensure it calls the do_button_press
# method when the user presses it
button = ttk.Button(frame, text=’Change’, command=self.do_button_press)
# Create and add a drawing surface within the window
# Make a traffic light object instance variable
self.light = TrafficSignal(frame, 100, padding=25)
#self.light.config(padding=25)
# Position button and canvas objects
button.grid(row=0, column=0)
self.light.grid(row=0, column=1)
# Start the GUI event loop
root.mainloop()

def do_button_press(self):
“”” The window manager calls this function when the user

presses the graphical button. “””
self.light.change()

# Main program ———————————————————————

# Create and execute a traffic light window
NewTrafficLightApp()

Our redesigned TrafficSignal class and inheritance makes it easy to add functionality by adding new
traffic light types. Listing 14.12 (movablelight.py) augments the TrafficSignal class, enabling clients to
reposition the traffic light’s center to a given (x,y) location within the graphics window.

Listing 14.12: movablelight.py

import tkinter as tk
import tkinter.ttk as ttk

from trafficsignal import TrafficSignal

14.2. CLASS INHERITANCE 531

class MovableLight(TrafficSignal):
“”” Models a graphical traffic light that the user can reposition “””

def __init__(self, parent, width, initial_color=”red”):
“”” Makes a new movable traffic light object. The light’s

parent is the parent widget
The width of the light is width pixels.
The light’s initial color is initial_color. “””

# Call base class constructor
super().__init__(parent, width, initial_color)
self.place(x=0, y=0)

def move_to(self, x, y):
“”” Positions the light’s center at point (x, y) “””
center_x_offset = self.winfo_width() // 2
center_y_offset = self.winfo_height() // 2
self.x = x – center_x_offset
self.y = y – center_y_offset
self.place(x=self.x, y=self.y)

Listing 14.13 (movablelighttest.py) is a small application that allows the user to move the traffic light image
to various places in the window via mouse click. The user changes the light by pressing the C key. The
program also exercises the inherited resize method by allowing the user to press the < key to shrink or > to grow the traffic light object.

Listing 14.13: movablelighttest.py

import tkinter as tk
import tkinter.ttk as ttk

from movablelight import MovableLight

class MovableLightTest:
“”” Graphical window that allows a user to move and resize

a traffic light object. “””

def __init__(self):
root = tk.Tk() # Create the main window
root.title(“Movable Traffic Light Test”) # Set title bar text
width, height = 800, 600
f = ttk.Frame(root, width=width, height=height)
f.pack()
# Place traffic light at the center of the window frame
print(“Frame width:”, f.winfo_width())
self.light_width = height//10
self.light = MovableLight(f, self.light_width, “green”)
f.bind(““, self.mouse_pressed)
f.bind(““, self.key_pressed)
f.focus_set() # Allow graphical window to receive key strokes
print(“width//2 =”, width//2, ” height//2 =”, height//2)
self.light.move_to(width//2, height//2)
# Start the GUI event loop
root.mainloop()

14.2. CLASS INHERITANCE 532

def mouse_pressed(self, event):
“”” The window manager calls this function when the user

presses the graphical button. “””
self.light.move_to(event.x, event.y)

def key_pressed(self, event):
“”” The window manager calls this function when the user

presses the graphical button. “””
ch = event.char
if ch == “>” or ch == “.”:

self.light_width += 5
self.light.resize(self.light_width)

def mouse_pressed(self, event):
“”” The window manager calls this function when the user

presses the graphical button. “””
self.light.move_to(event.x, event.y)
print(“Mouse pressed at”, event.x, “,”, event.y)

def key_pressed(self, event):
“”” The window manager calls this function when the user

presses the graphical button. “””
ch = event.char

14.2. CLASS INHERITANCE 535

Figure 14.3 Sample execution of Listing 14.15 (turnlighttest.py). The user can move the light by clicking
at a location within the window, and the keyboard controls the light’s size and color state.

if ch == “>” or ch == “.”:
print(“Resize not implemented”)
self.size += 1
self.light.resize(self.size)

elif ch == “<" or ch == ",": print("Resize not implemented") self.size -= 1 self.light.resize(self.size) elif ch == "C" or ch == "c": self.light.change() print("Key pressed") # Main program --------------------------------------------------------------------- # Create and execute a traffic light window TurnLightTest() Figure 14.3 shows a sample execution of Listing 14.15 (turnlighttest.py). Review the code in Listing 14.13 (movablelighttest.py) and Listing 14.15 (turnlighttest.py). Do you see anything troubling in the two applications? The two programs look almost identical. Both programs present the same interface to the user; that is, the same reactions to mouse clicks and button presses. The only differ- ence is the exact type of traffic light the user can manipulate. Listing 14.13 (movablelighttest.py) hardwires a MovableLight object into the code, while Listing 14.15 (turnlighttest.py) instead uses a TurnLight. Section 7.5 enumerates the disadvantages of code duplication. How can we eliminate the duplicated code in these two applications? We can parameterize the type of traffic light the program creates. List- ing 14.16 (parammovable.py) allows the user to select the type of light to manipulate. Listing 14.16: parammovable.py import tkinter as tk import tkinter.ttk as ttk ©2017 Richard L. Halterman Draft date: January 18, 2018 14.2. CLASS INHERITANCE 536 from movablelight import MovableLight from turnlight import TurnLight class ParameterizedMovable: """ Graphical window that allows a user to move and resize a traffic light object. """ def __init__(self, light_class): """ Creates a ParameterizedLightTester. light_class is the type of light to create; it must be MovableLight or one of its subclasses. """ root = tk.Tk() # Create the main window root.title("Movable Traffic Light Test") # Set title bar text width, height = 800, 600 f = ttk.Frame(root, width=width, height=height) f.pack() # Place traffic light at the center of the window frame print("Frame width:", f.winfo_width()) self.light_width = height//10 self.light = light_class(f, self.light_width, "green") f.bind("“, self.mouse_pressed)
f.bind(““, self.key_pressed)
f.focus_set() # Allow graphical window to receive key strokes
print(“width//2 =”, width//2, ” height//2 =”, height//2)
self.light.move_to(width//2, height//2)
# Start the GUI event loop
root.mainloop()

def mouse_pressed(self, event):
“”” The window manager calls this function when the user

presses the graphical button. “””
self.light.move_to(event.x, event.y)

def key_pressed(self, event):
“”” The window manager calls this function when the user

presses the graphical button. “””
ch = event.char
if ch == “>” or ch == “.”:

self.light_width += 5
self.light.resize(self.light_width)

elif ch == “<" or ch == ",": self.light_width -= 5 self.light.resize(self.light_width) elif ch == "C" or ch == "c": self.light.change() print("Key pressed") # Main program --------------------------------------------------------------------- # Create and execute a traffic light window print("What kind of light do you want play with?") light = input("S)tandard T)urn: ").upper() if light == 'S': ©2017 Richard L. Halterman Draft date: January 18, 2018 14.3. COMPOSITION VS. INHERITANCE 537 ParameterizedMovable(MovableLight) # Passing class, not an instance elif light == 'T': ParameterizedMovable(TurnLight) # Passing class, not an instance else: print(light, "is not a valid choice") We used a small bit of nongraphical code to allow the user to choose between the two traffic light types. The constructor of the ParameterizedMovable class in Listing 14.16 (parammovable.py) accepts a class, not an instance of a class, as an argument. We can do this because a class in Python is a real object (see Section 13.10). 14.3 Composition vs. Inheritance CAUTION! SECTION UNDER CONSTRUCTION Often we can choose between using composition or inheritance to leverage the functionality of an ex- isting class. The better choice is not always apparent. We can achieve the effects of inheritance using strictly composition and delegation. Our CountingStopwatch class in Listing 14.3 (countingstopwatch.py) uses inheritance to create the CountingStopwatch class from the simpler Stopwatch class. Listing 14.17 (countingstopwatch2.py) defines the class CountingStopwatch2 that behaves identically to CountingStopwatch, but it uses composition to reuse the functionality of Stopwatch. Clients would not perceive any functional differences between a CountingStopwatch instance and a CountingStopwatch2 instance. Listing 14.17: countingstopwatch2.py from stopwatch import Stopwatch class CountingStopwatch2: """ This counting stopwatch uses composition instead of inheritance. """ def __init__(self): # Create a stopwatch object to keep the time self.watch = Stopwatch() # Set number of starts to zero self._count = 0 def start(self): # Count this start message unless the watch already is running if not self.watch._running: self._count += 1 # Delegate other work to the stopwatch object self.watch.start() def stop(self): # Delegate to stopwatch object self.watch.stop() def reset(self): # Let the stopwatch object reset the time watch.reset() # Reset the count ©2017 Richard L. Halterman Draft date: January 18, 2018 14.3. COMPOSITION VS. INHERITANCE 538 self._count = 0 def elapsed(self): # Delegate to stopwatch object return self.watch.elapsed() def count(self): return self._count In order to retrofit Listing 14.4 (usecountingsw.py) to use our new counting stopwatch class change the import line from countingstopwatch import CountingStopwatch to be from countingstopwatch2 import CountingStopwatch2 and change the statement timer = CountingStopwatch() to be timer = CountingStopwatch2() With these changes the program works exactly the same as before. Apply the same changes to Listing 14.5 (stopwatchplay.py), and you will see similar results. While the inheritance version and the composition version both accomplish the same goals from the client’s perspective, notice that the composition version requires more code. With inheritance, if a method from the superclass needs no changes, the programmer omits its definition in the subclass. With compo- sition, however, every method meant to be used by clients in the original class must have a definition in the new class. If the new class does not need to change the method in any way, it simply delegates the work to the contained instance of the original class. We see this in the stop and elapsed methods in CountingStopwatch2. This can make a big difference in the work required to design a new class if the original class has many methods that need no change. We must maintain the interface of the original class if we to simulate the is a relationship without using inheritance. Good object-oriented designs often combine composition and inheritance to achieve useful results. Sup- pose we are building a software system that manages a manufacturing process. A physical temperature sensor attached to a piece of equipment relays temperature information to the software via a software ob- ject. The software expects to receive an instance of the TemperatureSensor class from the sensor. The TemperatureSensor class provides only two methods: read, which returns the current temperature in degrees Celsius of its attached hardware, and test, which puts the sensor into a self test mode. The soft- ware on the physical sensor that sends the TemperatureSensor objects to the system is propriety, and its license forbids reverse engineering to change its behavior. You are stuck with sensors that provide TemperatureSensor objects. Fortunately, since the part of the software system that uses the information sent by the sensors is made by the same company that provides the sensors, everything works well together. One day your company decides to replace the existing equipment management software with a new sys- tem offered by another vendor. The new system provides much greater control and monitoring capabilities, and the cost of the annual licensing fees are lower than the exiting system. There is a problem, however. The new system expects different kinds of sensors on the equipment to monitor. The sensors the new soft- ware requires send information via objects of type ThermalValue. The ThermalValue class provides only ©2017 Richard L. Halterman Draft date: January 18, 2018 14.3. COMPOSITION VS. INHERITANCE 539 a temperature method that returns the current temperature in degrees Fahrenheit. The new software does not provide the ability to self test a sensor. The overall manufacturing process uses hundreds of very expensive sensors. The cost to replace all the perfectly-functioning current sensors with sensors compatible with the new software would be enormous. Does you company have to forgo the software upgrade that can reduce costs and improve the manufacturing process? Fortunately there is a simple software solution. The following class adapts old, TemperatureSensor objects to work with the newer software that expects ThermalValue objects: class TemperatureSensorAdapter(ThermalValue): """ Adapts a TemperatureSensor object to appear as a ThermalValue object. """ def __init__(self, sensor): """ sensor is the TemperatureSensor object to adapt """ self._sensor = sensor def temperature(self): """ Converts the sensor input from Celsius to Fahrenheit """ return 9 * self._sensor.read() / 5 + 32 All you need to do is intercept the TemperatureSensor object from an existing sensor, create a new TemperatureSensorAdapter object from that TemperatureSensor object, and then send this TemperatureSensorAdapter object on to the new management and monitoring software. The new system receives a ThermalValue object, because a TemperatureSensorAdapter object is a ThermalValue object. Inheritance guarantees the is a relationship. The temperature method delegates most of its work to the contained TemperatureSensor object. The TemperatureSensor object provides the temperature, and the method merely needs to convert the temperature from Celsius to Fahrenheit to conform to the expectations of the new system. Since ThermalValue objects have no test method, we know the new software system will never at- tempt to call it. It is functionality that the TemperatureSensor provides that will never be used, so we safely can ignore it. Note that this solution uses both inheritance and composition. It is an example of an object-oriented design pattern. A design pattern provides a solution to a commonly occurring problem in software design (see https://en.wikipedia.org/wiki/Software design pattern). A design pattern does not provide an exact solution to a given problem; it instead shows how techniques such as inheritance and composition may be applied to solve problems of a particular kind. The link above describes over 50 design patterns. Each design pattern has a name, and the design pattern involved in our TemperatureSensorAdapter class is aptly named adapter. Our TemperatureSensorAdapter class adapts both the interface (the pro- vided method is named read, but the required method name is temperature) and computation (the pro- vided units are degrees Celsius, but the required units are degrees Fahrenheit). The adapter pattern is sometimes called the wrapper pattern because object serves as a wrapper around another object. In our example, a TemperatureSensorAdapter object wraps a ThermalValue object. Section 14.4 provides a working example of the use of the adapter design pattern. When it comes to choosing composition or inheritance for class resuse, which should you use? The prevailing wisdom says to prefer composition over inheritance. Composition provides greater flexibility at the cost of potentially more code to write. When you feel tempted to use inheritance, ask yourself if an ©2017 Richard L. Halterman Draft date: January 18, 2018 https://en.wikipedia.org/wiki/Software_design_pattern 14.4. MULTIPLE INHERITANCE 540 instance the new class philosophically is an instance of the original class. If the is a relationship makes sense, inheritance is probably the better choice; otherwise, use composition. Consider a motor vehicle. The drive train of a motor vehicle contains (sounds like composition) axles and wheels, among other essential parts. Each axle assembly consists of an axle and two wheels. Would it make sense to derive an axle assembly class from an axle class and add a left wheel object and a right wheel object as new instance variables? While this would work, we must ask: Is an axle assembly an axle (is a relationship)? No, an axle assembly has an axle and has two wheels (has a relationships), so composition is the better choice in this case. 14.4 Multiple Inheritance CAUTION! SECTION UNDER CONSTRUCTION In Python we can derive a class from multiple base classes through a technique known as multiple inheritance. This allows a class to blend the traits from more than one existing classes. Single inheritance is fairly straightforward, but the issues involved with multiple inheritance can be complex and subtle. One problem is ambiguity. Consider the following class definitions: class A(object): def f(self): print("A's f method") class B(object): def f(self): print("B's f method") class C(A): pass class D(A, B): pass Now consider an instance of class C: c_obj = C() What does the following print, if anything? c_obj.f() We do not see a method named f defined within class C, but its superclass, A, provides an f method; therefore, the statement prints A's f method because c_obj executes the f it inherits from its superclass. Next, we will create a D object, as shown here: d_obj = D() ©2017 Richard L. Halterman Draft date: January 18, 2018 14.4. MULTIPLE INHERITANCE 541 Class D does not override f, but it inherits method f from both A and B. The problem is this: A.f and B.f do two different things. What should the following statement print? d_obj.f() Does inheritance give favor to class A’s f method and exclude B’s f method? Does it instead invoke class B’s f method to the exclusion of A’s f method? Perhaps it executes both A’s f method and B’s f method? The statement actually prints A's f method Only one method executes, and it’s A’s method. If we modify the class definition of D to be class D(B, A): # Note change in base class ordering pass and change none of the other classes, the statement d_code.f() prints B's f method Changing the order of the listed superclasses in the class definition changes the behavior of the statement. This sensitivity to base class ordering and the ambiguity introduced when inheriting identically-named methods from multiple superclasses are just two of the issues that make multiple inheritance tricky. Python supports a kind of multiple inheritance called cooperative multiple inheritance. This means programmers must implement each class involved in a multiple inheritance hierarchy in a careful way to ensure every thing works properly. This also means it is more work (but not impossible) to involve a class in a multiple inheritance hierarchy that was not designed with multiple inheritance in mind. Multiple inheritance is not used as much as single inheritance; in fact, several widely-used modern object-oriented programming languages provide single inheritance but do not support multiple inheritance in the Python way does. Because multiple inheritance is a useful tool in some situations we will examine it briefly. Our foray into multiple inheritance requires a gentle warning. Python distinguishes itself from most other programming languages due to its relatively simple and straightforward way of allowing programmers to express solutions to problems. Python ordinarily presents a very low barrier for transforming thought into code. Programmers must be diligent at all times, of course, but, in order to implement multiple inheritance in a sound way, Python requires programmers to take extra when designing with multiple inheritance. Remember the ambiguity in subclasses introduced by multiple inheritance when superclass methods have the same name? We could be careful and make sure the methods in all our classes have unique names. Would this approach eliminate the ambiguity problem at the expense, perhaps, of creating mangled, unnatural names for some of our methods? Potentially convoluted names definitely are not a good idea, and, besides, this approach would not eliminate the ambiguity problem. Some methods have names that cannot change; for example, class constructors always are named __init__. To explore the complexities of multiple inheritance with constructors, consider the following two classes: class A(object): def __init__(self): ©2017 Richard L. Halterman Draft date: January 18, 2018 14.4. MULTIPLE INHERITANCE 542 print("Making an A object") self.value_A = 0 class B(object): def __init__(self): print("Making a B object") self.value_B = 1 Suppose now we define class C as class C(A, B): pass Our intention is that C objects should combine the capabilities of A objects and B objects; we want every C object to have both value_A and value_B instance variables. With single inheritance everything would work as expected. We do not provide a constructor for C, so, as with single inheritance, the creation of a C object would execute the superclass __init__ method, if it exists. Given our earlier experiment with multiple inheritance, what would you expect the following code to print? c_obj = C() # Make a C object print("===========") print(c_obj.__dict__) # Look at its instance variables Since class A was listed first in the list of superclasses, it prints Making an A object =========== {'value_A': 0} The creation of c_obj properly initialized only the A part of c_obj. As in single inheritance, adding a subclass constructor without calling super prevents any superclass constructors front executing. To show this, rewrite class C as class C(A, B): def __init__(self): print("Making a C object") self.value_C = 2 With this change the following code: c_obj = C() print("===========") print(c_obj.__dict__) prints Making a C object =========== {'value_C': 2} So we see neither the A initialization nor the B initialization occurred. As with single inheritance, we need to add a call to super: ©2017 Richard L. Halterman Draft date: January 18, 2018 14.4. MULTIPLE INHERITANCE 543 class C(A, B): def __init__(self): print("Making a C object") super().__init__() self.value_C = 2 but the result is still not quite what we want: Making a C object Making an A object =========== {'value_C': 2, 'value_A': 0} The construction process still omits the B constructor. The solution is to add a super call to all classes that are part of the multiple inheritance hierarchy: class A(object): def __init__(self): print("Making an A object") super().__init__() self.value_A = 0 class B(object): def __init__(self): print("Making a B object") super().__init__() self.value_B = 1 class C(A, B): def __init__(self): print("Making a C object") super().__init__() self.value_C = 2 Now when we create a C object, as in c_obj = C() print("===========") print(c_obj.__dict__) we finally achieve the desired behavior: Making a C object Making an A object Making a B object =========== {'value_B': 1, 'value_C': 2, 'value_A': 0} C objects now have all the expected instance variables and are properly initialized. The story does not end here, unfortunately. None of the constructors in our A, B, or C classes specified any parameters. What if one superclass contains an __init__ method that expects certain parameters, while another superclass specifies a different number and/or different types of parameters? If we change class B’s definition to be ©2017 Richard L. Halterman Draft date: January 18, 2018 14.4. MULTIPLE INHERITANCE 544 class B(object): def __init__(self, val): print("Making a B object") super().__init__() self.value_B = val and leave the definitions for class A and class C untouched, an attempt to create a C instance produces the following exception: Making a C object Making an A object Traceback (most recent call last): File "mi3_init.py", line 23, in
c_obj = C()

File “mi3_init.py”, line 16, in __init__
super().__init__()

File “mi3_init.py”, line 4, in __init__
super().__init__()

TypeError: __init__() missing 1 required positional argument: ‘val’

A’s constructor expects no arguments, while B’s constructor now requires a parameter to assign to its instance
variable. How can super.__init__() be called once and support passing different parameters to different
superclass constructors?

Python provides a couple of ways to address this dilemma. One is a “quick-and-dirty” fix, and the other
is the preferred approach. The quick-and-dirty fix works like this:

1. Remove the super calls from the constructors in classes A and B. Without removing these calls the
quick-and-dirty fix will fail in a manner similar to before.

2. Rewrite class C’s definition as follows:

class C(A, B):
def __init__(self):

print(“Making a C object”)
A.__init__(self)
B.__init__(self, 5)
self.value_C = 2

This approach explicitly calls the constructors for classes A and B directly.

This quick-and-dirty fix achieves the desired behavior in this case, but it makes for a far less flexible
design. If we add another superclass to class C’s list of superclasses, we must modify the code in C’s
constructor to work properly with the constructor of the additional superclass. Also, by removing the
super().__init__() calls in A and B, we render both classes unable to work properly if we want to
involve them in a better designed multiple inheritance hierarchy of classes.

The better design is more flexible and opens the door to more powerful programming techniques than
would be possible with the quick-and-dirty approach. We can call multiple superclass constructors that
expect a variety of different arguments by using keyword arguments, introduced in Section 11.7. The
following points outline a working design for object construction within the context of multiple inheritance:

1. Define one dummy class that inherits directly from the built-in object class. Its name can be any
valid identifier; here we will refer to it as Top. All other classes in the hierarchy will be derived
directly or indirectly from Top. This class should contain a constructor as described below.

14.4. MULTIPLE INHERITANCE 545

2. Every class we add to the multiple inheritance hierarchy should have a constructor with a definition
that begins as follows:

def __init__(self, **kwargs):

(There is nothing special about the name kwargs, and any valid identifier is acceptable, but the
convention is to use kwargs to indicate keyword arguments in a function or method definition.) This
allows the constructor to accept any number of any types of arguments, but it requires clients to use
keyword arguments when creating an instance of the class.

3. The following statement should appear in the body of every constructor, except for the Top class:

super().__init__(**kwargs)

This statement invokes the constructor for the next class in the inheritance hierarchy, where the exact
meaning of next class will appear later. The Top constructor does not call super and, thus, ensures
the chain of constructor calls terminates.

4. The constructor for each class should extract the arguments it needs, if any, from the keyword argu-
ments parameter.

5. Clients must supply all the keyword arguments that any constructors in the call chain of superclasses
expect.

Listing 14.18 (simplemultinherit.py) is very simple example that illustrates the general form of managing
class construction in a multiple inheritance hierarchy.

Listing 14.18: simplemultinherit.py

class Top(object):
def __init__(self, **kwargs):

pass # Terminate the constructor call chain

class A(Top):
def __init__(self, **kwargs):

print(“Making an A object”)
super().__init__(**kwargs)
self.value_A = 0

class B(Top):
def __init__(self, **kwargs):

print(“Making a B object”)
self.value_B = kwargs[‘val’]
kwargs.pop(‘val’) # Remove the parameter from the kwargs
super().__init__(**kwargs)

class C(A, B):
def __init__(self, **kwargs):

print(“Making a C object”)
super().__init__(**kwargs)
self.value_C = 2

c_obj = C(val=5) # Need to supply keyword argument here
print(“===========”)
print(c_obj.__dict__)

14.4. MULTIPLE INHERITANCE 546

Listing 14.18 (simplemultinherit.py) prints

Making a C object
Making an A object
Making a B object
===========
{‘value_B’: 5, ‘value_A’: 0, ‘value_C’: 2}

Suppose we have the following single inheritance hierarchy of classes:

class A(object):
def f(): # A defines method f

pass
class B(A): pass
class C(B): pass
class D(C):

def f(): # D overrides method f
pass

class E(D): pass
class F(E):

def f(): # F overrides method f
pass

which we can visualize as
object
↑
A
↑
B
↑
C
↑
D
↑
E
↑
F

where the arrow (↑) points from subclass to direct superclass; for example, E is a direct subclass of D. Also
notes that classes A, D, and F define methods named f. This means class D overrides A’s f method and F
overrides D’s f method.

The expression

self.f()

within any method of class F executes the f method defined in class F . Compare that to the same expression
appearing in class C. Since class C does not define (override) f, the executing program attempts to execute
the f method in the superclass of C; that is, B. Class B does not define (override) f, so the executing
program attempts to execute the f method in class A. Class A does provide a definition for method f, so the
actual code that executes is found in class A, even though it is called from a method appearing within class
C.

Now consider the expression

14.4. MULTIPLE INHERITANCE 547

super().f()

within a method of class F . The executing program first attempts to execute the method f found in class
E. Such a method does not exist, so the search continues to class D, which does contain an f method. The
code within method D.f executes.

For single inheritance the name super means what it appears to say in the expression super().f():
find and execute the f method of the closest superclass upward in the inheritance hierarchy that defines an
f method.

It is tempting to believe that the word super refers to superclasses. That always is true for single
inheritance, but multiple inheritance clouds the meaning of the super function. The order in which an
executing program attempts to resolve method calls is known as the method resolution order, or MRO for
short. For single inheritance, the MRO is easy to determine: starting with the given class, if you cannot find
the method being called within that class, walk up the hierarchy of classes until you find the nearest class
that defines the method. If the method is inherited, it will be defined in a superclass and eventually located.
If the method does not exist, the search terminates at class object and the interpreter raises an exception.

Every class has an mro method that reveals the MRO for that class. The method returns the list of classes
in method resolution order. Given the single inheritance hierarchy above, the following code reveals the
MRO for class F:

print(F.mro())

The statement prints

[, , , ,
, , ]

We can clean up the output considerably using a loop and taking advantage of the fact that every class has
a __name__ attribute that is the string representing the name of the class. The following code

for cls in F.mro():
print(cls.__name__, end=’ ‘)

else:
print()

displays

F E D C B A object

(Recall that the else clause associated with a while or for loop executes when the loop exits normally
without a break statement—see Section 5.6.)

Observe the ordering from left to right matches the order within the hierarchy from bottom to top. It
means calling super within a class D method, for example, will direct the method search immediately to
class C.

With multiple inheritance super does not always refer to a superclass. The following classes form a
relatively complex multiple inheritance relationship:

class A(object): pass
class B(object): pass
class C(A): pass
class D(A): pass

14.4. MULTIPLE INHERITANCE 548

Figure 14.4 The red numbers indicate the MRO for class I.

object

A B

C D F G

E H

3 4

7 8

class E(C, D): pass
class F(B): pass
class G(B): pass
class H(F, G): pass
class I(E, H): pass

The MRO for class I is

I E C D A H F G B object

We can better visualize the MRO in Figure 14.4. From the MRO we see that a call to super in a method
of class C would proceed to class D, and D is not a superclass of C. The name super, therefore, does not
always refer to a superclass.

The MRO does make sense. The process is this: keep moving up the hierarchy until moving up one
more time would mean visiting a class before one of its subclasses. In the example we can go from I to E
to C, but we cannot next go to A since we have yet to visit D, and D is a subclass of A. If we cannot go up,
we go sideways to the right. The right movement corresponds to the left-to-right ordering of superclasses
in a class definition.

Pictorially, in an MRO you never should visit a class that has an arrow coming into it from a class below
that you have not yet visited.

The MRO of class C is

C A object

Since this begins the MRO from C, super visits C’s superclass A first, not D. The MRO depends on which
class the search begins, even within the same hierarchy.

The following code complicates the hierarchy slightly:

14.4. MULTIPLE INHERITANCE 549

Figure 14.5 The red numbers indicate the MRO for class I in the more complicated hierarchy.

object

A B

C D F G

E H

7 8

class A(object): pass
class B(object): pass
class C(A): pass
class D(A): pass
class F(B): pass
class E(C, D, F): pass
class G(B): pass
class H(D, F, G): pass
class I(E, H): pass

The MRO for class I for this hierarchy is

I E C H D A F G B object

Figure 14.5 illustrates the MRO in this more complicated hierarchy. In this case we proceed from I to E
to C. The next step up would be A, but we have yet to visit D, a subclass of A. We cannot visit D, however,
because we have yet to visit H, a subclass of D. The leaves H as the next class to visit. Remember, we attempt
to go up, if possible, so we visit its leftmost superclass, D. After D we visit A, but we cannot go up to object
because we have yet to visit F, G, and B. These classes, in order, round out the MRO for I. No class will
appear more than once in an MRO.

Armed with our relatively limited theoretical knowledge of multiple inheritance we now can build a
more interesting example. First, Listing 14.19 (top.py) establishes our Top class described earlier. Top
allows us to build a cooperative multiple inheritance hierarchy that allows the various class constructors to
accept varied arguments.

Listing 14.19: top.py

class Top(object):
def __init__(self, **kwargs):

14.4. MULTIPLE INHERITANCE 550

pass # Terminate the constructor call chain

For this example we will take a break from Tk graphics and revisit Turtle graphics. Consider List-
ing 14.20 (graphicalobject.py), a class that represents a graphical object that a user may reposition within a
Turtle graphics window.

Listing 14.20: graphicalobject.py

from top import Top

class GraphicalObject(Top):
“”” A graphical object that allows the user to reposition

it anywhere within the window using the mouse.
Contains all the code to manage the Turtle graphics
environment. “””

def __init__(self, **kwargs):
“”” Initializes a GraphicalObject object

Keyword args include:
screen is the Turtle graphics screen.
turtle is the Turtle graphics pen.
initially appear at location (x, y). “””

super().__init__(**kwargs) # See discussion about super constructor
print(“Initializing graphical object”)
self.screen = kwargs[‘screen’]
self.turtle = kwargs[‘turtle’]
self.x = kwargs[‘x’]
self.y = kwargs[‘y’]
self.screen.delay(0) # Do not slowly trace drawing
self.turtle.speed(0) # Make turtle’s actions as fast as possible
self.turtle.hideturtle() # Make the turtle invisible
self.screen.onclick(self.do_click) # Set mouse press handler
self.move_to(x=kwargs[‘x’], y=kwargs[‘y’])

def run(self):
“”” Run the graphical program. “””
self.screen.mainloop()

def draw(self):
“”” Renders the object within the window.

Derived classes override this method to meet their specific
needs. “””

pass

def do_click(self, x, y):
“”” Called when the user presses the mouse button.

(x, y) is the new location of the display. “””
self.move_to(x, y) # Move to a new location
self.draw() # Redraw at new location

def move_to(self, x, y):
“”” Relocates a Movable object to position (x, y). “””
self.x, self.y = x, y

The line

14.4. MULTIPLE INHERITANCE 551

class GraphicalObject(Top):

indicates the superclass of GraphicalObject is our Top class from before. Note the beginning of the
constructor definition:

def __init__(self, **kwargs):

In the GraphicalObject constructor we explicitly invoke the superclass constructor via super:

super().__init__(**kwargs)

Every class in the multiple inheritance hierarchy, except those derived directly from object, must call
__init__ via super and pass keyword arguments. This form of the constructor invocation with super
makes cooperative multiple inheritance possible. It enables the constructors for other classes in the hierar-
chy to accept different numbers of parameters. The price to pay for this versatility is this: clients must use
keyword arguments for passing all parameters to class constructors.

Notice that the draw method is empty. This is because the GraphicalObject class is an abstract notion,
and it is up to derived classes to specify the exact behavior needed to draw the object.

Listing 14.21 (dot.py) derives the Dot class from GraphicalObject and overrides the draw method to
simply draw a red circle within the window.

Listing 14.21: dot.py

from graphicalobject import GraphicalObject

class Dot(GraphicalObject):
“”” A simple, round circle graphical object “””
def __init__(self, **kwargs):

“”” Initializes a dot object with a given Turtle screen, pen,
and (x, y) position “””

super().__init__(**kwargs)

def draw(self):
“”” Renders the dot in the Turtle graphics window “””
self.turtle.penup() # Move pen
self.turtle.setpos(self.x, self.y)
self.turtle.pendown()
self.turtle.fillcolor(“red”)
self.turtle.begin_fill()
self.turtle.circle(20)
self.turtle.end_fill()

Listing 14.22 (testdot.py) exercises the Dot class.

Listing 14.22: testdot.py

from dot import Dot
from turtle import Screen, Turtle

def main():
# Make a Dot object
d = Dot(screen=Screen(), turtle=Turtle(), x=10, y=20)

14.4. MULTIPLE INHERITANCE 552

Figure 14.6 An image of one execution of Listing 14.22 (testdot.py) after the user has clicked the mouse in
various locations.

# Run the graphical program
d.run()

if __name__ == “__main__”:
main()

Figure 14.6 shows the state of an execution of the Listing 14.22 (testdot.py) after the user has clicked the
mouse in various locations. The draw method does not clear the window, so each mouse click draws a new
dot image in a different position without erasing it in its previous spot.

Suppose we want to combine the functionality of our nongraphical digital stopwatch (Listing 14.8
(digitalstopwatch.py)) with capability of a graphical object. The user should be able to click a location
within the graphical window, and the digital stopwatch’s display will appear at that point. The user still
should be able to start, stop, and reset the stopwatch as desired. We also would like to leverage existing
code as much as possible. One way we can do this is via multiple inheritance.

Listing 14.23 (timer.py) updates Listing 13.6 (stopwatch.py) to better support multiple inheritance. The
only changes are the use of super in the constructor and a print message to ensure the constructor executes
as expected.

Listing 14.23: timer.py

from time import clock
from top import Top

class Timer(Top):
“”” Provides stopwatch objects that that programmers

can use to time the execution time of portions of
a program. “””

def __init__(self, **kwargs):
“”” Makes a new stopwatch ready for timing. “””
super().__init__(**kwargs) # New code here

14.4. MULTIPLE INHERITANCE 553

print(“Initializing stopwatch”) # New code here
self.reset()

def start(self):
“”” Starts the stopwatch, unless it is already running.

This method does not affect any time that may have
already accumulated on the stopwatch. “””

if not self._running:
self._start_time = clock() – self._elapsed
self._running = True # Clock now running

def stop(self):
“”” Stops the stopwatch, unless it is not running.

Updates the accumulated elapsed time. “””
if self._running:

self._elapsed = clock() – self._start_time
self._running = False # Clock stopped

def reset(self):
“”” Resets stopwatch to zero. “””
self._start_time = self._elapsed = 0
self._running = False

def elapsed(self):
“”” Reveals the stopwatch running time since it

was last reset. “””
if not self._running:

return self._elapsed
else:

return clock() – self._start_time

Listing 14.24 (digitaltimer.py) updates Listing 14.8 (digitalstopwatch.py), providing a constructor.

Listing 14.24: digitaltimer.py

from timer import Timer

class DigitalTimer(Timer):
def __init__(self, **kwargs): # New code here

super().__init__(**kwargs) # New code here
print(“Initializing digital stopwatch”) # New code here

def digital_time(self):
“”” Returns a string representation of the elapsed time

in hours : minutes : seconds. “””
# Compute time in hours, minutes, and seconds
seconds = round(self.elapsed())
hours = seconds // 3600 # Compute total hours
seconds %= 3600 # Update seconds remaining
minutes = seconds // 60 # Compute minutes
seconds %= 60 # Update seconds remaining
# Each digit occupies two spaces; pad with leading zeros, if necessary
return “{0:0>2}:{1:0>2}:{2:0>2}”.format(hours, minutes, seconds)

14.4. MULTIPLE INHERITANCE 554

Listing 14.25 (movabletimer.py) defines a class named MovableTimer that inherits from both DigitalTimer
and GraphicalObject.

Listing 14.25: movabletimer.py

from digitaltimer import DigitalTimer
from graphicalobject import GraphicalObject
from turtle import Screen, Turtle

#class MovableTimer(DigitalTimer, GraphicalObject):
class MovableTimer(GraphicalObject, DigitalTimer):

“”” A graphical digital timer that allows the user to reposition
its display anywhere within the window using the mouse.
Contains all the code to manage the Turtle graphics
environment. “””

def __init__(self, **kwargs):
“”” Sets the graphical environment and initial position of the

display.
(x, y) is the display’s initial position “””

super().__init__(**kwargs)
print(“Initializing MovableTimer”)
self.screen.listen() # Receive keypress events
self.screen.onkey(self.start_timer, “s”) # Key to start the timer
self.screen.onkey(self.stop_timer, “t”) # Key to stop the timer
self.screen.onkey(self.reset_timer, “r”) # Key to reset the timer
self.screen.ontimer(self.update, 500) # Set timer event

def draw(self):
“”” Renders the digital stopwatch within the window. “””
self.turtle.clear() # Clear the screen
self.turtle.penup() # Move pen
self.turtle.setpos(self.x, self.y)
self.turtle.pendown()
self.turtle.write(self.digital_time(), font=(“Arial”, 48, “normal”))

def start_timer(self):
“”” Starts the timer. “””
self.start()

def stop_timer(self):
“”” Stops the timer. “””
self.stop()

def reset_timer(self):
“”” Resets the timer to 0:00:00. “””
self.reset()

def update(self):
“”” Updates the program’s view of the global stopwatch object.

Called every one-half second. “””
self.draw() # Draw the digital display
self.screen.ontimer(self.update, 500) # Call the update function again after one-half second

14.4. MULTIPLE INHERITANCE 555

def main():
clock = MovableTimer(screen=Screen(), turtle=Turtle(), x=10, y=20)
clock.run()

if __name__ == “__main__”:
main()

Observe that, unlike Dot objects, MovableTimer objects erase themselves when the user moves them. This
means that there always will be only one stopwatch display appearing within the window at a time.

The multiple inheritance in this case means that a MovableTimer object is a DigitalTimer instance
and is a GraphicalObject instance, as the following interactive session confirms:

>>> from graphicalobject import *
>>> from movabletimer import *
>>> from turtle import *
>>> x = MovableTimer(Screen(), Turtle(), 30, 45)
Initializing stopwatch
Initializing digital stopwatch
Initializing graphical object
Initializing MovableTimer
>>> type(x)

>>> isintance(x, MovableTimer)
Traceback (most recent call last):

File ““, line 1, in
NameError: name ‘isintance’ is not defined
>>> isinstance(x, MovableTimer)
True
>>> isinstance(x, GraphicalObject)
True
>>> isinstance(x, DigitalTimer)
True
>>> isinstance(x, int)
False

This means that any function or method that works with a GraphicalObject as a parameter will work fine
if passed a MovableTimer instance. Similarly, any function or method that expects a DigitalStopwatch
argument will work properly if passed a MovableTimer object.

Since Python supports cooperative multiple inheritance, how can we deal with a class that does not
cooperate? Suppose we have a class from a library that we do not control; that is, we cannot change the
source code of the class. Specifically, consider Listing 14.26 (box.py).

Listing 14.26: box.py

class Box:
“”” A square box object “””
def __init__(self, screen, pen, x, y, width):

“”” Initializes a box object with a given Turtle screen, pen,
(x, y) position, and width “””

self._screen = screen
self._pen = pen
self._x_val = x

14.4. MULTIPLE INHERITANCE 556

self._y_val = y
self._width = width

def position(self, x, y):
“”” Positions the box at (x,y) “””
self._x_val = x
self._y_val = y

def render(self):
“”” Renders the box in the Turtle graphics window “””
self._pen.penup() # Move pen
self._pen.setpos(self._x_val – self._width/2,

self._y_val – self._width/2)
self._pen.setheading(0)
self._pen.pendown()
self._pen.fillcolor(“blue”)
self._pen.begin_fill()
self._pen.forward(self._width)
self._pen.left(90)
self._pen.forward(self._width)
self._pen.left(90)
self._pen.forward(self._width)
self._pen.left(90)
self._pen.forward(self._width)
self._pen.left(90)
self._pen.end_fill()

The Box class is reminiscent of the Dot class from Listing 14.21 (dot.py). The Box class, however, is not
a subclass of GraphicalObject. The constructor for Box does not use the expected keyword arguments,
and it does not have a draw method. Clearly, the Box class does not cooperate with the classes in our
GraphicalObject multiple inheritance hierarchy.

Fortunately there is a relatively easy way to make use of the capabilities the Box class provides within
our hierarchy. Section 14.3 introduced the adapter design pattern. We can create a new class that adapts
Box to meet our needs. Listing 14.27 (boxadapter.py) does exactly that.

Listing 14.27: boxadapter.py

from graphicalobject import GraphicalObject
from box import Box

class BoxAdapter(GraphicalObject):
“”” A simple, square box graphical object.

BoxAdapter is a GraphicalObject.
BoxAdapter has a Box. “””

def __init__(self, **kwargs):
“”” Initializes an adapted box object with a given Turtle

screen, pen, and (x, y) position “””
self.box = Box(kwargs[‘screen’], kwargs[‘turtle’],

kwargs[‘x’], kwargs[‘y’], kwargs[‘width’])
super().__init__(**kwargs)

def move_to(self, x, y):
“”” Repositions the box to (x,y) “””
self.box.position(x, y)

14.4. MULTIPLE INHERITANCE 557

def draw(self):
“”” Renders the box in the Turtle graphics window “””
#self.box.position(self.x, self.y)
self.box.render()

Every BoxAdapter object contains a Box object. The BoxAdapter methods delegate their work to the
equivalent methods in Box. The constructor expects keyword arguments and calls super with keyword
arguments, exactly as every good GraphicalObject subclass constructor should. The constructor unpacks
the keyword arguments for Box’s constructor. The BoxAdapter class inherits run and do_click from
GraphicalObject.

Listing 14.28 (testbox.py) demonstrates that our new BoxAdapter class is fully cooperative.

Listing 14.28: testbox.py

from boxadapter import BoxAdapter
from turtle import Screen, Turtle

def main():
# Make a Box object via the adapter
b = BoxAdapter(screen=Screen(), turtle=Turtle(),

x=20, y=20, width=30)
# Run the graphical program
b.run()

if __name__ == “__main__”:
main()

Figure 14.7 shows the state of an execution of the Listing 14.22 (testdot.py) after the user has clicked the
mouse in various locations.

As an aside, the type constructor enables dynamic class definitions. The following statement:

MyClass = type(“MyClass”, (object,), {})

defines an empty class named MyClass. Note that assignment statement is equivalent to the following
source code:

class MyClass(object):
pass

The second argument to the type constructor is a tuple of base classes. The expression (object,) repre-
sents a tuple that contains one element; the following interactive session shows why the trailing comma is
necessary:

>>> x = (1)
>>> x
1
>>> y = (1,)
>>> y
(1,)
>>> y[0]

14.5. UNIT TESTING 558

Figure 14.7 An image of one execution of Listing 14.28 (testbox.py) after the user has clicked the mouse
in various locations.

1
>>> x[0]
Traceback (most recent call last):

File ““, line 1, in
TypeError: ‘int’ object is not subscriptable

Here we see that (1) is just the integer 1, and (1,) is the tuple that contains the integer 1.

The third argument to the type constructor is a dictionary that establishes class variables for the class
(not instance variables for instances of the class, see Section 13.10).

As with dynamically added instance variables (see Section 13.9), the ability to define classes on the fly
is valuable but rarely needed in most applications.

14.5 Unit Testing

CAUTION! SECTION UNDER CONSTRUCTION

We created a rudimentary testing class in Section 13.7. Python provides a considerably more powerful
testing framework in its unittest module. Unit testing is a well-established technique for evaluating the
correctness of software components (see https://en.wikipedia.org/wiki/Unit testing). Unit testing
involves testing individual units of a software system in isolation to determine if they behave as advertised.
Examples of individual software units include functions, methods, objects, and modules.

Python’s unittest module is easy to use. The following steps explain how to use the unit testing
module for simple testing:

1. Import the unittest module.

2. Import the code to test as necessary.

https://en.wikipedia.org/wiki/Unit_testing

14.5. UNIT TESTING 559

3. Derive a class from unittest.TestCase.

4. Add methods for each test to perform.

• Each method’s name must have the prefix test.

• Each method must accept only the self parameter.

• Add to the method’s body any code required to perform the test.

• Within the method call the assertEqual method to compare a computed value to an expected
value.

5. Add the following code to the test program:

if __name__ == ‘__main__’:
unittest.main()

Listing 13.13 (testliststuff.py) in Section 13.7 uses our home-grown FunctionTester object to test some
functions. Listing 14.29 (testlist2.py) uses Python’s standard unittest module to test the same functions
in

Listing 14.29: testlist2.py

import unittest

###### The original functions from before ################################

def max_of_three_bad(x, y, z):
“”” Attempts to determine and return the maximum of three

numeric values. “””
result = x
if y > result:

result = y
elif z > result:

result = z
return result

def max_of_three_good(x, y, z):
“”” Computes and returns the maximum of three numeric values. “””
result = x
if y > result:

result = y
if z > result:

result = z
return result

def sum(lst):
“”” Attempts to compute and return the sum of all the elements in

a list of integers. “””
total = 0
for i in range(1, len(lst)):

total += lst[i]
return total

14.5. UNIT TESTING 560

# maximum has a bug (it has yet to be written!)
def maximum(lst):

“”” Computes the maximum element in a list of integers. “””
return 0 # maximum not yet implemented

###### Some new code to test ###########################################

class ListManager(object):
def __init__(self, lst):

super().__init__()
self.lst = lst

def get(self, idx):
return self.lst[idx] # Subject to range exception

###### The test class ##################################################

class TestFunctionsEtc(unittest.TestCase):
# Some test cases to test max_of_three_bad
def test_max_of_three_bad_1(self):

self.assertEqual(max_of_three_bad(2, 3, 4), 4)

def test_max_of_three_bad_2(self):
self.assertEqual(max_of_three_bad(4, 3, 2), 4)

def test_max_of_three_bad_3(self):
self.assertEqual(max_of_three_bad(3, 2, 4), 4)

# Some test cases to test max_of_three_good
def test_max_of_three_good_1(self):

self.assertEqual(max_of_three_bad(2, 3, 4), 4)

def test_max_of_three_good_2(self):
self.assertEqual(max_of_three_bad(4, 3, 2), 4)

def test_max_of_three_good_3(self):
self.assertEqual(max_of_three_bad(3, 2, 4), 4)

# Some test cases to test maximum
def test_maximum_1(self):

self.assertEqual(maximum([2, 3, 4, 1]), 4)

def test_maximum_2(self):
self.assertEqual(maximum([4, 3, 2, 1]), 4)

def test_maximum_3(self):
self.assertEqual(maximum([-2, -3, 0, -21]), 0)

# Some test cases to test sum
def test_sum_1(self):

self.assertEqual(sum([0, 3, 4]), 7)

def test_sum_2(self):

14.5. UNIT TESTING 561

self.assertEqual(sum([-3, 0, 5]), 2)

# Some code that can throw an exception
def test_list_manager_1(self):

lm = ListManager([1, 2, 3])
self.assertEqual(lm.get(2), 3)

def test_list_manager_2(self):
lm = ListManager([1, 2, 3])
self.assertEqual(lm.get(3), 3)

def test_list_manager_3(self):
lm = ListManager([1, 2, 3])
self.assertEqual(lm.get(0), 1)

def test_list_manager_4(self):
lm = ListManager([1, 2, 3])
self.assertEqual(lm.get(0), 0)

if __name__ == ‘__main__’:
unittest.main()

Notice that the class TestFunctionsEtc inherits from unittest.TestCase. This means our TestFunctionsEtc
class will have all the capabilities required to work properly in Python’s unit testing framework. All the
methods within the TestFunctionsEtc class that begin with the prefix test represent tests to perform.
All the methods in the TestFunctionsEtc class happen to begin with test, but test classes in general can
include other, non-test, methods as well. These can be helper methods that the test methods invoke.

Within each test method a statement such as

self.assertEqual(lm.get(0), 0)

tests the value of the first argument of assertEqual to the second argument. The first argument is the
actual value, and the second argument is the expected value. The assertEqual method checks to see if
they match. If the actual and expected value match, the test passes. If the two values do not match, the test
fails. If attempting to evaluate the actual value produces an exception, the test is classified as an error.

The output of Listing 14.29 (testlist2.py) begins with the line

.E.FF..F..FF..F

This line contains 15 characters—exactly the number of methods named with the prefix test within our
TestFunctionsEtc class. A dot (.) indicates a test that passed, an F represents a failed test, and an E
indicates the test produced an exception (run-time error). An important point is that the test framework
does not execute the tests in the same order that the test methods appear in the source code. The test
execution order is alphabetical (actually lexicographic—the same ordering that the < operator imposes on Python string objects) by method name. The rest of the program’s output provides details about each test failure or error. The next several lines of output include ====================================================================== ERROR: test_list_manager_2 (__main__.TestFunctions) ---------------------------------------------------------------------- ©2017 Richard L. Halterman Draft date: January 18, 2018 14.5. UNIT TESTING 562 Traceback (most recent call last): File "testlist2.py", line 91, in test_list_manager_2 self.assertEqual(lm.get(3), 3) File "testlist2.py", line 44, in get return self.lst[idx] # Subject to range exception IndexError: list index out of range ====================================================================== FAIL: test_list_manager_4 (__main__.TestFunctions) ---------------------------------------------------------------------- Traceback (most recent call last): File "testlist2.py", line 99, in test_list_manager_4 self.assertEqual(lm.get(0), 0) AssertionError: 1 != 0 ====================================================================== FAIL: test_max_of_three_bad_1 (__main__.TestFunctions) ---------------------------------------------------------------------- Traceback (most recent call last): File "testlist2.py", line 49, in test_max_of_three_bad_1 self.assertEqual(max_of_three_bad(2, 3, 4), 4) AssertionError: 3 != 4 After detailing several more test failures, the program’s output concludes with ---------------------------------------------------------------------- Ran 15 tests in 0.004s FAILED (failures=6, errors=1) Here we see that out of 15 tests only eight tests passed, and seven did not pass. One of the seven tests did not pass due to a run-time exception. The unittest package includes a family of over 30 methods related to assertEqual. These meth- ods all have the prefix assert and include such tests as assertTrue, assertFalse, assertRaises, assertNotEqual, assertLess, assertLessEqual, assertListEqual, assertAlmostEqual, assertIs, assertIn, and assertNotIn. In addition to the large variety of assert methods, the TestCase class provides the setUp and tearDown methods that we chose not to override in our TestFunctionsEtc class. The testing framework automati- cally will execute the setUp method before each test method runs and automatically execute the tearDown method after each test method executes (even if the test method raises an exception). To demonstrate how this works, see how the addition of these two methods affects the output of Listing 14.29 (testlist2.py): class TestFunctionsEtc(unittest.TestCase): def setUp(self): print("Setting up ...") def tearDown(self): print("... tearing down.") # Other parts of class remain the same . . . The infrastructure that executes the tests is known as the test runner. We saw the work of the test runner ©2017 Richard L. Halterman Draft date: January 18, 2018 14.6. CUSTOM EXCEPTIONS 563 is the program’s output when run in the console. Graphical IDEs can visualize the test results in other ways, such as using green and red bars to indicate tests successes and failures. 14.6 Custom Exceptions Chapter 12 introduced Python’s exception handling infrastructure. Now that we are familiar with inheri- tance we can understand better how it works and even create our own custom exception types. Consider the following brief interactive session: >>> v = ValueError()
>>> v
ValueError()
>>> isinstance(v, ValueError)
True
>>> isinstance(v, TypeError)
False
>>> isinstance(v, Exception)
True

We can see that ValueError is a subclass of Exception. Figure 14.8 shows a portion of Python’s class hier-
archy of standard exceptions. The diagram omits GeneratorExit, which is a direct subclass of BaseException.
It also omits 56 other standard classes derived directly or indirectly from Exception. Almost every stan-
dard exception class is a direct or indirect subclass of Exception Amongst the standard exception classes,
only BaseException, KeyboardInterrupt, SystemExit, and GeneratorExit are not related via inheri-
tance to the Exception class. Due to the is a relationship imposed by inheritance, any exception object of
a class other than the four excluded types mentioned above is compatible with the Exception type. This
explains why we use Exception as the “catch-all” exception type used in an exception handler (see Sec-
tion 12.5). The reason that we do not usually use BaseException as the catch-all type is we normally do
not want to intervene when the user presses Ctrl C to exit the program or when the program itself calls
sys.exit. The Exception type covers all the exceptions that we ordinarily care to handle.

Even though Python provides 68 standard exception classes, we may not find one that exactly meets our
needs, especially now that we can define our own custom types via classes. Inheritance makes it easy to
define our own custom exception types. Listing 13.6 (stopwatch.py) defines a simple stopwatch timer class.
Suppose we wish to consider an attempt to stop a nonrunning stopwatch an error worthy of an exception.
We could reuse a standard exception, but which one? The following shows an attempt with ValueError:

class Stopwatch:
# Other details about the class omitted …
def stop(self):

“”” Stops the stopwatch, unless it is not running.
Updates the accumulated elapsed time. “””

if self._running:
self._elapsed = clock() – self._start_time
self._running = False # Clock stopped

else:
raise ValueError(“Attempt to stop a stopped clock”)

As desired, this revised Stopwatch.stop method will raise an exception when a client attempts to stop a
stopped stopwatch, but is this the best approach?

14.6. CUSTOM EXCEPTIONS 564

Figure 14.8 A small portion of the class hierarchy of Python’s standard exceptions. This diagram omits 1
other standard class derived directly from BaseException and 56 other classes derived directly or indirectly
from Exception.

ExceptionKeyboardInterrupt

BaseException

SystemExit

object

ArithmeticError LookupError

ZeroDivisionError OverflowError IndexError KeyError

ValueError

14.6. CUSTOM EXCEPTIONS 565

We can use help function (see Section 6.3) in the interactive interpreter to get information about
ValueError; the first few lines it prints is

>>> help(ValueError)
Help on class ValueError in module builtins:

(The remainder of help’s output provides information about ValueError’s methods.) Notice that help
lists ValueError’s MRO (see Section 14.4), but, more importantly, it gives the meaning of the ValueError
exception. ValueError is supposed to indicate an “inappropriate argument value.” This meaning does not
match well with an attempt to stop a stopped stopwatch.

Another problem is this: What if use our Stopwatch class to time code that can produce its own
ValueError exception? How can any exception handling code we might write in this situation distin-
guish between an error with a Stopwatch object and a legitimate ValueError that the other code may
raise?

What we need is a StopwatchException class. Making such a class turns out to be remarkably easy;
the following class meets the requirement:

class StopwatchException(Exception):
pass

The StopwatchException class inherits from Exception, but its empty class body means that StopwatchException
adds nothing to what the Exception class already offers. The value that StopwatchException adds is this:
it defines a new exception type that can participate as a first-class citizen in Python’s exception handling
infrastructure. We can rewrite the Stopwatch.stop method as

class Stopwatch:
# Other details about the class omitted …
def stop(self):

“”” Stops the stopwatch, unless it is not running.
Updates the accumulated elapsed time. “””

if self._running:
self._elapsed = clock() – self._start_time
self._running = False # Clock stopped

else:
raise StopwatchException()

Exception handling code now can distinguish between a stopwatch error and a true ValueError:

try:
# Some code that may raise a StopwatchException or ValueError
# exception

except ValueError:

14.7. EXERCISES 566

pass # Add code to process ValueError
except StopwatchException:

pass # Add code to process StopwatchException
except Exception:

pass # Add code to process all other normal exceptions

Because we derived StopwatchException from Exception, a “catch-all” except block will catch a StopwatchException
object even if a try statement lacks an explicit StopwatchException-specific except block.

14.7 Exercises

CAUTION! SECTION UNDER CONSTRUCTION

1. What two major ways does Python provide for reusing classes during class design?

2. Which kind of relationship amongst classes does composition represent, has is, is a, or something
else?

3. Which kind of relationship amongst classes does inheritance represent, has is, is a, or something
else?

4. What is maximum of superclasses a class can have using single inheritance?

5. Some physical stopwatches allow their users to store lap times up to a certain number. Use the
Stopwatch class from Listing 13.6 (stopwatch.py) and composition to design a new stopwatch class
that includes a lap timer. Your class should provide a lap method that works as follows:

• A newly created stopwatch object has no lap times stored in its memory.

• Invoking the reset method clears all lap times from a stopwatch’s memory.

• Invoking the lap method on a nonrunning stopwatch has no effect.

• Invoking the lap method on a running stopwatch with no stored lap times records the elapsed
time since the invocation of start.

• Invoking the lap method on a running stopwatch with stored lap times records the elapsed time
since the most recent invocation of lap.

Your class also should provide a method named lap_times that returns a list stored lap times. It
should return the empty list if the stopwatch has no stored lap times.

6. Implement the stopwatch with lap timer from Question 5, but use inheritance instead of composition.

7. Consider the following class X:

class X(object):
def identify(self):

print(“I’m an X object”)

567

Chapter 15

Algorithm Quality

The previous chapters emphasized the mechanics of the Python programming language. We have seen
how to manage variables, arithmetic, conditional execution, iteration, functions, parameters, objects, lists,
tuples, dictionaries, sets, exceptions, custom types, and inheritance. Our main concern has been using these
features to construct programs that correctly implement algorithms to solve problems. Sometimes correct
algorithms are subtly difficult to get right, and their logic errors can evade even careful testing.

Program correctness always is the primary goal of software construction, but correctness is not the only
goal. Two different programs may produce the exact same results in all cases, and yet one objectively may
be considered better than the other. This difference in quality has nothing to do with source code style
issues, variable names, or the code’s apparent complexity. The different is this: Despite the two programs
producing the same results, one program effectively works and the other does not! It turns out that it is
not hard to devise and implement an algorithm that correctly solves a problem but takes too much time to
complete its work. The program, therefore, does not meet the user’s needs, as the user cannot wait long
enough for the result.

In this chapter we examine several different kinds of algorithms, each of with that deal with practical
problems, and along the way we address correctness and efficiency concerns.

15.1 Good Algorithms Versus Bad Algorithms

Suppose we wish to determine if the elements in a list (Chapter 10) of integers appear in ascending order.
(Non-decreasing order is the more precise term, as it allows for duplicate elements.) The following function
correctly solves the problem:

def is_ascending(lst):
for i in range(len(lst) – 1):

for j in range(i + 1, len(lst)):
if lst[i] > lst[j]:

return False
return True

The nested loop first compares the first (0th index) element to all the elements that follow. If the first
element is indeed smaller than all the others, it continues by comparing the second element to all of the
elements that follow the second element. The third time through the outer loop the function compares the

15.1. GOOD ALGORITHMS VERSUS BAD ALGORITHMS 568

third element to all the elements that follow the third element. If at any time the the inner loop finds an
element smaller than the element controlled by the outer loop, the function immediately returns False. On
the other hand, if the elements in the list are in ascending order, the nested loop must continue until it finally
compares the next-to-the-last element to the last element. At that point the function returns True.

This is_ascending function is correct. If the first element is less than all the elements that follow
the first element, and the second element is less than all the elements that follow the second element, and
the third element is less than all the elements that follow the third element, etc., all the elements must be
arranged in non-decreasing order.

Next, consider the following competing algorithm:

def is_ascending2(lst):
for i in range(len(lst) – 1):

if lst[i] > lst[i + 1]:
return False

return True

The is_ascending2 function uses the mathematical principle of transitivity. The transitive property of
inequality for integers is this: If x ≤ y and y ≤ z, then x ≤ z. The is_ascending2 function compares the
first element to the second element, the second element to the third, the third to the fourth, etc., until it
finally compares the next to the last element to the last element. If the function detects any element out of
order, it returns False immediately. If it makes it all the way to the end of the list, the function returns
True. Because of transitivity, if the loop gets to the end of the list, we know that the first element is no
larger than all the follow it; we need not compare the first element directly with each and every element that
follows it.

Both the is_ascending and is_ascending2 functions return the same result when presented with the
same list. We say that the two functions are functionally equivalent. If correctness is our only criterion,
neither function is better than the other.

The is_ascending2 function is simpler than the is_ascending function because it uses a single loop
rather than a nested loop. Apparent code complexity by itself is not a reliable criterion for judging the
quality of an algorithm. We must determine which function computes its result quicker. Sometimes more
complex code is faster than simpler code because the more complex code employs special tricks to speed
up its processing.

Suppose we need to assess the ordering of the elements in a list containing n integers. To better evaluate
the two functions we will consider using a list with its elements arranged in non-decreasing order. This
prevents either function from returning early—both must make a full scan over all the elements in the list
before returning True. The following compares the two functions:

• is ascending. In the case of is_ascending, the outer loop must iterate n−1 times. The inner loop
scans n− 1 elements within the first iteration of the outer loop. During each iteration of the outer
loop the inner loops scans one fewer element than it did on the previous outer loop iteration. This
means the inner loop iterates n− 1 times on the first iteration of the outer loop, n− 2 times on the
second iteration of the outer loop, n−3 times on the third iteration of the outer loop, etc. As a result
the if statement executes

(n−1)+(n−2)+(n−3)+ . . .+(n− [n−3])+(n− [n−2])+(n− [n−1])

times. Observe that this expression simplifies to

(n−1)+(n−2)+(n−3)+ . . .+3+2+1

15.1. GOOD ALGORITHMS VERSUS BAD ALGORITHMS 569

Exactly how many times is this, in terms of the size of the list n? We can use some algebra to simplify
the above expression. Let

s = (n−1)+(n−2)+(n−3)+ . . .+3+2+1

Because of the commutative property of addition it does not matter which direction we perform the
addition. We can just as well write the right side of the equation backwards as

s = 1+2+3+ . . .+(n−3)+(n−2)+(n−1)

A fact from algebra states that adding two equations results in an equation. If we add the forwards
and backwards equations together, we get

s = (n−1) + (n−2) + (n−3) + . . . + 3 + 2 + 1
+ s = 1 + 2 + 3 + . . . + (n−3) + (n−2) + (n−1)

2s = n + n + n + . . . + n + n + n

The expression on the right side of the equals sign contains n− 1 terms—it is number of times the
outer loop iterates. Each term, n, is identical. We thus are adding n to itself n− 1 times. This is
simply a multiplication, so we can rewrite the equation as

2s = n(n−1)

Solving for s, we get:

s =
n(n−1)

2
=

n2−n
2

This means for a list containing n elements is_ascending must perform the if comparison up to
n2−n

2
times.

• is ascending2. The analysis of is_ascending2 is much simpler. For a sorted list the loop must
iterate n−1 times. This means for a list containing n elements is_ascending2 must perform the if
comparison up to n−1 times.

When the lists are small, we will not be able to detect a difference in the execution speeds of the two
functions. Consider a list with 5 elements. In this case is_ascending’s if statement would execute
52−5

2
=

25−5
2

= 10 times, and is_ascending2’s if statement would execute 5− 1 = 4 times. While

is_ascending executes its if statement
10
4
= 2.5 times more than does is_ascending2, the comparison

within the if statement is simple and computers are fast, so we will not be able to detect the difference in
execution times.

What happens if we increase the list’s size by a factor of 100, from five to 500? The is_ascending

function will execute its if statement
5002−500

2
=

250,000−500
2

= 124,750 times. In the case of the
is_ascending2 function we get 500− 1 = 499. Notice that is_ascending is no longer executing its if
statement 2.5 times as often as is_ascending2; rather the is_ascending function now is performing the

comparison
124,750

499
= 250 times more often than is_ascending2!

As the list’s length grows, the performance gap grows even more. For a list of size 5,000 the is_ascending

function will execute its if statement
50002−5000

2
= 12,497,500 times. In the case of the is_ascending2

15.1. GOOD ALGORITHMS VERSUS BAD ALGORITHMS 570

function we get 5,000− 1 = 4,999. The is_ascending function now is performing the comparison
12,497,500

4999
= 2,500 times more often than is_ascending2!

Listing 15.1 (ascendingplot.py) performs an experiment to test our mathematical analysis. It com-
pares the performance of the two algorithms on lists of growing lengths. The list sizes consist of the the
squares of the integers from zero to 200 in increments of 20; that is, 02 = 0,202 = 400,402 = 1600,602 =
3600, . . . ,2002 = 40,000. Besides printing the performance figures to the console, Listing 15.1 (ascendingplot.py)
uses the Plotter object from Listing 13.14 (plotobj.py) to plot the performance curves.

Listing 15.1: ascendingplot.py

from time import clock
from math import sqrt
from plotobj import Plotter

def is_ascending(lst):
“”” Returns True if lst contains elements

in nondecreasing order as determined by
the < operator. Returns False if the elements of lst are not in order. Throws an exception if lst is not a list or its elements are not compatible with the < operator. """ for i in range(len(lst) - 1): for j in range(i + 1, len(lst)): if lst[i] > lst[j]:
return False

return True

def is_ascending2(lst):
“”” Returns True if lst contains elements

return False
return True

def compute_time(size, data1, data2):
“”” Compares the performance of the is_ascending and

is_ascending2 functions on a list of a given size.
Prints the results of the executions and appends the
results to the data1 and data2 lists for further processing. “””

print(“List size:”, size)
my_list = list(range(size)) # Make list [0, 1, 2, 3, …, size – 1]
start = clock() # Start the clock

15.1. GOOD ALGORITHMS VERSUS BAD ALGORITHMS 571

ans = is_ascending(my_list) # Compute answer
elapsed1 = clock() – start # Stop the clock
print(” is_ascending: {} Elapsed: {:12.7f}”.format(ans, elapsed1))
start = clock() # Start the clock
ans = is_ascending2(my_list) # Compute answer
elapsed2 = clock() – start # Stop the clockt
print(” is_ascending2: {} Elapsed: {:12.7f}”.format(ans, elapsed2))
print(” Speedup: {:6.1f}”.format(elapsed1/elapsed2)) # Compute speedup
print()
data1.append((size, elapsed1))
data2.append((size, elapsed2))

def main():
“”” Compares the performance of the is_ascending and

is_ascending2 functions on lists of various sizes. “””
data1, data2 = [], []

# Compute results for sizes in the range 0…40,000
max_size = 40000
# Sizes used are 0**2 = 0, 20**2 = 400, 40**2 = 1600, 60**2 = 3600,
# etc. up to 200**2 = 40,000
for size in (x**2 for x in range(0, round(sqrt(max_size)) + 1, 20)):

compute_time(size, data1, data2)

# Create a plotter object
plt = Plotter(600, 600, 0, max_size, 0, 120)

# Plot the curves
plt.pen.width(4)
plt.plot_data(data1, “blue”)
plt.plot_data(data2, “red”)

# Wait for user interaction
plt.interact()

if __name__ == ‘__main__’:
main()

The following shows a sample run of Listing 15.1 (ascendingplot.py):

List size: 0
is_ascending: True Elapsed: 0.0000026
is_ascending2: True Elapsed: 0.0000154
Speedup: 0.2

List size: 400
is_ascending: True Elapsed: 0.0105160
is_ascending2: True Elapsed: 0.0000727
Speedup: 144.6

List size: 1600
is_ascending: True Elapsed: 0.1632568
is_ascending2: True Elapsed: 0.0002386

15.1. GOOD ALGORITHMS VERSUS BAD ALGORITHMS 572

Speedup: 684.1

List size: 3600
is_ascending: True Elapsed: 0.8197846
is_ascending2: True Elapsed: 0.0005183
Speedup: 1581.6

List size: 6400
is_ascending: True Elapsed: 2.5957844
is_ascending2: True Elapsed: 0.0009212
Speedup: 2817.9

List size: 10000
is_ascending: True Elapsed: 6.3051484
is_ascending2: True Elapsed: 0.0014296
Speedup: 4410.3

List size: 14400
is_ascending: True Elapsed: 13.0304075
is_ascending2: True Elapsed: 0.0020309
Speedup: 6416.0

List size: 19600
is_ascending: True Elapsed: 24.1843773
is_ascending2: True Elapsed: 0.0027695
Speedup: 8732.4

List size: 25600
is_ascending: True Elapsed: 43.8347709
is_ascending2: True Elapsed: 0.0060735
Speedup: 7217.3

List size: 32400
is_ascending: True Elapsed: 71.5207196
is_ascending2: True Elapsed: 0.0076400
Speedup: 9361.3

List size: 40000
is_ascending: True Elapsed: 120.1243236
is_ascending2: True Elapsed: 0.0062690
Speedup: 19161.7

The is_ascending2 function consistently outperforms is_ascending, but both functions execute in less
than one second for lists of length 3,600 or less. This means if our application deals only with smaller
lists, we may not notice the difference. As the list size grows, however, the performance difference grows
dramatically. The is_ascending function requires over two minutes to process a list of size 40,000, while

the is_ascending2 function takes less than
1

1,000
second—the is_ascending2 function is almost 20,000

times faster than is_ascending! The left window in Figure 15.1 illustrates the difference graphically. The
Plotter object in Listing 15.1 (ascendingplot.py) plots the curves shown in the left window of Figure 15.1.
The blue curve shows the growth of is_ascending’s execution time as the number of list elements grow
from zero to 20,000. The red line shows the corresponding increase in is_ascending2’s execution time.
Given the scale required to plot is_ascending’s curve, the curve for is_ascending2 barely deviates from
the x axis.

15.1. GOOD ALGORITHMS VERSUS BAD ALGORITHMS 573

Figure 15.1 The left window shows the graphical output of Listing 15.1 (ascendingplot.py). The right
window shows the graphical output of Listing 15.2 (ascendingtheory.py). The left window plots of the
experimental results comparing the performance of is ascending to is ascending2. The blue curve
shows the growth of is ascending’s execution time as the number of list elements grow from zero to
20,000. The red line shows the corresponding increase in is ascending2’s execution time. Given the scale
required to plot is ascending’s curve, the curve for is ascending2 barely deviates from the x axis. The

right window plots the function
n2−n

2
with the green line and n−1 with the brown line. The vertical axis

scales are not the same absolute values in both graphs, as the left graph measures execution time in seconds
and the right graph counts if statement executions. The shape of the curves indicate that the mathematical
analysis correctly captures the relative rates of growth of execution time between the is ascending and
is ascending2 functions.

15.1. GOOD ALGORITHMS VERSUS BAD ALGORITHMS 574

How do these experimental results compare with our earlier analysis? Listing 15.2 (ascendingtheory.py)

does not call either Python function but rather plots the f (n) =
n2−n

2
and f (n) = n− 1 mathematical

functions over the same range of values as the list sizes tested in Listing 15.1 (ascendingplot.py).

Listing 15.2: ascendingtheory.py

from time import clock
from math import sqrt
from plotobj import Plotter

def main():
“”” Compares the theoretical performance of the is_ascending and

is_ascending2 functions on lists of various sizes. “””
data1, data2 = [], []

# Compute results for sizes in the range 0…40,000
max_size = 40000
# Sizes used are 0**2 = 0, 20**2 = 400, 40**2 = 1600, 60**2 = 3600,
# etc. up to 200**2 = 40,000

# Create a plotter object
plt = Plotter(600, 600, 0, max_size, 0, 750000000)

# Plot the curves
plt.pen.width(4)
data1 = [(x, (x**2 – x)/2) for x in

(x**2 for x in range(0, round(sqrt(max_size)) + 1, 20))]
data2 = [(x, x – 1) for x in

(x**2 for x in range(0, round(sqrt(max_size)) + 1, 20))]

plt.plot_data(data1, “green”)
plt.plot_data(data2, “brown”)

plt.interact()

if __name__ == ‘__main__’:
main()

The absolute numbers the functions compute will be very different from the numbers that Listing 15.1
(ascendingplot.py) produced. This is because the functions that Listing 15.2 (ascendingtheory.py) plots
represent a count of if statement executions while Listing 15.1 (ascendingplot.py) plots execution time in
seconds. If our analysis is correct, however, the shape of the curves should be similar. The right window of
Figure 15.1 shows the graphical output of Listing 15.2 (ascendingtheory.py). Note that shapes of the curves
in the left and right windows match. This means the experimental results confirm our earlier analysis. As
the list size grows, the time difference between the two functions increases. While both is_ascending and
is_ascending2 are correct algorithms, is_ascending2 is objectively better than is_ascending.

Examine again the curves in Figure 15.1 that correspond to the execution time of the is_ascending2
Python function (red curve in the left graph) and the f (n) = n−1 mathematical function that represents if
statement execution counts (brown curve in the right graph). Both appear to be flat, but this is due to the
extreme large scale of the vertical axis. If both axes used the same scale, these curves would be lines rising

15.1. GOOD ALGORITHMS VERSUS BAD ALGORITHMS 575

Figure 15.2 Result of plotting f (n) =
n2−n

2
(green line) versus f (n) = n−1 (brown line) using the same

scale for the horizontal and vertical axes. This scale provides a more realistic view of the is ascending2
function, as it really does take longer to execute as the list grows. It also emphasizes the badness of the
is ascending function, which is the really steep green line that barely moves away from the y axis.

at a 45°angle. If we change the plotter object constructor call in Listing 15.2 (ascendingtheory.py) from

# Create a plotter object
plt = Plotter(600, 600, 0, max_size, 0, 750000000)

# Create a plotter object (x and y axes use the same scale)
plt = Plotter(600, 600, 0, max_size, 0, max_size)

the scale of the vertical axis will be the same as the horizontal axis, and the program will produce the plot
shown in Figure 15.2. This scale provides a more realistic view of the is_ascending2 function, as it really

does take longer to execute as the list size grows. The function f (n) =
n2−n

2
is a parabola, but using the

same scale for both axes over the full range of list sizes makes the function look almost like a vertical line!
This perspective especially emphasizes the badness of the bad algorithm.

Note that both is_ascending and is_ascending2 scan as few elements as necessary to return a nega-
tive result. They both return False immediately upon detecting an element that is out of order. As an even
more extreme example of a correct but bad algorithm, is_ascending3 always performs the same amount
of work regardless of the list’s ordering:

def is_ascending3(lst):
result = True # List is ordered unless determined otherwise
for i in range(len(lst) – 1):

for j in range(i + 1, len(lst)):
if lst[i] > lst[j]:

15.2. SORTING 576

result = False # Found an out-of-order element
return result

The is_ascending3 function is just as correct as the is_ascending and is_ascending2 functions because
once the is_ascending3 function sets its result variable to False it can never reset it back to True.
Either it detects a reason to set result to False or it never changes it from its default value it assigned
at the beginning. Given a list with its first element larger than its second element, the is_ascending
and is_ascending2 functions both will return False upon the first execution of their if statement. The
is_ascending3 function, however, will unnecessarily go through the whole list checking all the elements!

It seems computers are never fast enough or have enough memory to satisfy all our desires for software
performance. Faster computers only serve to increase our expectations for applications that perform more
complex tasks on larger data sets. As we have seen in the simple example above, the choice of algorithm
can make a dramatic difference in the performance of a task. A correct algorithm can be so bad that even the
fastest computer cannot enable it to solve a particular problem in an acceptable amount of time. A different
algorithm, however, may be able to solve the same problem quickly on even a slow machine.

Computer scientists have been studying algorithms for decades and have established algorithms for
common software tasks. These algorithms typically work on a collection of data. While even bad algorithms
perform acceptably on small data sets, the trick is find algorithms that continue to perform acceptably as
the data size scales up.

15.2 Sorting

Lists, introduced in Chapter 10, are convenient structures for storing large amounts of data. Sorting—
arranging the elements within a list into a particular order—is a common activity. For example, a list
of integers may be arranged in ascending order (that is, from smallest to largest). A list of strings may be
arranged in lexicographical (commonly called alphabetical) order. Many sorting algorithms exist, and some
perform much better than others. We will consider one sorting algorithm that is relatively easy to describe
and implement.

Python lists have a sort method (Section 10.10) that orders the elements in a list. Similar to the
reversed function (Section 10.2), the __builtins__ module provides a sorted function the returns an
iterable object. If the elements of a list can be ordered, we can use sorted to visit its elements in sorted
order. The following code:

for elem in sorted([34, 2, 22, 70, 16, 8]):
print(elem, end=” “)

print()

prints

2 8 16 22 34 70

Unlike the list.sort method, the sorted function does not disturb the contents of the original list.

Why implement a sorting algorithm when Python provides the standard sorted function and list.sort
method? Writing a sort function gives us an opportunity to exercise our problem solving skills. It also gives
us more practice using and manipulating lists. The experience we gain though the process better equips us
to tackle problems we may encounter that have no solution in the standard library.

The selection sort algorithm is relatively easy to implement and easy to understand how it works. Its

15.2. SORTING 577

performance is acceptable for smaller lists. If A is a list, and i represents a list index, selection sort works
as follows:

1. Set n = length of list A.

2. Set i = 0.

3. Examine all the elements A[ j], where i < j < n. (This simply means to consider all the elements in the list from index i+1 to the last position in the list.) If any of these elements is less than A[i], then exchange A[i] with the smallest of these elements. (This ensures that all elements after position i are greater than or equal to A[i].) 4. If i is less than n−1, increase i by 1 and go to Step 2. 5. Done; list A is sorted. The command to “go to Step 2” in Step 4 represents a loop. When the value of i in Step 4 equals n, the algorithm goes to Step 5 and terminates with a sorted list. We can begin to translate the above description into Python as follows: n = len(A) for i in range(n - 1): # Examine all the elements A[j], where i < j < n. # If any of these A[j] is less than A[i], # then exchange A[i] with the smallest of these elements. The first statement implements Step 1, and the for statement nicely packages Steps 2 and 4. The yet-to-be- implemented body of the for statement encompasses Step 3. The directive at Step 3 beginning with “Examine all the elements A[ j], where i < j < n” also must be implemented as a loop. We continue refining our implementation with: n = len(A) for i in range(n - 1): # Examine all the elements A[j], where i < j < n. for j in range(i + 1, n): # Find an element smaller than A[i], if possible # If any A[j] is less than A[i], # then exchange A[i] with the smallest of these elements. In order to determine if any of the elements is less than A[i], we introduce a new variable named small. The purpose of small is to keep track of the position of the smallest element found so far. We will set small equal to i initially because we wish to locate any element less than the element located at position i. n = len(A) for i in range(n - 1): # small is the position of the smallest value we've seen # so far; we use it to find the smallest value less than A[i] small = i for j in range(i + 1, n): if A[j] < A[small]: small = j # Found a smaller element, update small # If small changed, we found an element smaller than A[i] if small != i: # exchange A[small] and A[i] ©2017 Richard L. Halterman Draft date: January 18, 2018 15.2. SORTING 578 Listing 15.3 (sortintegers.py) provides the complete Python implementation of the selection_sort function within a program that tests it out. Listing 15.3: sortintegers.py from random import randint def random_list(): """ Produce a list of pseudorandom integers. The list's length is chosen pseudorandomly in the range 3-20. The integers in the list range from -50 to 50. """ result = [] count = randint(3, 20) for i in range(count): result.append(randint(-50, 50)) return result def selection_sort(lst): """ Arranges the elements of list lst in ascending order. Physically rearranges the elements of lst. """ n = len(lst) for i in range(n - 1): # Note: i, small, and j represent positions within lst # lst[i], lst[small], and lst[j] represent the elements at # those positions. # small is the position of the smallest value we've seen # so far; we use it to find the smallest value less # than lst[i] small = i # See if a smaller value can be found later in the list # Consider all the elements at position j, where i < j < n for j in range(i + 1, n): if lst[j] < lst[small]: small = j # Found a smaller value # Swap lst[i] and lst[small], if a smaller value was found if i != small: lst[i], lst[small] = lst[small], lst[i] def main(): """ Tests the selection_sort function """ for n in range(10): col = random_list() print(col) selection_sort(col) print(col) print('==============================') ©2017 Richard L. Halterman Draft date: January 18, 2018 15.2. SORTING 579 main() One run of Listing 15.3 (sortintegers.py) produces: [-23, 47, -3, 4, 5, -46, 26, -27] [-46, -27, -23, -3, 4, 5, 26, 47] ============================== [32, -10, -4, 41, 10, -1, -31, 3, 28, -31, -33, 46, -45, -6, 37] [-45, -33, -31, -31, -10, -6, -4, -1, 3, 10, 28, 32, 37, 41, 46] ============================== [11, -19, 20, 43, -19, 20, -18, -17] [-19, -19, -18, -17, 11, 20, 20, 43] ============================== [9, -22, -41, 35, 10, 48, 9, 14, -20] [-41, -22, -20, 9, 9, 10, 14, 35, 48] ============================== [-38, -3, -7, 41, -8, -11, -23, 9, -47, 38] [-47, -38, -23, -11, -8, -7, -3, 9, 38, 41] ============================== [-47, 1, -37, 16, -40, -14, 2, 38, 43, 19, 45] [-47, -40, -37, -14, 1, 2, 16, 19, 38, 43, 45] ============================== [8, 39, 35, -42] [-42, 8, 35, 39] ============================== [-8, -22, -13, 47, -28, -46, -21, -42, 27, 14, 47, -21, 2, -47] [-47, -46, -42, -28, -22, -21, -21, -13, -8, 2, 14, 27, 47, 47] ============================== [37, -21, -32, -7] [-32, -21, -7, 37] ============================== [33, -42, -26, 35, 37, 36, -1, 47, 24, 5, 41, -6, 48, 6, 43] [-42, -26, -6, -1, 5, 6, 24, 33, 35, 36, 37, 41, 43, 47, 48] ============================== Notice than in each case the selection_sort function rearranges the elements in the pseudorandomly generated list into correct ascending order. To check the correctness of our sort we need to be sure that: • the sorted list contains the same number of elements as the original, unsorted list, • no elements in the original list are missing, • no elements in the sorted list appear more frequently than they did in the original, unsorted list, and • the elements appear in ascending order. The output of Listing 15.3 (sortintegers.py) provides evidence that our selection_sort function is work- ing correctly. ©2017 Richard L. Halterman Draft date: January 18, 2018 15.3. FLEXIBLE SORTING 580 15.3 Flexible Sorting What if we wish to change the behavior of the sorting function in Listing 15.3 (sortintegers.py) so that it arranges the elements in descending order instead of ascending order? It is actually an easy modification; simply change the line if lst[j] < lst[small]: to be if lst[j] > lst[small]:

What if instead we want to change the sort so that it sorts the elements in ascending order except that all
the even numbers in the list appear before all the odd numbers? This modification would be a little more
complicated, but, with some effort, we could modify our selection_sort function to achieve this effect.

The next question is more intriguing: How can we rewrite the selection_sort function so that, by
passing an additional parameter, it can sort the list in any way we want?

Consider the following comparison function:

def less_than(m, n):
return m < n Ordinarily a function such as this one would not be very helpful. Rather than calling this function it is easier (and more efficient) to use the < operator directly. With this less_than function, however, we can rewrite the line if lst[j] < lst[small]: as if less_than(lst[j], lst[small]): This initially does not seem to buy us much—it appears only to make the code a bit more obscure. Notice that to change the way the if statement compares we need to change the name of the function. If we have a greater_than function, for example, we could use it in the place of less_than. Admittedly, changing a function name generally requires more typing than changing a single symbol (< to >); however, we will see
that it gives us the ability to build a sort function that can order its elements in many different ways.

We can make our sort function more flexible by passing an ordering function as an additional parameter
(see Section 8.5 for examples of functions as parameters to other functions). Listing 15.4 (flexiblesort.py)
arranges the elements in a list two different ways using the same selection_sort function.

Listing 15.4: flexiblesort.py

def random_list():
“””
Produce a list of pseudorandom integers.
The list’s length is chosen pseudorandomly in the
range 3-20.
The integers in the list range from -50 to 50.
“””
from random import randrange
result = []
count = randrange(3, 20)

15.3. FLEXIBLE SORTING 581

for i in range(count):
result += [randrange(-50, 50)]

return result

def less_than(m, n):
“”” Returns true if m is less than n; otherwise, returns false “””
return m < n def greater_than(m, n): """ Returns true if m is greater than n; otherwise, returns false """ return m > n

def selection_sort(lst, cmp):
“””
Arranges the elements of list lst in ascending order.
The comparer function cmp is used to order the elements.
The contents of lst are physically rearranged.
“””
n = len(lst)
for i in range(n – 1):

# Note: i, small, and j represent positions within lst
# lst[i], lst[small], and lst[j] represent the elements at
# those positions.
# small is the position of the smallest value we’ve seen
# so far; we use it to find the smallest value less
# than lst[i]
small = i
# See if a smaller value can be found later in the list
# Consider all the elements at position j, where i < j < n. for j in range(i + 1, n): if cmp(lst[j], lst[small]): small = j # Found a smaller value # Swap lst[i] and lst[small], if a smaller value was found if i != small: lst[i], lst[small] = lst[small], lst[i] def main(): """ Tests the selection_sort function """ original = random_list() # Make a random list working = original[:] # Make a working copy of the list print('Original: ', working) selection_sort(working, less_than) # Sort ascending print('Ascending: ', working) working = original[:] # Make a working copy of the list print('Original: ', working) selection_sort(working, greater_than) # Sort descending print('Descending:', working) ©2017 Richard L. Halterman Draft date: January 18, 2018 15.4. SEARCH 582 main() The output of Listing 15.4 (flexiblesort.py) is Original: [-8, 24, -46, -7, -26, -29, -44] Ascending: [-46, -44, -29, -26, -8, -7, 24] Original: [-8, 24, -46, -7, -26, -29, -44] Descending: [24, -7, -8, -26, -29, -44, -46] The comparison function passed to the sort routine customizes the sort’s behavior. The basic structure of the sorting algorithm does not change, but its notion of ordering is adjustable. If the second parameter to selection_sort is less_than, the function arranges the elements ascending order. If the second param- eter instead is greater_than, the function sorts the list in descending order. More creative orderings are possible with more elaborate comparison functions. Selection sort is a relatively efficient simple sort, but more advanced sorts are, on average, much faster than selection sort, especially for large data sets. One such general purpose sort is Quicksort, devised by C. A. R. Hoare in 1962. Quicksort is the fastest known general purpose sort. 15.4 Search Searching a list for a particular element is a common activity. We examine two basic strategies: linear search and binary search. 15.4.1 Linear Search Listing 15.5 (linearsearch.py) uses a function named locate that returns the position of the first occurrence of a given element in a list; if the element is not present, the function returns None. Listing 15.5: linearsearch.py def locate(lst, seek): """ Returns the index of element seek in list lst, if seek is present in lst. Returns None if seek is not an element of lst. lst is the list in which to search. seek is the element to find. """ for i in range(len(lst)): if lst[i] == seek: return i # Return position immediately return None # Element not found def format(i): """ Prints integer i right justified in a 4-space horizontal area. Prints "****" if i > 9,999.
“””
if i > 9999:

15.4. SEARCH 583

print(“****”) # Too big!
else:

print(“{0:>4}”.format(i))

def show(lst):
“””
Prints the contents of list lst
“””
for item in lst:

print(“{0:>4}”.format(item), end=”) # Print element right justifies in 4 spaces
print() # Print newline

def draw_arrow(value, n):
“””
Print an arrow to value which is an element in a list.
n specifies the horizontal offset of the arrow.
“””
print((‘{0:>’ + str(n) + ‘}’).format(” ˆ “))
print((‘{0:>’ + str(n) + ‘}’).format(” | “))
print((‘{0:>’ + str(n) + ‘}{1}’).format(” +– “, value))

def display(lst, value):
“””
Draws an ASCII art arrow showing where
the given value is within the list.
lst is the list.
value is the element to locate.
“””
show(lst) # Print contents of the list
position = locate(lst, value)
if position != None:

position = 4*position + 7 # Compute spacing for arrow
draw_arrow(value, position)

else:
print(“(“, value, ” not in list)”, sep=”)

print()

def main():
a = [100, 44, 2, 80, 5, 13, 11, 2, 110]
display(a, 13)
display(a, 2)
display(a, 7)
display(a, 100)
display(a, 110)

main()

Note, for example, that if n is 20, the expression

‘{0:>’ + str(n) + ‘}’).format(” ˆ “)

15.4. SEARCH 584

right justifies the string ‘ ˆ ‘ within 20 spaces; that is,

‘ ˆ ‘

The output of Listing 15.5 (linearsearch.py) is

100 44 2 80 5 13 11 2 110
ˆ
|
+– 13

100 44 2 80 5 13 11 2 110
ˆ
|
+– 2

100 44 2 80 5 13 11 2 110
(7 not in list)

100 44 2 80 5 13 11 2 110
ˆ
|
+– 100

100 44 2 80 5 13 11 2 110
ˆ
|
+– 110

The key function in Listing 15.5 (linearsearch.py) is locate; all the other functions simply lead to a more
interesting display of locate’s results. If locate finds a match, the function immediately returns the
position of the matching element; otherwise, if after examining all the elements of the list locate cannot
find the element sought, the function returns None. Here None indicates the function could not return a valid
answer. The calling code, in this example the display function, must ensure that locate’s result is not
None before attempting to use the result as an index into a list.

The kind of search performed by locate is known as linear search, since the algorithm takes a straight
line path from the beginning of the list to the end of the list considering each element in order. Figure 15.3
illustrates linear search.

15.4.2 Binary Search

Linear search is acceptable for relatively small lists, but the process of examining each element in a large
list is time consuming. An alternative to linear search is binary search. In order to perform binary search, a
list must be in sorted order. Binary search exploits the sorted structure of the list using a clever but simple
strategy that quickly zeros in on the element to find:

1. If the list is empty, return None.

2. Check the element in the middle of the list. If that element is what you are seeking, return its position.
If the middle element is larger than the element you are seeking, perform a binary search on the first
half of the list. If the middle element is smaller than the element you are seeking, perform a binary
search on the second half of the list.

15.4. SEARCH 585

Figure 15.3 Linear search first considers the element at index 0, then index 1, then index 2, etc. until it finds
the element it seeks or reaches the back of the list. The algorithm progresses through the list in a straight
line without jumping around.

lst
100 2 80

1 20 3

5 64 7

13 11 244 110

8
13?

lst = [100, 44, 2, 80, 5, 13, 11, 2, 110]

x = locate(lst, 13)

This approach is analogous to looking for a telephone number in the phone book in this manner:

1. Open the book at its center. If the name of the person is on one of the two visible pages, look at the
phone number.

2. If not, and the person’s last name is alphabetically less the names on the visible pages, apply the
search to the left half of the open book; otherwise, apply the search to the right half of the open book.

3. Discontinue the search with failure if the person’s name should be on one of the two visible pages
but is not present.

We can implement the binary search algorithm as a Python function as shown in Listing 15.6 (binarysearch.py).

Listing 15.6: binarysearch.py

def binary_search(lst, seek):
“””
Returns the index of element seek in list lst,
if seek is present in lst.
Returns None if seek is not an element of lst.
lst is the list in which to search.
seek is the element to find.
“””
first = 0 # Initialize the first position in list
last = len(lst) – 1 # Initialize the last position in list
while first <= last: # mid is middle position in the list mid = first + (last - first + 1)//2 # Note: Integer division if lst[mid] == seek: return mid # Found it elif lst[mid] > seek:

last = mid – 1 # continue with 1st half

15.4. SEARCH 586

else: # v[mid] < seek first = mid + 1 # continue with 2nd half return None # Not there def format(i): """ Prints integer i right justified in a 4-space horizontal area. Prints "****" if i > 9,999.
“””
if i > 9999:

print(“****”) # Too big!
else:

print(“{0:4>}”.format(i))

def show(lst):
“””
Prints the contents of list lst
“””
for item in lst:

print(“{0:4>}”.format(item), end=”) # Print element right justifies in 4 spaces
print() # Print newline

position = 4*position + 7 # Compute spacing for arrow
draw_arrow(value, position)

else:
print(“(“, value, ” not in list)”, sep=”)

print()

def main():
a = [2, 5, 11, 13, 44, 80, 100, 110]
display(a, 13)

15.4. SEARCH 587

display(a, 2)
display(a, 7)
display(a, 100)
display(a, 110)

main()

In the binary_search function:

• The initializations of first and last:

first = 0 # Initialize the first position in list
last = len(lst) – 1 # Initialize the last position in list

ensure that first is less than or equal to last for a nonempty list. If the list is empty, first is zero,
and last is equal to len(lst) – 1 = 0−1 = −1. So in the case of an empty list the function will
skip the loop and return None. This is correct behavior because an empty list cannot possibly contain
any item we seek.

• The calculation of mid ensures that first ≤ mid ≤ last.

• If mid is the location of the sought element (checked in the first if statement), the loop terminates,
and returns the correct position.

• The elif and else blocks ensure that either last decreases or first increases each time through
the loop. Thus, if the loop does not terminate for other reasons, eventually first will be larger than
last, and the loop will terminate. If the loop terminates for this reason, the function returns None.
This is the correct behavior.

• The modification to either first or last in the elif and else blocks exclude irrelevant elements
from further search. The number of elements to consider is cut in half each time through the loop.

Figure 15.4 illustrates how binary search works.

The implementation of the binary search algorithm is more complicated than the simpler linear search
algorithm. Ordinarily simpler is better, but for algorithms that process data structures that potentially hold
large amounts of data, more complex algorithms employing clever tricks that exploit the structure of the
data (as binary search does) often dramatically outperform simpler, easier-to-code algorithms.

For a fair comparison of linear vs. binary search, suppose we want to locate an element in a sorted list.
An ordered list is essential for binary search, but it can be helpful for linear search as well. The revised
linear search algorithm for ordered lists is

# This version requires list lst to be sorted in
# ascending order.
def linear_search(lst, seek):

i = 0 # Start at beginning
n = len(lst) # Length of list
while i < n and lst[i] <= seek: if lst[i] == seek: return i # Return position immediately return None # Element not found ©2017 Richard L. Halterman Draft date: January 18, 2018 15.4. SEARCH 588 Figure 15.4 Binary search begins in the middle of an ordered list. The algorithm jumps forward or backward as needed in decreasing stride amounts. Each successive probe reduces the number of elements in its search space by one-half. lst 10 20 28 1 20 3 29 5 64 7 33 34 4514 48 8 33? 5 lst = [10, 14, 20, 28, 29, 33, 34, 45, 48] x = locate(lst, 33) Notice that, as in the original version of linear search, the loop will terminate when it has examined all the elements, but this version will terminate early when it encounters an element larger than the sought element. Since the list is sorted, there is no need to continue the search once the search has found an element larger than the value sought; seek cannot appear after a larger element in a sorted list. Suppose a list to search contains n elements. In the worst case—looking for an element larger than any currently in the list—the loop in linear search takes n iterations. In the best case—looking for an element smaller than any currently in the list—the function immediately returns without considering any other elements. The number of loop iterations thus ranges from 1 to n, and so on average linear search requires n2 comparisons before the loop finishes and the function returns. Now consider binary search. After each comparison the size of the list remaining to consider is one-half the original size. If the binary search algorithm does not locate the element on its first probe, the number of remaining elements to search is n2 . The next time through the loop, the number of elements left to consider drops to n4 , then n 8 , and so forth. The problem of determining how many times a set of things can be divided in half until only one element remains can be solved with a base-2 logarithm. For binary search, the worst case scenario of not finding the sought element requires the loop to make log2 n iterations. How does this analysis help us determine which search is better? The quality of an algorithm is judged by two key characteristics: • How much time (processor cycles) does it take to run? • How much space (memory) does it take to run? In our situation, both search algorithms process the list with only a few extra local variables, so for large lists they both require essentially the same space. The big difference here is speed. Binary search performs more elaborate computations each time through the loop, and each operation takes time, so perhaps binary search is slower. Linear search is simpler (fewer operations through the loop), but perhaps its loop executes many more times than the loop in binary search, so overall it is slower. ©2017 Richard L. Halterman Draft date: January 18, 2018 15.4. SEARCH 589 We can deduce the faster algorithm in two ways: empirically and analytically. An empirical test is an experiment; we carefully implement both algorithms and then measure their execution times. The analyt- ical approach analyzes the source code to determine how many operations the computer’s processor must perform to run the program on a problem of a particular size. Listing 15.7 (searchcompare.py) gives us some empirical results. Listing 15.7: searchcompare.py """ Compares the running times of linear search and binary search on lists of various sizes. """ def binary_search(lst, seek): """ Returns the index of element seek in list lst, if seek is present in lst. lst must be in sorted order. Returns None if seek is not an element of lst. lst is the list in which to search. seek is the element to find. """ first = 0 # Initially the first element in list last = len(lst) - 1 # Initially the last element in list while first <= last: # mid is middle of the list mid = first + (last - first + 1)//2 # Note: Integer division if lst[mid] == seek: return mid # Found it elif lst[mid] > seek:

last = mid – 1 # continue with 1st half
else: # v[mid] < seek first = mid + 1 # continue with 2nd half return None # Not there def ordered_linear_search(lst, seek): """ Returns the index of element seek in list lst, if seek is present in lst. lst must be in sorted order. Returns None if seek is not an element of lst. lst is the list in which to search. seek is the element to find. """ i = 0 n = len(lst) while i < n and lst[i] <= seek: if lst[i] == seek: return i # Return position immediately i += 1 return None # Element not found ©2017 Richard L. Halterman Draft date: January 18, 2018 15.4. SEARCH 590 def run_search(lst, seeks, search, trials): """ Searches for all the elements in an ordered list (lst) using search function search. Averages the running time over trials runs. Returns the average time. """ from time import clock n = len(lst) elapsed = 0 start = clock() # Start the clock for i in range(trials): for elem in seeks: i = search(lst, elem) if i != lst[i]: print("error") stop = clock() # Stop the clock elapsed += stop - start return elapsed/trials # Average time for search def test_searches(lst, seeks, trials): """ Measures the running times of ordered linear search and binary search on a given list. Averages the times over n runs. """ # Find each element using ordered linear search lin = run_search(lst, seeks, ordered_linear_search, trials) # Find each element using binary search bin = run_search(lst, seeks, binary_search, trials) # Print the results print('{0:6} {1:10.5f} {2:10.5f} {3:8.1f}'\ .format(len(lst), lin, bin, lin/bin)) def make_search_set(n): """ Make a list of elements to seek """ from random import randrange result = [] for i in range(n): result += [randrange(n)] return result def main(): """ Makes a table comparing the running times of ordered linear search vs. binary search on lists of various sizes. """ # Number of trials over which to average the results trials = 10 # Print table header ©2017 Richard L. Halterman Draft date: January 18, 2018 15.4. SEARCH 591 print(' Size Linear Binary Speedup') print('-----------------------------------------') # Small lists: 10 to 100, in steps of 10 for size in range(10, 100, 10): test_list = list(range(size)) seek_list = make_search_set(size) test_searches(test_list, seek_list, trials) # Medium lists: 100 to 1,000, in steps of 100 for size in range(100, 1000, 100): test_list = list(range(size)) seek_list = make_search_set(size) test_searches(test_list, seek_list, trials) # Large lists: 1,000 to 5,000, in steps of 500 for size in range(1000, 5001, 500): test_list = list(range(size)) seek_list = make_search_set(size) test_searches(test_list, seek_list, trials) if __name__ == '__main__': main() The main function in Listing 15.7 (searchcompare.py) builds lists of sequential integer values, [1, 2, 3, ...] of various sizes. The program assigns each of these lists in turn to the test_list variable. The program also builds lists of random integer values (referenced via seek_list) to be used as search candidates for each test_list. It then passes these lists off to the test_searches function to measure the running times of the two search functions. The test_searches function, in turn, calls the run_search function to test a particular search function. The run_search function uses the elements from main’s seek_list as search candidates. The run_search function searches for all the elements in seek_list a specified number of times and averages the running times. The main function directs test_searches to average 10 runs for each of the list sizes. On one system, Listing 15.7 (searchcompare.py) produces the following table: Size Linear Binary Speedup ----------------------------------------- 10 0.00003 0.00003 1.2 20 0.00012 0.00006 2.0 30 0.00024 0.00012 1.9 40 0.00036 0.00016 2.3 50 0.00049 0.00021 2.3 60 0.00082 0.00026 3.1 70 0.00104 0.00032 3.2 80 0.00138 0.00039 3.6 90 0.00202 0.00043 4.7 100 0.00245 0.00049 5.0 200 0.00868 0.00115 7.5 300 0.01962 0.00185 10.6 400 0.03215 0.00262 12.3 500 0.05158 0.00342 15.1 600 0.07590 0.00437 17.4 700 0.10805 0.00522 20.7 800 0.13329 0.00600 22.2 900 0.17307 0.00687 25.2 ©2017 Richard L. Halterman Draft date: January 18, 2018 15.4. SEARCH 592 Table 15.1 Analysis of Linear Search Algorithm. The n2 loop iterations is based on the average time to locate an element. The function will execute exactly one of the two return statements during a given call, so each is given a cost of 12 . Operation Times Total Action Operation(s) Count Executed Cost i = 0 = 1 1 1 n = len(lst) =, len 2 1 2 while i < n and lst[i] <= seek: <, and, <=, [] 4 n2 2n if lst[i] == seek: [], == 2 n2 n return i return 1 12 1 2 return None return 1 12 1 2 Total time units 3n+4 1000 0.20985 0.00780 26.9 1500 0.49346 0.01256 39.3 2000 0.85834 0.01739 49.4 2500 1.39785 0.02284 61.2 3000 1.95955 0.02802 69.9 3500 2.71689 0.03321 81.8 4000 3.56608 0.03960 90.1 4500 4.45774 0.04446 100.3 5000 7.73395 0.04983 155.2 The rightmost column of the table shows the speedup factor of binary search over ordered linear search. Notice that the speedup increases as the list length grows. For lists that contain more than 4,500 elements binary search is more than 100 times faster than linear search. Empirically, binary search performs dramatically better than linear search. The left side of Figure 15.5 plots the results produced by Listing 15.7 (searchcompare.py) for lists containing up to 1,000 elements. In addition to empirical observations, we can judge which algorithm is better by analyzing the source code for each function. Each arithmetic operation, assignment, logical comparison, function call, and list access requires time to execute. We will assume each of these activities requires one unit of processor “time.” This assumption is not strictly true, but it will give good results for relative comparisons. Since we will follow the same rules when analyzing both search algorithms, the relative results for comparison will be close enough for our purposes. We first consider linear search. We determined that, on average, the loop makes n2 iterations for a list of size n. The initialization of i happens only one time during each call to linear_search. All other activity involved with the loop except the return statements happens n2 times. The function returns either i or None, and it may excute at most one return statement during each call. Table 15.1 shows the breakdown for linear search. The results in Table 15.1 indicate the running time of the linear_search function can be expressed as a simple mathematical linear function: f (n) = 3n + 4. Next, we consider binary search. We determined that in the worst case the loop in binary_search iterates log2 n times if the list contains n elements. The binary_search function performs the two initial- izations before the loop just once per call. Most of the actions within the loop occur log2 n times, except that only one return statement can be executed per call, and in the if/elif/else statement only one path can be chosen per loop iteration. Table 15.2 shows the complete analysis of binary search. We see that the execution time for binary search can be expressed as the logarithmic function 12log2 n+6. ©2017 Richard L. Halterman Draft date: January 18, 2018 15.5. RECURSION REVISITED 593 Table 15.2 Analysis of Binary Search Algorithm. Each time through the loop the function executes either the elif or else statement, so each one is charged is charged 12 its actual cost. Operation Times Total Action Operation(s) Count Executed Cost first = 0 = 1 1 1 last = len(lst) - 1 =, len, - 3 1 3 while first <= last: <= 1 log2 n log2 n mid=first+(last-first+1)//2 =, +, -, +, // 5 log2 n 5log2 n if lst[mid] == seek: [], == 2 log2 n 2log2 n return mid return 1 1 1 elif lst[mid] > seek: [], > 2 log2 n 2log2 n

last = mid – 1 =, – 2 12 log2 n log2 n
else: 0 0

first = mid + 1 =, + 2 12 log2 n log2 n
return None return 1 1 1

Total time units 12log2 n+6

Figure 15.5 compares the empirical results with the analytical results for lists containing 100 to 1,000
elements. The left side of Figure 15.5 plots the values produced by Listing 15.7 (searchcompare.py), and
the right side of Figure 15.5 plots the two functions 3n+ 4 and 12log2 n+ 6. In these two graphs we can
compare the growth rates of the two search techniques by examining the shapes of the curves. Notice how
closely the two graphs compare to each other. In both graphs the gap between the linear search curve and
binary search curve increasingly widens at the same rate as the list size incrases. The binary search curve
appears to be effectively flat, although it really is growing very slowly, much more slowly than the linear
search curve. The bottom line is that binary search is fast even for large lists.

15.5 Recursion Revisited

In Section 8.3 we saw recursive functions for factorial and greatest common divisor. Suppose we have a
recursive function named f that accepts a single parameter. Recall that recursion works in the following
manner:

1. If function f’s argument selects the base case of the recursion, return the default answer;

2. otherwise, do something with the argument and invoke f with an argument that is closer to the base
case.

We can restate this in a more informal way:

1. If f’s argument represents a trivial problem, return the default, easy answer.

2. If f’s argument represents a nontrivial problem, return the result of computing part of the problem
and combining it with the solution to a smaller or simpler problem.

The phase “the solution to a smaller or simpler problem” is the recursive call. As the recursion progresses,
the function works on smaller and/or simpler problems until it reaches a trivial problem, at which point the
recursive process is over.

15.5. RECURSION REVISITED 594

Figure 15.5 Linear search vs. binary search. The two graphs plot the execution speeds of ordered linear
search and binary search on lists with 100 to 1,000 elements. The graph on the left plots data from timing
the program’s execution. The graph on the right plots the functions derived from analyzing the Python
source code. Notice how closely the two graphs correspond.

500

1000

1500

2000

2500

3000

3500

1 2 3 4 5 6 7 8 9 10

0.05

0.1

0.15

0.2

0.25

1 2 3 4 5 6 7 8 9 10

Empirical Results Analytical Results

Linear searchLinear search

Binary search Binary search

100 200 300 400 500 600 700 800 900 1000 100 200 300 400 500 600 700 800 900 1000

List Size List Size
O

p
e
ra

ti
o

n
s

T
im

e
(

se
c
o

n
d

Many data structures lend themselves to recursive algorithms. Consider the task of counting the occur-
rences of a particular element within a list. We will name the function count, and it will accept a list and an
additional parameter that represents the element to count. Given a correctly implemented count function,
the following code fragment,

lst1 = [21, 19, 31, 22, 14, 31, 22, 6, 31]
print(count(lst1, 31))
lst2 = [‘FRED’, [2, 3], 44, ‘WILMA’, ‘FRED’, 8, ‘BARNEY’]
print(count(lst2, ‘FRED’))
print(count(lst2, ‘BETTY’))
print(count([], 16))

should print

3
2
0
0

We will think about the problem recursively. What should the function do if the list is empty? Is this a
trivial problem? What should the function do if the list is not empty?

If the list is empty, the problem is trivial. No matter what we are trying to count, it will not appear in an
empty list. In this case the count function simply can return zero.

What if the list is not empty? We can look at the first element. If the first element is equal to the value
we wish to count, we know we have one occurrence, so the answer is one plus the number of times the
value appears in the rest of the list. If the first element is not equal to the value we wish to count, the answer
is just the number of times the value appears in the rest of the list.

15.5. RECURSION REVISITED 595

Do you see that “the number of times the value appears in the rest of the list” is a recursive call on a
shorter list? Each recursive call processes a shorter and shorter list until the list is empty (the trivial case).
All along the chain of recursive function calls the function is either adding one or not adding one to count’s
ultimate answer. Listing 15.8 (recursivecount.py) implements our recursive count function.

Listing 15.8: recursivecount.py

def count(lst, item):
“”” Counts the number of occurrences of item within the list lst “””
if len(lst) == 0: # Is the list empty?

return 0 # Nothing can appear in an empty list
else:

# Count the occurrences in the rest of the list
# (all but the first element)
count_rest = count(lst[1:], item)
if lst[0] == item:

return 1 + count_rest
else:

return count_rest

def main():
lst1 = [21, 19, 31, 22, 14, 31, 22, 6, 31]
print(count(lst1, 31))
lst2 = [‘FRED’, [2, 3], 44, ‘WILMA’, ‘FRED’, 8, ‘BARNEY’]
print(count(lst2, ‘FRED’))
print(count(lst2, ‘BETTY’))
print(count([], 16))

if __name__ == ‘__main__’:
main()

The expression count([21, 19, 31, 14, 31, 6, 31], 31) would evaluate as

count([21, 19, 31, 14, 31, 6, 31], 31) = count([19, 31, 14, 31, 6, 31], 31)
= count([31, 14, 31, 6, 31], 31)
= 1 + count([14, 31, 6, 31], 31)
= 1 + count([31, 6, 31], 31)
= 1 + 1 + count([6, 31], 31)
= 1 + 1 + count([31], 31)
= 1 + 1 + 1 + count([], 31)
= 1 + 1 + 1 + 0
= 1 + 1 + 1
= 1 + 2
= 3

While the count function in Listing 15.8 (recursivecount.py) works properly, it has one, potentially big
disadvantage. Each time the function’s execution selects the recursive route it slices the list. Slicing a list
creates a copy of the list (see Section 10.7). This means every call to count in the recursive call chain makes
a complete copy of the list, except for the first element of each successive list. If the list is long, this can
unnecessarily consume a large amount of the computer’s memory. How big can it get? Consider an initial
call to count that passes a list of 1,000 elements. The first recursive call passes a new list of 999 elements.

15.5. RECURSION REVISITED 596

The second recursive call passes a new list of 998 elements, and so forth. By the time it completes, the
count will have created 999 extra lists, holding a combined total of 499,500 elements. The space required
to process the list is about 500 times the size of original list. Not only does the recursion use more memory,
copying the list takes time. This excessive list copying slows down the program’s execution.

It would be better to implement the count function so that it does not make any copies. Listing 15.9
(inplacecount.py) implements a recursive count function that makes no copies of the list.

Listing 15.9: inplacecount.py

def count_helper(lst, pos, item):
“”” Counts the number of occurrences of item within the list

lst. pos represents the current position under
examination within the list. “””

if pos == len(lst): # Are we past the end of the list?
return 0 # Nothing can appear past the end

else:
# Count the occurrences in the rest of the list
# (all but the first element)
count_rest = count_helper(lst, pos + 1, item)
if lst[pos] == item:

return 1 + count_rest
else:

return count_rest

def count(lst, item):
“”” Counts the number of occurrences of item within the list

lst. Delegates the work to the recursive count_helper
function, passing zero as the initial position (which is
the index of the first element in the list). “””

return count_helper(lst, 0, item)

if __name__ == ‘__main__’:
main()

Listing 15.9 (inplacecount.py) uses two functions to do the counting. Its count function merely calls
count_helper with the proper initial parameters. The count_helper function does all the interesting
work. Instead of creating copies of the list, count_helper accepts an additional parameter, an index, for
the recursion to keep track of its position within the list. The list parameter is an alias of the original list,
not a copy. When a function can process a list without making a copy, we say the function processes the
list in place.

Listing 15.9 (inplacecount.py) exposes the count_helper function, making it available to the main
function and other code. If the programmer’s intention is for only the count function to use count_helper,

15.5. RECURSION REVISITED 597

we can make it local to count, as Listing 15.10 (inplacecountlocal.py) illustrates (see Section 8.9 for more
information about local function definitions).

Listing 15.10: inplacecountlocal.py

def count(lst, item):
“”” Counts the number of occurrences of item within the list

lst. Delegates the work to the recursive count_helper
function, passing zero as the initial position (which is
the index of the first element in the list). “””

def count_helper(pos):
“”” Local function counts the number of occurrences of an

item within a list.
pos represents the current position under examination

within the list.
lst and item are nonlocal variables from the outer context. “””

if pos == len(lst): # Are we past the end of the list?
return 0 # Nothing can appear past the end

else:
# Count the occurrences in the rest of the list
# (all but the first element)
count_rest = count_helper(pos + 1)
if lst[pos] == item:

return 1 + count_rest
else:

return count_rest

# Body of count function
return count_helper(0)

if __name__ == ‘__main__’:
main()

In Listing 15.10 (inplacecountlocal.py), the count_helper function is inaccessible outside of the count
function. Note also that the count_helper function can access count’s lst and item parameters directly.
This reduces count_helper’s parameter count to one.

You may be thinking that it wold be simpler to implement our counting function with a loop in a manner
similar to linear search:

def count(lst, item):
cnt = 0 # Initialize item count
for elem in lst:

15.5. RECURSION REVISITED 598

if elem == item:
cnt += 1 # Found an item, count it

return cnt

This processes the list in place and does not use recursion. This version of count actually is superior to both
recursive versions. As we saw in Section 8.3, every function call requires a little extra time and memory.
If two functions—one iterative and one recursive—faithfully implement the same algorithm, the iterative
version will be more efficient.

A recursive function does have one distinct advantage over a non-recursive function, though. A recur-
sive function does not just call itself; the self-call eventually returns back to the site of its invocation. Each
recursive invocation has its own parameters and creates its own local variables. When the function returns
to itself, it “remembers” its original parameters and local variables the way they were before the recursive
invocation. We say the function unwinds back to its previous state.

Listing 15.11 (recursivememory.py) demonstrates the unwinding power of recursion.

Listing 15.11: recursivememory.py

from random import randint

def rec(n, depth):
“”” Prints the value of the parameter n and local variable

rand before and after the recursive call.
n is the parameter of interest.
depth represents the depth of the recursion. “””

rand = randint(0, 1000) # Make a random number
print(‘ ‘ * depth, ‘Entering: n =’, n, ‘ rand =’, rand)
if n == 0:

print(‘ ‘ * depth, ‘ *** Recursion over ***’)
else:

rec(n – 1, depth + 1)
print(‘ ‘ * depth, ‘Exiting: n =’, n, ‘ rand =’, rand)

rec(10, 0)

The rec function in Listing 15.11 (recursivememory.py) is recursive. The first parameter, n, is the parameter
of interest. The second parameter, depth, reflects the depth of the recursion. The depth variable controls
the indentation level of each printed line.

Listing 15.11 (recursivememory.py) prints

Entering: n = 10 rand = 716
Entering: n = 9 rand = 970

Entering: n = 8 rand = 21
Entering: n = 7 rand = 835

Entering: n = 6 rand = 11
Entering: n = 5 rand = 759

Entering: n = 4 rand = 168
Entering: n = 3 rand = 65

Entering: n = 2 rand = 86
Entering: n = 1 rand = 238

Entering: n = 0 rand = 991
*** Recursion over ***

15.5. RECURSION REVISITED 599

Exiting: n = 0 rand = 991
Exiting: n = 1 rand = 238

Exiting: n = 2 rand = 86
Exiting: n = 3 rand = 65

Exiting: n = 4 rand = 168
Exiting: n = 5 rand = 759

Exiting: n = 6 rand = 11
Exiting: n = 7 rand = 835

Exiting: n = 8 rand = 21
Exiting: n = 9 rand = 970

Exiting: n = 10 rand = 716

Observe that the unwinding of the recursive calls restores the original values of the parameter n and local
variable rand. Since rand is assigned pseudo-probablistically, it is not possible to restore its original value
without first storing it somewhere for later retrieval. The function-call-and-return process automatically
takes care of saving and restoring the previous values of local variables.

It is more difficult to write a non-recursive function that has this ability to unwind itself to a previous
program state. Such non-recursive implementations usually offer no efficiency advantages. Listing 15.12
(nonrecursivememory.py) provides a non-recursive version of the rec function.

Listing 15.12: nonrecursivememory.py

from random import randint

def nonrec(n, depth):
“”” Prints the value of the parameter n and local variable

rand before and after the recursive call.
n is the parameter of interest.
depth represents the depth of the recursion. “””

history = []
while n != 0:

rand = randint(0, 1000) # Make a random number
history += [(n, depth, rand)] # Remember original values of n and depth
print(‘ ‘ * depth, ‘Entering: n =’, n, ‘ rand =’, rand)
n -= 1
depth += 1

print(‘ ‘ * depth, ‘ *** Recursion over ***’)
while len(history) > 0:

n, depth, rand = history[-1]
del history[-1]
print(‘ ‘ * depth, ‘Exiting: n =’, n, ‘ rand =’, rand)

nonrec(10, 0)

The output of Listing 15.12 (nonrecursivememory.py) is identical to the output of Listing 15.11 (recursivememory.py).
Listing 15.12 (nonrecursivememory.py) uses two separate, sequential loops and an accessory list to simulate
the recursive behavior of Listing 15.11 (recursivememory.py). The purpose of the local history list is to
remember the current state of the variables n, depth, and rand so the executing program can restore their
values after the simulated recursion “returns.” The extra space for the history list and extra time spent
managing the history list is comparable to the space and time the recursive function requires. It is much
easier to allow the magic of recursion to automatically take care of saving and restoring the function’s local
variables and parameters.

15.6. LIST PERMUTATIONS 600

The ability of a function to remember its current state, call itself on a subproblem, and return to its
previous state is essential to some algorithms. Section 15.6 explores one such algorithm.

15.6 List Permutations

Sometimes it is useful to consider all the possible arrangements of the elements within a list. A sorting
algorithm, for example, must work correctly on any initial arrangement of elements in a list. To test a sort
function, a programmer could check to see to see if it produces the correct result for all arrangements of
a relatively small list. We saw in Section 5.4 that an arrangement of a sequence of ordered items is called
a permutation. Listing 5.20 (permuteabc.py) prints all the permutations of the sequence ABC. We need
something more flexible: a function that generates all the possible permutations of any list. The function
will accept a list as a parameter and return a list containing all the permutations of the parameter. (Note that
the return value is a list of lists.) Listing 15.13 (listpermutations.py) contains functions that build a new list
containing all the permutations of a given list.

Listing 15.13: listpermutations.py

def perm(lst, begin, result):
“”” Creates a list (result) containing all the permutations of the

elements of a given list (lst), beginning with a
specified index (begin).
This is a helper function for the permutations function. “””

end = len(lst) – 1 # Index of the last element
if begin == end:

result += [lst[:]] # Copy lst into result
else:

for i in range(begin, end + 1): # Consider all indices
# Interchange the element at the first position
# with the element at position i
lst[begin], lst[i] = lst[i], lst[begin]
# Recursively permute the rest of the list
perm(lst, begin + 1, result)
# Undo the earlier interchange
lst[begin], lst[i] = lst[i], lst[begin]

def permutations(lst):
“”” Returns a list containing all the permutations of the

orderings of the elements of a given list (lst).
Delegates the hard work to the perm function. “””

result = []
perm(lst, 0, result)
return result

def main():
“”” Tests the permutations function. “””
a = list(range(3)) # Make list [0, 1, 2]
print(‘List:’, a) # Print the list
# Generate and print all permutations of the list
print(‘Permutations:’, permutations(a))

15.6. LIST PERMUTATIONS 601

if __name__ == ‘__main__’:
main()

Listing 15.13 (listpermutations.py) prints

List: [0, 1, 2]
Permutations: [[0, 1, 2], [0, 2, 1], [1, 0, 2], [1, 2, 0], [2, 1, 0], [2, 0, 1]]

Examining program’s output closely, we see it is a list that contains all the permutations of the list [0, 1, 2].

The perm function in Listing 15.13 (listpermutations.py) is a recursive function, as it calls itself inside
of its definition. We have seen how recursion can be an alternative to iteration; however, the perm function
here uses both iteration and recursion together to generate all the arrangements of a list. At first glance,
the combination of these two algorithm design techniques as used here may be difficult to follow, but we
actually can understand the process better if we ignore some of the details of the code.

First, notice that in the recursive call the argument begin is one larger. This means as the recursion
progresses the beginning index keeps increasing until it reaches the index of the last element in the list. The
recursion terminates when begin becomes equal to the last index.

In its simplest form the function looks like this:

def perm(lst, begin, result):
end = len(lst) – 1 # Index of the last element
if begin == end:

# Add the current list to the list of permutations
else:

# Do the interesting part of the algorithm

Let us zoom in on the interesting part of the algorithm (less the comments):

for i in range(begin, end + 1):
lst[begin], lst[i] = lst[i], lst[begin]
perm(lst, begin + 1, result)
lst[begin], lst[i] = lst[i], lst[begin]

If the mixture of iteration and recursion is confusing, eliminate iteration! If a loop iterates a fixed number of
times, you may replace the loop with the statements in its body duplicated that number times; for example,
we can rewrite the code

for i in range(5):
print(i)

print(0)
print(1)
print(2)
print(3)
print(4)

Notice that the loop is gone. This process of transforming a loop into the series of statements that the loop
would perform is known as loop unrolling. Compilers and interpreters can unroll loops behind the scenes

15.6. LIST PERMUTATIONS 602

to make the code’s execution faster. After unrolling the loop, the loop control variable (in this case i) is
gone, so there is no need to initialize i (done once) and, more importantly, no need to check and update i
during each iteration of the loop. Eliminating these tasks, especially the check and update within the loop,
reduces the work the program must do, thereby speeding up its execution.

Our purpose for unrolling the loop in perm is not to optimize it. Instead we are trying to understand
better how the algorithm works. In order to unroll perm’s loop, we will consider the case for lists containing
exactly three elements. In this case we would hardcode the for statement in the perm function as

for i in range(begin, 3):
lst[begin], lst[i] = lst[i], lst[begin]
perm(lst, begin + 1, result)
lst[begin], lst[i] = lst[i], lst[begin]

and we can unroll this code into

lst[begin], lst[0] = lst[0], lst[begin] # Swap
perm(lst, begin + 1, result)
lst[begin], lst[0] = lst[0], lst[begin] # Swap back

lst[begin], lst[1] = lst[1], lst[begin] # Swap
perm(lst, begin + 1, result)
lst[begin], lst[1] = lst[1], lst[begin] # Swap back

lst[begin], lst[2] = lst[2], lst[begin] # Swap
perm(lst, begin + 1, result)
lst[begin], lst[2] = lst[2], lst[begin] # Swap back

Once the loop is gone, we see we have simply a series of recursive calls of perm sandwiched by element
swaps. The first swap interchanges an element in the list with the first element. The second swap reverses
the effects of the first swap. This series of swap-call perm-swap back operations allows each element in
the list to have its turn being the first element in the permuted list. The perm recursive call generates
all the permutations of the rest of the list. Figure 15.6 traces the recursive process of generating all the
permutations of the list [0,1,2]. The leftmost third of Figure 15.6 shows the original contents of the list
and the initial call of perm. The three branches represent the three iterations of the for loop: i varying
from begin (0) to the last index (2). The lists indicate the state of the list after the first swap but before the
recursive call to perm.

The middle third of Figure 15.6 shows the state of the list during the first recursive call to perm. The
two branches represent the two iterations of the for loop: i varying from begin (1) to the last index (2).
The lists indicate the state of the list after the first swap but before the next recursive call to perm. At this
level of recursion the element at index zero is fixed, and the remainder of the processing during this chain
of recursion is restricted to indices greater than zero.

The rightmost third of Figure 15.6 shows the state of the list during the second recursive call to perm.
At this level of recursion the elements at indices zero and one are fixed, and the remainder of the processing
during this chain of recursion is restricted to indices greater than one. This leaves the element at index two,
but this represents the base case of the recursion because begin (2) equals the index of the last element (2).
In this case the function makes no more recursive calls to itself. The function merely adds a copy of the
current list to the list of permutations.

The arrows in Figure 15.6 represent a call to, or a return from, perm. They illustrate the recursive call
chain. The arrows pointing left to right represent a call, and the arrows pointing from right to left represent
a return from the function. The numbers associated with arrow indicate the order in which the calls and

15.6. LIST PERMUTATIONS 603

Figure 15.6 A tree mapping out the recursive process of the perm function operating on the list [0, 1,
2]. The second column from the left shows the original contents of the list after the first swap but before
the first recursive call to perm. The swapped elements appear in red. The third column shows the contents
of the list at the second level of recursion. In the third column the elements at index zero are fixed, as this
recursion level is using begin with a value of one instead of zero. The for loop within this recursive call
swaps the elements highlighted in red. The rightmost column is the point where begin equals the index of
the last element, and so the perm function does not call itself, effectively terminating the recursion. The
numbers on the arrows trace the order in which the program makes the calls to, and returns from, the perm
function.

[0,1,2]

[1,0,2]

[2,1,0]

[0,1,2]

[0,2,1]

[1,0,2]

[1,2,0]

[2,1,0]

[2,0,1]

[0,1,2]

[0,2,1]

[1,0,2]

[1,2,0]

[2,1,0]

[2,0,1]

3
4

7
8

13
14

17
18

23
24

27
28

1
0

11
20

2
13

begin = 0

end = 2

begin = 1

end = 2

begin = 2

end = 2

i = 0

i = 1

i = 2

i = 1

i = 2

Initial call to permute Recursive call Base case

i = 1

i = 2

i = 1

15.6. LIST PERMUTATIONS 604

returns occur during the execution of perm.

We can augment the perm function to better illustrate the iterative and recursive processes. With a
technique known as code instrumentation, we will add statements that provide insight into the algorithm’s
progression. The term instrumentation mirrors its meaning outside the realm of programming. A motor
vehicle, for example, has an instrument panel containing several different instruments. The speedometer
indicates the vehicle’s current speed, and the tachometer provides the vehicle’s engine’s RPMs. Neither
of these devices is absolutely essential for driving the vehicle, but they do give the driver more precise
information about the state of the driving experience.

Listing 15.14 (perminstrumented.py) instruments the perm function by adding print statements that
indicate state of its list as it loops and calls itself recursively.

Listing 15.14: perminstrumented.py

def perm(lst, begin, result, depth):
“”” Creates a list (result) containing all the permutations of the

elements of a given list (lst), beginning with a
specified index (begin).
Printing statements report the progression of the
function’s recursion. The depth parameter indicates the
depth of the recursion.
This is a helper function for the permutations function. “””

print(‘ ‘ * depth, ‘begin =’, begin)
end = len(lst) – 1 # Index of the last element
if begin == end:

result += [lst[:]] # Copy lst into result
print(‘ ‘ * depth, ‘ *’)

else:
for i in range(begin, end + 1):

# Interchange the element at the first position
# with the element at position i
lst[begin], lst[i] = lst[i], lst[begin]
print(‘ ‘ * depth, ‘ ‘, lst[begin], ‘<-->‘, lst[i], ‘ ‘, lst)
# Recursively permute the rest of the list
perm(lst, begin + 1, result, depth + 1)
# Undo the earlier interchange
lst[begin], lst[i] = lst[i], lst[begin]

def permutations(lst):
“”” Returns a list containing all the permutations of the

orderings of the elements of a given list (lst).
Delegates the hard work to the perm function. “””

result = []
perm(lst, 0, result, 0) # Initial call with depth = 0
return result

def main():
a = list(range(3))
print(permutations(a))

if __name__ == ‘__main__’:

15.6. LIST PERMUTATIONS 605

Figure 15.7 Output of Listing 15.14 (perminstrumented.py). The nested, inner sections show the recursive
executions that place the element at index one. The outer sections represent the initial recursive calls the
establish the element at index zero. The asterisk (*) indicates the end of the recursion. Note that the
recursion ends exactly when begin is 2. Since 2 is the last index, there is no need to continue.

Permutations
with 0 first

Permutations
with 1 first

Permutations
with 2 first

Permutations
with 1 second

Permutations
with 2 second

Permutations
with 0 second

Permutations
with 2 second

Permutations
with 1 second

Permutations
with 0 second

main()

Figure 15.7 shows the output of Listing 15.14 (perminstrumented.py).

Now that we have a function that produces a list containing all the permutations of a given list in a
regular fashion, we must admit that the function is practical only for relatively small lists. Consider a list
that contains just 25 elements. How many distinct permutations are there of this list? The factorial function
counts the number of ways of arranging the elements in a sequence:

25! = 15,511,210,043,330,985,984,000,000

Thus, our lowly list containing just 25 elements has 15,511,210,043,330,985,984,000,000 distinct permu-
tations. Computers are fast and easily deal with large numbers, so this should not be a problem, should
it? If each element of the list occupied just one byte of storage (the actual size is more then one byte), one
permutation of the list containing 25 eleemnts would require 25 bytes or memory. The list containing all

15.6. LIST PERMUTATIONS 606

the permutations would require

25 bytes ·25! = 387,780,251,083,274,649,600,000,000 bytes
≈ 387,780 zettabytes

(1 zettabyte = 1 billion terabytes.) 387,780 zettabytes is about 140,000 times greater than 2.7 zettabytes, the
estimated total data storage space in all media (hard drives, solid state drives, CDs, DVDs, tape, etc.) found
on the planet (see http://en.wikipedia.org/wiki/Zettabyte). It is safe to assume that your laptop or
desktop would not have enough RAM to hold the list of all permutations. Besides, if your program could
generate one permutation each nanosecond (an unreasonably fast rate even with today’s fastest processors),
the program would require

25! nanoseconds = 15,511,210,043,330,985,984,000,000 nanoseconds
≈ 15,511,210,043,330,986 seconds
≈ 4,308,669,456,481 hours
≈ 179,527,894,020 days
≈ 491,857,244 years

Most users would be unwilling to wait almost five million centuries for the list of permutations that, by the
way, is too large to store on any computer system on the planet!

Listing 15.13 (listpermutations.py) is impractical for all but relatively small lists because the perm func-
tion does not return until after building the list containing all the permutations. The basic algorithm is
sound, however, and fortunately we can salvage it nicely using generators. (We first explored generators in
Section 8.8.) Instead of producing the entire list of permutations, our function will yield each permutation
one at a time.

We know that a function that produces a generator must use a yield statement rather than return.
What we have yet to see is how this works with recursion.

The perm function in Listing 15.13 (listpermutations.py) adds a new list permutation to its result list
with the following statement in its base case:

result += [lst[:]] # Copy lst into result

The expression lst[:] makes a copy of the lst. We want to yield a copy of the list instead of adding a
copy of it to another list. This is an easy change, as we rewrite the statement to be

yield lst[:] # Yield a copy of lst

We covered the base case perfectly, what happens in the recursive case? Recursive generators are a little dif-
ferent from the iterative generators we saw earlier. Since the if block contains a yield statement, the else
block needs one as well. What we want to yield is what the recursive call to perm eventually yields when
it reaches its base case. When we need to yield a value from a recursive call we must use the yield from
statement. The yield from statement indicates the generator should yield the result that the chain of recur-
sive calls ultimately yields when it reaches its terminal base case. Listing 15.15 (generatepermutations.py)
shows how to use yield and yield from in a recursive generator.

Listing 15.15: generatepermutations.py

def perm(lst, begin):

http://en.wikipedia.org/wiki/Zettabyte

15.6. LIST PERMUTATIONS 607

“”” Generates the sequence of all the permutations of the
elements of a given list (lst), beginning with a
specified index (begin).
This is a helper function for the permutations function. “””

end = len(lst) – 1 # Index of the last element
if begin == end:

yield lst[:] # Yield a copy of lst
else:

for i in range(begin, end + 1): # Consider all indices
# Interchange the element at the first position
# with the element at position i
lst[begin], lst[i] = lst[i], lst[begin]
# Recursively permute the rest of the list
yield from perm(lst, begin + 1)
# Undo the earlier interchange
lst[begin], lst[i] = lst[i], lst[begin]

def permutations(lst):
“”” Generates the sequence of all the permutations of the

elements of list lst.
Delegates the hard work to the perm function. “””

yield from perm(lst, 0)

def main():
“”” Tests the permutations function. “””
a = list(range(3)) # Make list [0, 1, 2]
print(‘List:’, a) # Print the list
# Generate and print all permutations of the list
for p in permutations(a):

print(p, end=’ ‘)
print()

if __name__ == ‘__main__’:
main()

Listing 15.15 (generatepermutations.py) prints

List: [0, 1, 2]
[0, 1, 2] [0, 2, 1] [1, 0, 2] [1, 2, 0] [2, 1, 0] [2, 0, 1]

The permutations function must yield the result of the call to perm, so the yield from statement ap-
pears there as well. This is because the permutations function itself does not create the value; instead,
permutations relies on the perm function to create the value. A function that relies on another function
to create the yielded value must use yield from. Note that this is is consistent with the way yield from
works with recursion.

Note that since we are no longer building a physical list, we do not need the extra result parameter in
the perm function.

The perm function in our generator code creates and yields just one permutation at a time. If the caller
does not store each generated list but merely prints it out or uses it in some other way and discards it
before obtaining the next list, the program will not run into the memory limitations of the original version.

15.6. LIST PERMUTATIONS 608

This does not help the time it takes to produce all the permutations; however, the generator perm function
“returns” a permutation immediately, thus avoiding the problems with the original version that tried to
make all the permutations before returning. This means the caller can get into and out of the function
quickly. While the program still would require centuries to complete its execution if asked to print all the
permutations of a list with 25 elements, it could print the first 100 permutations very quickly:

lst = list(range(25))
count = 0
for p in permutations(lst): # Too many to see them all!

print(p, end=’ ‘)
count += 1
if count == 100:

break # Just print the first 100 permutations
print()

Note that we can always build a list of permutations with our generator version of the permutations
function by using the list conversion function: The statement

lst = list(permutations([0, 1, 2]))

builds such a list. Be aware, however, that just as in the non-generator version, memory and time constraints
limit the size of the list used in a statement like this one.

While Listing 15.15 (generatepermutations.py) is a good exercise in recursive list processing, the
Python standard library provides a generator-like object named permutations in the itertools mod-
ule that works almost like our permutations function. Surprisingly, the standard permutations generator
produces tuples instead of lists, as Listing 15.16 (stdpermutations.py) demonstrates.

Listing 15.16: stdpermutations.py

# Use the standard permutations function to list
# the possible arrangements of elements in a list.

from itertools import permutations

def main():
a = [0, 1, 2]
for p in permutations(a):

print(p, end=’ ‘)
print()

main()

Listing 15.16 (stdpermutations.py) produces

(0, 1, 2) (0, 2, 1) (1, 0, 2) (1, 2, 0) (2, 0, 1) (2, 1, 0)

In order to more match the behavior of Listing 15.15 (generatepermutations.py) we must convert each
tuple to a list. Listing 15.17 (stdpermutations2list.py) uses the list constructor function to perform the
conversion.

Listing 15.17: stdpermutations2list.py

15.7. RANDOMLY PERMUTING A LIST 609

# Use the standard permutations function to list
# the possible arrangements of elements in a list.

from itertools import permutations

def main():
a = [0, 1, 2]
for p in permutations(a):

print(list(p), end=’ ‘)
print()

main()

Listing 15.17 (stdpermutations2list.py) produces

[0, 1, 2] [0, 2, 1] [1, 0, 2] [1, 2, 0] [2, 0, 1] [2, 1, 0]

It is evident that the standard permutations object uses a different algorithm because it orders the results
differently from Listing 15.15 (generatepermutations.py).

15.7 Randomly Permuting a List

We have seen that generating all the permutations of a large list is computationally intractable. Often,
however, we merely need to produce one permutation chosen at random. For example, we may need to
randomly rearrange the contents of an ordered list so that we can test a sort function to see if it will produce
the original list. We could generate all the permutations, put each one in a list, and select a permutation
at random from that list. This approach is inefficient, especially as the length of the list to permute grows
larger. Fortunately, we can randomly permute the contents of a list easily and quickly. Listing 15.18
(randompermute.py) contains a function named permute that randomly permutes the elements of a list.

Listing 15.18: randompermute.py

from random import randrange

def permute(lst):
“””
Randomly permutes the contents of list lst
“””
n = len(lst)
for i in range(n – 1):

pos = randrange(i, n) # i <= pos < n lst[i], lst[pos] = lst[pos], lst[i] def main(): """ Tests the permute function that randomly permutes the contents of a list ©2017 Richard L. Halterman Draft date: January 18, 2018 15.7. RANDOMLY PERMUTING A LIST 610 """ a = [1, 2, 3, 4, 5, 6, 7, 8] print('Before:', a) permute(a) print('After :', a) main() Notice that the permute function in Listing 15.18 (randompermute.py) uses a simple un-nested loop and no recursion. The permute function varies the i index variable from 0 to the index of the next to last element in the list. The function pseudorandomly chooses an index greater than i using randrange (see Section 6.6), and the function then exchanges the elements at position i and the random position. At this point all the elements at position i and smaller are fixed and will not change as the function’s execution continues. The function then increments index i for the next iteration and continues its work until it has considered all acceptable values for i. To be correct, our permute function must be able to generate any valid permutation of the list. It is important also that our permute function is able produce all possible permutations with equal probability; said another way, we do not want our permute function to generate some permutations more often than others. The permute function in Listing 15.18 (randompermute.py) is fine, but consider a slight variation of the algorithm: def faulty_permute(lst): """ An attempt to randomly permute the contents of list lst """ n = len(lst) for i in range(n - 1): pos = randrange(0, n) # 0 <= pos < n lst[i], lst[pos] = lst[pos], lst[i] Do you see the difference between faulty_permute and permute? In faulty_permute, the random index is chosen from all valid list indices, whereas permute restricts the random index to valid indices greater than or equal to i. This means that any element within lst can be exchanged with the element at position i during any loop iteration. While this approach may superficially appear to be just as good as permute, it in fact produces an uneven distribution of permutations. Listing 15.19 (comparepermutations.py) exercises each permutation function 1,000,000 times on the list [1, 2, 3] and tallies each permutation. There are exactly six possible permutations of this three-element list. Listing 15.19: comparepermutations.py from random import randrange # Randomly permute a list def permute(lst): """ Randomly permutes the contents of list lst """ n = len(lst) for i in range(n - 1): pos = randrange(i, n) # i <= pos < n lst[i], lst[pos] = lst[pos], lst[i] ©2017 Richard L. Halterman Draft date: January 18, 2018 15.7. RANDOMLY PERMUTING A LIST 611 # Randomly permute a list? def faulty_permute(lst): """ An attempt to randomly permute the contents of list lst """ n = len(lst) for i in range(n): pos = randrange(0, n) # 0 <= pos < n lst[i], lst[pos] = lst[pos], lst[i] def classify(a): """ Classify a list as one of the six permutations """ sum = 100*a[0] + 10*a[1] + a[2] if sum == 123: return 0 elif sum == 132: return 1 elif sum == 213: return 2 elif sum == 231: return 3 elif sum == 312: return 4 elif sum == 321: return 5 else: return -1 def report(a): """ Report the accumulated statistics """ print("1,2,3: ", a[0]) print("1,3,2: ", a[1]) print("2,1,3: ", a[2]) print("2,3,1: ", a[3]) print("3,1,2: ", a[4]) print("3,2,1: ", a[5]) def run_test(perm, runs): """ Uses a permutation function to generate the permutations of the list [1,2,3] perm: the permutation function to test runs: the number permutations to perform """ # The list to permute original = [1, 2, 3] # permutation_tally list keeps track of each permutation pattern # permutation_tally[0] counts {1,2,3} # permutation_tally[1] counts {1,3,2} # permutation_tally[2] counts {2,1,3} # permutation_tally[3] counts {2,3,1} # permutation_tally[4] counts {3,1,2} ©2017 Richard L. Halterman Draft date: January 18, 2018 15.7. RANDOMLY PERMUTING A LIST 612 # permutation_tally[5] counts {3,2,1} permutation_tally = 6 * [0] # Clear all the counters for i in range(runs): # Run runs times # working holds a copy of original is gets permuted and tallied working = original[:] # Permute the list with the permutation algorithm perm(working) # Count this permutation permutation_tally[classify(working)] += 1 report(permutation_tally) # Report results def main(): # Each test performs one million permutations runs = 1000000 print("--- Random permute #1 -----") run_test(permute, runs) print("--- Random permute #2 -----") run_test(faulty_permute, runs) main() In Listing 15.19 (comparepermutations.py)’s output, permute #1 corresponds to our original permute func- tion, and permute #2 is the faulty_permute function. The output of Listing 15.19 (comparepermutations.py) reveals that the faulty permutation function favors some permutations over others: --- Random permute #1 ----- 1,2,3: 166176 1,3,2: 166957 2,1,3: 167012 2,3,1: 166668 3,1,2: 166182 3,2,1: 167005 --- Random permute #2 ----- 1,2,3: 148811 1,3,2: 184870 2,1,3: 185251 2,3,1: 184763 3,1,2: 148200 3,2,1: 148105 In one million runs, the permute function provides a fairly even distribution of the six possible permutations of [1, 2, 3]. The distributions are not all exactly the same, but we would expect minor differences due to the variations that randomness introduces. On the other hand, the faulty_permute function generates the permutations [1, 3, 2], [2, 1, 3], and [2, 3, 1] more often than the permutations [1, 2, 3], [3, 1, 2], and [3, 2, 1]. To see why faulty_permute misbehaves, we need to examine all the permutations it can produce during one call. Figure 15.8 shows a hierarchical structure that maps out how faulty_permute transforms its list parameter each time through the for loop. The top of the tree shows the original list, [1, 2, 3]. The second row shows the three possible resulting lists after the first iteration of the for loop. The leftmost ©2017 Richard L. Halterman Draft date: January 18, 2018 15.7. RANDOMLY PERMUTING A LIST 613 Figure 15.8 A tree mapping out the ways in which faulty permute can transform the list [1, 2, 3] at each iteration of its for loop 123 213 321123 213 321123 231 231 312123213 132 312 231 213 321 132 123 231 123 132 321 132 123 312 231 213 132 213 231 132 213 231 123 312 321 213 321 312 Figure 15.9 A tree mapping out the ways in which permute can transform the list [1, 2, 3] at each iteration of its for loop 123 123 123 132 213 213 231 321 321 312 list represents the element at index zero swapped with the element at index zero (effectively no change). The second list on the second row represents the interchange of the elements at index 0 and index 1. The third list on the second row results from the interchange of the elements at positions 0 and 2. The underlined elements represent the elements most recently swapped. If only one item in the list is underlined, the function merely swapped the item with itself. The bottom row contains all the possible outcomes of the faulty_permute function given the list [1, 2, 3]. As Figure 15.8 shows, the lists [1, 3, 2], [2, 1, 3], and [2, 3, 1] each appear five times in the last row, while [1, 2, 3], [3, 1, 2], and [3, 2, 1] each appear only four times. There are a total of 27 possible outcomes, so some permutations appear 4 27 = 14.815% of the time, while the others appear 5 27 = 18.519% of the time. When generating one million permutations we would get 14.815% · 1,000,000 = 148150, and 18.519 · 1,000,000 = 185190. Notice that these numbers agree with our experimental results from Listing 15.19 (comparepermutations.py). Compare Figure 15.8 to Figure 15.9. The second row of the tree for permute is identical to the second row of the tree for faulty_permute, but the third rows are different. The second time through its loop the permute function does not attempt to exchange the element at index zero with any other elements. We see that none of the first elements in the lists in row three are underlined. The third row contains exactly one instance of each of the possible permutations of [1, 2, 3]. This means that the correct permute function is not biased towards any of the individual permutations, and so the function can generate all the ©2017 Richard L. Halterman Draft date: January 18, 2018 15.8. REVERSING A LIST 614 permutations with equal probability. The permute function has a 1 6 = 16.667% probability of generating a particular permutation. Over 1,000,000 trials, we would expect each permutation to occur 166667 times. This number agrees with our the experimental results of Listing 15.19 (comparepermutations.py). 15.8 Reversing a List Listing 15.20 (listreverse.py) contains a recursive function named rev that accepts a list as a parameter and returns a new list with all the elements of the original list in reverse order. Listing 15.20: listreverse.py def rev(lst): return [] if len(lst) == 0 else rev(lst[1:]) + lst[0:1] print(rev([1, 2, 3, 4, 5, 6, 7])) Python has a standard function, reversed, that accepts a list parameter. The reversed function does not return a list but instead returns an iterable object that works like a generator or range within a for loop (see Section 5.3). Listing 15.21 (reversedexample.py) shows how reversed can be used to print the contents of a list backwards. Listing 15.21: reversedexample.py for item in reversed([1, 2, 3, 4, 5, 6, 7]): print(item, end=" ") print() Listing 15.21 (reversedexample.py) prints 7 6 5 4 3 2 1 We can use the list conversion function to make a new list object out of the iterator object that reversed creates: rev = list(reversed([1, 2, 3, 4, 5, 6, 7]) Section 10.10 introduced the reverse method that modifies a list by reversing its elements in place. The following code x = [1, 2, 3, 4] print(x) x.reverse() print(x) prints [1, 2, 3, 4] [4, 3, 2, 1] The reverse of the list class method does not use any extra space since it does not create a new list but merely repositions the elements in the existing list object. You can use the reverse method if you need an ©2017 Richard L. Halterman Draft date: January 18, 2018 15.9. MEMOIZATION 615 actual reversed list, as opposed to using the iterator reversed that provides merely a backwards traversal of the list. Note that after calling the reverse method on a list, calling reverse a second time restores the list to its original ordering. 15.9 Memoization We know a program can use variables to remember values as it executes. A programmer must be able to predict the number of values the program must manage in order to write enough variables in the code. A dictionary provides an opportunity to create an arbitrary amount of new storage during a program’s execution. We will consider a simple problem that demonstrates the value of the dynamic storage provided by dictionaries. Section 8.3 introduced the Fibonacci number sequence. That section provided a function to compute the nth Fibonacci number, reproduced here: def fibonacci(n): """ Returns the nth Fibonacci number. """ if n <= 0: return 0 elif n == 1: return 1 else: return fibonacci(n - 2) + fibonacci(n - 1) This fibonacci function is correct, but it does not scale well—its execution time grows significantly as its parameter, n, increases. The problem is this: when computing a solution for a particular Fibonacci number the function can repeat exactly the same work multiple times. Figure 15.10 illustrates the repetitive work performed by the call fibonacci(5). As we can see from the figure, the function’s recursive execution calls fibonacci(1) five times during the computation of fibonacci(5). We can verify the results shown in Figure 15.10 by augmenting our fibonacci function with a global dictionary that counts function calls. Listing 15.22 (fibonacciinstrumented.py) provides the complete program. Listing 15.22: fibonacciinstrumented.py # This dictionary will keep track of the number of calls to the # fibonacci function. call_counter = {} def fibonacci(n): """ Returns the nth Fibonacci number. """ # Count the call if n not in call_counter: call_counter[n] = 1 else: call_counter[n] += 1 if n <= 0: return 0 elif n == 1: return 1 else: return fibonacci(n - 2) + fibonacci(n - 1) ©2017 Richard L. Halterman Draft date: January 18, 2018 15.9. MEMOIZATION 616 Figure 15.10 The hierarchy of recursive function calls that result from the call fibonacci(5). Note that the recursion process calls fibonacci(1) five times. Caller 1 1 12 2 1 23 0 0 11 fibonacci(0) fibonacci(2) fibonacci(1) fibonacci(1) fibonacci(3) fibonacci(4) 3 2 34 fibonacci(5) 5 5 0 0 11 fibonacci(0) fibonacci(2) fibonacci(1) 1 1 12 0 0 11 fibonacci(0) fibonacci(2) fibonacci(1) fibonacci(1) fibonacci(3) ©2017 Richard L. Halterman Draft date: January 18, 2018 15.9. MEMOIZATION 617 # Call fibonacci(5) print("fibonacci(5) = ", fibonacci(5)) print() # Report the total number of calls to the fibonacci function print("Argument Calls") print("-----------------") for args, calls in sorted(call_counter.items()): print(" ", args, " ", calls); Listing 15.22 (fibonacciinstrumented.py) prints fibonacci(5) = 5 Argument Calls ----------------- 0 3 1 5 2 3 3 2 4 1 5 1 Note the results that Listing 15.22 (fibonacciinstrumented.py) prints agree exactly with the call count shown in Figure 15.10. As we compute larger Fibonacci numbers, the amount of repeated work wors- ens quickly; for example, the call fibonacci(20) recursively calls fibonacci(1) 6,765 times! For addi- tional emphasis, the call fibonacci(35) recursively calls fibonacci(1), fibonacci(2), fibonacci(3), fibonacci(4), and fibonacci(5) over one million times each! We may be tempted to care less about the program’s repeated work—after all, it is the computer doing the work, not us. Unfortunately, the computer, even though it is very fast, requires some amount of time to perform any task. As we multiply the number of tasks a program must do to solve a problem, the time to compute the solution increases, and, in the case of factorial, the time increases dramatically. We can improve the performance of our fibonacci function using a technique known as memoization (not to be confused with the word memorization which means to commit something to memory). Memo- ization is an algorithm design technique that records the result of a specific computation so that result can be used as needed at a later time during the algorithm’s execution. It is as if the executing program “makes a note to itself” or “stores the result in a memo.” When the program needs the result of an identical com- putation in the future, if simply reads the memo with the answer it stored earlier. In this way the program avoids repeating the work. Memoization is especially useful for problems that consist of subproblems that overlap and appear to require multiple computations with identical input. Listing 15.23 (fibonacci.py) uses a dictionary to cache previously computed Fibonacci numbers. It demonstrates the dramatic speedup that memoization affords. Listing 15.23: fibonacci.py from time import clock from random import randrange def fibonacci(n): ©2017 Richard L. Halterman Draft date: January 18, 2018 15.9. MEMOIZATION 618 """ Returns the nth Fibonacci number recursively. """ if n <= 0: return 0 elif n == 1: return 1 else: return fibonacci(n - 2) + fibonacci(n - 1) # Dictionary for caching the results of the fibonacci2 function ans = {0:0, 1:1} # Precompute the results for 0 and 1 def fibonacci2(n): """ Returns the nth Fibonacci number. Caches a recursively computed result to be used when needed in the future. Provides a huge performance improvement over the recursive version. """ if n not in ans.keys(): result = fibonacci2(n - 2) + fibonacci2(n - 1) ans[n] = result return ans[n] def time_it(f, ns): """ f is a function that accepts a single parameter. ns is a list. Measures the time for function f to process each element in ns. Returns the cumulative elapsed time. """ start_time = clock() for i in ns: #print("{:>4}: {:>8}”.format(i, f(i)))
print(f(i), end=” “)

end_time = clock()
return end_time – start_time # Return elapsed time

def main():
“”” Tests the performance of the fibonacci and fibonacci2 functions. “””

# Make a list of pseudorandom integers in the range 1…50
numbers = []
for i in range(10):

numbers.append(randrange(40) + 1)

# Print the numbers
print(numbers)

# Compare the two Fibonacci functions
print(“Time:”, time_it(fibonacci, numbers))
print(“——————“)
print(“Time:”, time_it(fibonacci2, numbers))

if __name__ == “__main__”:
main()

15.9. MEMOIZATION 619

One run of Listing 15.23 (fibonacci.py) produces the following output:

[23, 40, 32, 7, 8, 1, 29, 30, 10, 36]
28657 102334155 2178309 13 21 1 514229 832040 55 14930352
Time: 80.61978684888133
——————
28657 102334155 2178309 13 21 1 514229 832040 55 14930352
Time: 0.00012145362886428757

Listing 15.23 (fibonacci.py) clearly demonstrates the power of memoization. The non-memoized ver-
sion requires almost a minute and a half to compute the Fibonacci numbers for a list of 10 relatively small

values, while the memoized version takes less than
1

1,000
of a second for the same list of values. The

memoized version is over 600,000 times faster than the non-memoized version.

Figure 15.11 shows the recursion tree for our memoized Fibonacci function computing the fifth Fi-
bonacci number. It assumes the fibonacci2 has not previously been called, and so at the initial call at the
top of the tree the global ans dictionary contains only the 0 and 1 keys. The figure shows only nine invo-
cations of fibonacci2, compared to 15 invocations of the non-memoized fibonacci function. If you add
the function call counting instrumentation used in Listing 15.22 (fibonacciinstrumented.py) to fibonacci2,
you will find the numbers it reports agrees with Figure 15.11.

If our goal is simply to remove the redundant computations during recursion, we can make the caching
dictionary local to a function, as shown here:

def fibonacci3(n):
# Local dictionary for caching the results of the fib function
ans = {0:0, 1:1} # Precompute the results for 0 and 1

# Local function
def fib(n):

“”” Returns the nth Fibonacci number. Caches a
recursively computed result to be used when needed
in the future. Provides a huge performance improvement
over the recursive version. “””

nonlocal ans
if n not in ans.keys():

result = fib(n – 2) + fib(n – 1)
ans[n] = result

return ans[n]

return fib(n)

Each call to fibonacci3 starts with a fresh ans dictionary containing only the base case keys 0 and 1. It
calls a local helper function, fib, which performs the recursion. The fib function avoids redundant compu-
tations using the ans dictionary to which it has access. If a program needs to compute only one Fibonacci
number in the course of its execution, fibonacci3 will be just as fast as fibonacci2 when computing the
same number. If, however, a program needs to compute Fibonacci numbers multiple times, fibonacci2
may be the better choice. The global dictionary that fibonacci2 uses maintains its contents between func-
tion calls, and so it is more likely to have the desired result memoized from an earlier invocation.

15.9. MEMOIZATION 620

Figure 15.11 The hierarchy of recursive function calls that result from the call fibonacci2(5). Note that
the calls of fibonacci(2) and fibonacci(3) on the right side of the tree need no recursive calls; this is
because their earlier calls on the left side of the tree stored their results in the global ans dictionary for
instant retrieval.

Caller

2 1 23

fibonacci2(3)

fibonacci2(4)

3 2 34

fibonacci2(5)

5 5

fibonacci2(2)

1 1 12

0 0 11

fibonacci2(0)

fibonacci2(2)

fibonacci2(1)

fibonacci2(3)

0 0 11

fibonacci2(0) fibonacci2(1)

1 1 12

0 0 11

fibonacci2(0)

fibonacci2(2)

fibonacci2(1)

A
Use value

cached at A
Use value

cached at B

15.9. MEMOIZATION 621

One disadvantage of the global ans dictionary is that other functions within the program may acciden-
tally or maliciously manipulate its contents causing fibonacci2’s results to be unreliable. To help avoid
this problem you can put fibonacci2 and ans into a separate module. Rename ans to _ans to make a point
to callers that _ans is off limits to their code.

Another application of memoization is finding the longest common subsequence of two sequences. A
sequence is simply an ordered list of elements, as in a Python list, tuple, or string. Most typically the
elements of a sequence all will have the same type. A subsequence is a sequence formed from another
sequence by removing elements without changing the relative order of the remaining elements. As an
example, consider the sequence of characters in the Python list [“A”, “B”, “C”, “D”]. The complete set
of subsequences is

[]
[“A”]
[“B”]
[“A”, “B”]
[“C”]
[“A”, “C”]
[“B”, “C”]
[“A”, “B”, “C”]
[“D”]
[“A”, “D”]
[“B”, “D”]
[“A”, “B”, “D”]
[“C”, “D”]
[“A”, “C”, “D”]
[“B”, “C”, “D”]
[“A”, “B”, “C”, “D”]

Note that the empty sequence is a subsequence of any sequence (even itself), and any sequence is its own
subsequence.

The longest common subsequence (LCS) problem is this: given two sequences of symbols, find the
longest subsequence that is common to both sequences. This problem is related to genome sequencing
problems in computational biology. The LCS problem has a relatively simple recursive solution. We will
use a Python string to represent a sequence, where each character is a symbol in the sequence. With this
representation, the string “ACD” is a subsequence of “ABCD”. The following function computes the LCS of
two strings:

def LCS(X, Y):
“”” Computes the longest common subsequence of strings X and Y. “””

result = “” # No symbols in common unless determined otherwise
if len(X) > 0 and len(Y) > 0: # No symbols in common if either string is empty

Xrest = X[1:] # String X without its first symbol
Yrest = Y[1:] # String Y without its first symbol
if X[0] == Y[0]: # Do the first symbols of both strings match?

# An LCS will include this shared symbol plus the LCS of rest
# of both strings
result = X[0] + LCS(Xrest, Yrest)

else:
# Compare string X to the string Y, excluding Y’s first symbol
X_Y1 = LCS(X, Yrest)

15.9. MEMOIZATION 622

# Compare string X, excluding X’s first symbol, to string Y
X1_Y = LCS(Xrest, Y)
# Choose longer of the two computed sequences
result = X_Y1 if len(X_Y1) > len(X1_Y) else X1_Y

return result

The LCS function is correct, but its recursive invocations suffer a similar fate to our original fibonacci
function—they unnecessarily recompute multiple times the LCS of identical string pairs. As an example,
the call LCS(“ABCBDAB”, “BDCABA”) will recompute recursively the LCS of the subsequences “BDAB” and
“ABA” three times. These multiple, superfluous recomputations render this LCS function impractical for all
but relatively short sequences.

The following LCS_memoized function adapts the original LCS function to use memoization:

def LCS_memoized(X, Y):
“”” Computes the longest common subsequence of strings X and Y.

Caches intermediate results in a memoization dictionary so they
do not need to be recomputed over and over again. “””

memo = {} # Start with empty memoization storage

def LCS(X, Y):
“”” Computes the longest common subsequence of strings X and Y. “””
nonlocal memo # Memoization storage for computed results
# Check first to see if we already have computed
if (X, Y) in memo:

result = memo[X, Y] # LCS of X and Y already computed, so use previous value
else:

result = “” # No symbols in common unless determined otherwise
if len(X) > 0 and len(Y) > 0: # No symbols in common if either string is empty

Xrest = X[1:] # String X without its first symbol
Yrest = Y[1:] # String Y without its first symbol
if X[0] == Y[0]: # First symbols of both strings match

result = X[0] + LCS(Xrest, Yrest)
else:

X_Y1 = LCS(X, Yrest)
X1_Y = LCS(Xrest, Y)
# Choose longest
result = X_Y1 if len(X_Y1) > len(X1_Y) else X1_Y

# Remember this result for X and Y to avoid recomputing it in the future
memo[X, Y] = result

return result # End of local LCS function definition

result = LCS(X, Y) # Call the local LCS function
#print(“******** Stored memos:”, len(memo))
return result

Note that the memoization dictionary is local to LCS_memoized. Each time a caller invokes LCS_memoized
the memoization dictionary begins empty. The memoization dictionary is valid only for the two specific
strings that the caller passes. It would be unwise to make the memoization dictionary global; otherwise, if an
application ran a long time repeatedly calling LCS_memoized with many different strings, a global dictionary
would grow continuously. This unbounded growth potentially would exhaust the memory available to the

15.9. MEMOIZATION 623

application. The LCS_memoized function uses the dictionary merely to eliminate the redundant recursive
recomputations.

Listing 15.24 (lcsmemo.py) tests out both the memoized and non-memoized versions of our LCS func-
tions. It performs multiple runs on the same data to achieve more accurate measurements. It then plots the
results using Turtle graphics.

Listing 15.24: lcsmemo.py

from stopwatch import Stopwatch # Our Stopwatch class from before
from random import choice
from turtle import *

def LCS(X, Y):
“”” Computes the longest common subsequence of strings X and Y. “””

result = ” # No symbols in common unless determined otherwise
if len(X) > 0 and len(Y) > 0: # No symbols in common if either string is empty

Xrest = X[1:] # String X without its first symbol
Yrest = Y[1:] # String Y without its first symbol
if X[0] == Y[0]: # Do the first symbols of both strings match?

# An LCS will include this shared symbol plus the LCS of rest
# of both strings
result = X[0] + LCS(Xrest, Yrest)

else:
# Compare string X to the string Y, excluding Y’s first symbol
X_Y1 = LCS(X, Yrest)
# Compare string X, excluding X’s first symbol, to string Y
X1_Y = LCS(Xrest, Y)
# Choose longer of the two computed sequences
result = X_Y1 if len(X_Y1) > len(X1_Y) else X1_Y

return result

def LCS_memoized(X, Y):
“”” Computes the longest common subsequence of strings X and Y.

Caches intermediate results in a memoization dictionary so they
do not need to be recomputed over and over again. “””

memo = {} # Start with empty memoization storage

result = memo[X, Y] # LCS of X and Y already computed, so use previous value
else:

result = ” # No symbols in common unless determined otherwise
if len(X) > 0 and len(Y) > 0: # No symbols in common if either string is empty

Xrest = X[1:] # String X without its first symbol
Yrest = Y[1:] # String Y without its first symbol
if X[0] == Y[0]: # First symbols of both strings match

result = X[0] + LCS(Xrest, Yrest)
else:

15.9. MEMOIZATION 624

X_Y1 = LCS(X, Yrest)
X1_Y = LCS(Xrest, Y)
# Choose longest
result = X_Y1 if len(X_Y1) > len(X1_Y) else X1_Y

# Remember this result for X and Y to avoid recomputing it in the future
memo[X, Y] = result

return result

result = LCS(X, Y)
print(“******** Stored memos:”, len(memo))
return result

def highlight(seq1, seq2):
“”” Highlights the characters of seq2 within seq1. “””
pos1, pos2 = 0, 0
print(seq1) # Print the string on one line
while pos1 < len(seq1): if pos2 < len(seq2) and seq1[pos1] == seq2[pos2]: print('ˆ', end='') # Print "ˆ" if characters match pos2 += 1 else: print(' ', end='') # Print a space to move to the next position pos1 += 1 print() def compare_LCS(seq1, seq2): """ Computes the longest common subsequence of seq 1 and seq2 in two different ways and compares the execution times of the two approaches. """ timer_std = Stopwatch() # Each function has its own stopwatch timer_memo = Stopwatch() # to keep track of elapsed time independently timer_std.start() # Time the standard LCS function subseq_std = LCS(seq1, seq2) timer_std.stop() timer_memo.start() # Time the memoized LCS function subseq_memo = LCS_memoized(seq1, seq2) timer_memo.stop() # Report results print(seq1) print(seq2) print(subseq_std, len(subseq_std), '(Standard: {:f})'.format(timer_std.elapsed())) print(subseq_memo, len(subseq_memo), '(Memoized: {:f})'.format(timer_memo.elapsed())) print() # Show the computed longest common subsequences highlight(seq1, subseq_std) highlight(seq2, subseq_std) print() highlight(seq1, subseq_memo) highlight(seq2, subseq_memo) return timer_std.elapsed(), timer_memo.elapsed() ©2017 Richard L. Halterman Draft date: January 18, 2018 15.9. MEMOIZATION 625 def build_random_string(n, symbols): """ Builds a string of length n with characters selected pseudorandomly from the string parameter symbols. """ result = "" while len(result) < n: result = result + choice(symbols) # Add a random character from symbols return result def plot(data): """ Plots the data from the LCS vs. Memoized LCS experiments. """ # Compute bounds for the graphing w = window_width() h = window_height() x_origin = -w/2 + 15 y_origin = -h/2 + 15 xrange = len(data) # Number of data points # Determine the range of y values yrange = max(max(data, key=lambda d0: d0[0])[0], max(data, key=lambda d1: d1[1])[1]) # These scaling factors ensure the points will fit onto the plot xscale = 0.9*w/xrange yscale = 0.9*h/yrange def plot_curve(index, color): """ Local function to plot data from one of the functions. index refers to the slice of the data. color is the line and point color. """ penup() pencolor(color) setposition(x_origin, y_origin) pendown() for length, times in enumerate(data): setposition(x_origin + xscale*length, y_origin + yscale*times[index]) dot() #print("Plotting", length, x_origin + xscale*length, # y_origin + yscale*times[index]) hideturtle() # Do not show the pen delay(0) # No need to animate the drawing title("Longest Common Subsequence vs. Memoized LCS") # Draw axes pencolor("black") pensize(3) penup() # x axis setposition(x_origin, y_origin) pendown() ©2017 Richard L. Halterman Draft date: January 18, 2018 15.9. MEMOIZATION 626 forward(w - 30) penup() # y axis setposition(x_origin, y_origin) left(90) pendown() forward(h - 30) pensize(2) # Draw first curve plot_curve(0, "blue") # Draw second curve plot_curve(1, "red") exitonclick() def main(): N = 10 # Number of times to perform a series of experiments max_length = 18 # Maximum string length for experiments # Make a list of tuples for measuring the time to compute the # LCS two different ways; initialize all the times to zero data = [(0, 0) for _ in range(max_length)] # Perform the series of experiments N times to produce # more reliable results for runs in range(N): # The series of experiments consists of computing the LCS # of two strings of increasing length for i in range(max_length): print(">>> Run”, runs, ” String length”, i)
# Construct two random DNA base sequences
seq1 = build_random_string(i, “ACGT”)
seq2 = build_random_string(i, “ACGT”)

# Perform an experiment to time the two LCS functions
lcs_time, memo_time = compare_LCS(seq1, seq2)
# Accumulate the times
data[i] = data[i][0] + lcs_time, data[i][1] + memo_time

print(data)
plot(data)

if __name__ == ‘__main__’:
main()

Figure 15.12 shows the graph plotted by one run of Listing 15.24 (lcsmemo.py).

15.9. MEMOIZATION 627

Figure 15.12 A graph produced by one run of Listing 15.24 (lcsmemo.py). The horizontal axis represents
the length of the strings, increasing to the right. The vertical axis represents the program’s running time.
The blue line plots the accumulated time consumed by the non-memoized function, and the red line plots
the accumulated time of the memoized version of the function. Note that difference in execution times
increases dramatically as strings become longer, and the memoized version continues to perform well even
with longer strings.

15.10. EXERCISES 628

15.10 Exercises

1. Complete the following function that reorders the contents of a list so they are reversed from their
original order. For example, a list containing the elements 2, 6, 2, 5, 0, 1, 2, 3 would be transformed
into 3, 2, 1, 0, 5, 2, 6, 2. Note that your function must physically rearrange the elements within the
list, not just print the elements in reverse order.

def reverse(lst):
# Add your code…

2. Complete the following function that reorders the contents of a list of integers so that all the even
numbers appear before any odd number. The even values are sorted in ascending order with respect
to themselves, and the odd numbers that follow are also sorted in ascending order with respect to
themselves. For example, a list containing the elements 2, 1, 10, 4, 3, 6, 7, 9, 8, 5 would be trans-
formed into 2, 4, 6, 8, 10, 1, 3, 5, 7, 9 Note that your function must physically rearrange the elements
within the list, not just print the elements in the desired order.

def special_sort(lst):
# Add your code…

3. Create a special comparison function to be passed to our flexible selection sort function. The special
comparison function should enable the sort function to arrange the elements of a list in the order
specified in Exercise 2.

4. Complete the following function that filters negative elements out of a list. The function returns the
filtered list and the original list is unchanged. For example, if a list containing the elements 2, −16,
2, −5, 0, 1, −2, −3 is passed to the function, the function would return the list containing 2, 2, 0, 1.
Note the original ordering of the nonnegative values is unchanged in the result.

def filter(a):
# Add your code…

5. Complete the following function that shifts all the elements of a list backward one place. The last
element that gets shifted off the back end of the list is copied into the first (0th) position. For example,
if a list containing the elements 2, 1, 10, 4, 3, 6, 7, 9, 8, 5 is passed to the function, it would be
transformed into 5, 2, 1, 10, 4, 3, 6, 7, 9, 8 Note that your function must physically rearrange the
elements within the list, not just print the elements in the shifted order.

def rotate(lst):
# Add your code…

6. Complete the following function that determines if the number of even and odd values in an integer
list is the same. The function would return true if the list contains 5, 1, 0, 2 (two evens and two odds),
but it would return false for the list containing 5, 1, 0, 2, 11 (too many odds). The function should
return true if the list is empty, since an empty list contains the same number of evens and odds (0 for
both). The function does not affect the contents of the list.

def balanced(a):
# Add your code…

7. Complete the following function that returns true if a list lst contains duplicate elements; it returns
false if all the elements in lst are unique. For example, the list [2, 3, 2, 1, 9] contains duplicates

15.10. EXERCISES 629

(2 appears more than once), but the list [2, 1, 0, 3, 8, 4] does not (none of the elements appear
more than once).

An empty list has no duplicates. The function does not affect the contents of the list.

def has_duplicates(lst):
# Add your code…

8. Can linear search be used on an unsorted list? Why or why not?

9. Can binary search be used on an unsorted list? Why or why not?

10. How many different orderings are there for the list [4, 3, 8, 1, 10]?

11. Complete the following function that determines if two lists contain the same elements, but not nec-
essarily in the same order. The function would return true if the first list contains 5, 1, 0, 2 and the
second list contains 0, 5, 2, 1. The function would return false if one list contains elements the other
does not or if the number of elements differ. This function could be used to determine if one list is a
permutation of another list. The function does not affect the contents of either list.

def is_permutation(a, b):
# Add your code…

12. Listing 15.13 (listpermutations.py) contains the following statement:

result += [lst[:]]

(a) What happens if you change the statement to the following?

result += [lst]

(b) Explain why this modified statement produces the result that it does.

13. Write a nonrecursive version of the rev function shown in Listing 15.20 (listreverse.py).

14. Write an function that reverses a list in place. Do not use the reverse method.

15.10. EXERCISES 630

631

Chapter 16

Representing Relationships with
Graphs

Python dictionaries are ideal for representing relationships among things. Much of what modern civilization
uses computers to do involves managing relationships at some level. Mathematical graph theory models
such relationships. This chapter introduces graph algorithms useful to computer scientists.

16.1 Introduction to Graphs

Figure 16.1 shows the routes between cities for a particular airline. The circles in the figure represent
airports, and the associated labels represent airport code names (for example, ATL is Hartsfield-Jackson
Atlanta International Airport near Atlanta, Georgia). A line connecting two circles indicates a direct nonstop
flight between two airports.

The circles and lines make up a mathematical graph, or simply graph. A graph represents relationships
among things. A circle on the graph is known as a vertex (plural: vertices), or node. A line connecting two
vertices is called an edge, or arc. Two vertices connected directly by an edge are adjacent; two vertices not
connected directly by an edge are non-adjacent. Two adjacent vertices are related to each other in some
way; for example, in the airline routes graph two airports are related if a direct flight between them exists.

Graph theory is a distinct area within mathematics that studies graphs. Graph theory is concerned with
connections amongst vertices. Figure 16.2 shows the bare graph with the background map removed. From
the mathematician’s point of view, the positioning of the vertices in a graph visualization is irrelevant, so
the graph in Figure 16.3 is identical to the graph in Figure 16.2.

In a directed graph (or digraph for short) the edges have a direction; that is, vertex a may be adjacent to
vertex b with vertex b not being adjacent to vertex a. Figure 16.4 visualizes a directed graph. In the figure
the arrow pointing from vertex d to vertex f indicates that d is related to f . This means f is adjacent to d,
but observe that d is not adjacent to f . Since edges connect c and d both ways, c is adjacent to d, and d is
adjacent to c.

Mathematical graphs are useful for representing a large number of practical, real-world problems. De-
velopers can model these problems in software using concepts from graph theory and implement solutions
based on graph theoretic algorithms. For this reason, graph theory is of particular interest to computer
scientists.

16.1. INTRODUCTION TO GRAPHS 632

Figure 16.1 A map showing the routes between cities for an airline. The circles in the figure represent
airports, and the associated labels are airport code names (for example, ATL is Hartsfield-Jackson Atlanta
International Airport near Atlanta, Georgia). A line connecting two circles indicates a direct nonstop flight
between two airports. (The image of the United States map is adapted from https://commons.wikimedia.
org/wiki/File:Blank US Map.svg.)

ATL

MIA

DCA

DFW

LAX

SFO DEN
MCI

ORD
LGA

SEA

https://commons.wikimedia.org/wiki/File:Blank_US_Map.svg
https://commons.wikimedia.org/wiki/File:Blank_US_Map.svg

16.1. INTRODUCTION TO GRAPHS 633

Figure 16.2 The airline routes graph with the background map removed.

ATL

MIA

DCA

DFW

LAX

SFO DEN
MCI

ORD
LGA

SEA

Figure 16.3 In mathematic graph theory, the positioning of vertices in a visualization of the graph is irrele-
vant. This graph is equivalent to the graph shown in Figure 16.2.

ATL

MIA

DCA

DFWLAX

SFO

DEN

MCI
ORD

LGASEA

16.1. INTRODUCTION TO GRAPHS 634

Figure 16.4 A visualization of a directed graph. Note that arrows represent directed edges.

c f

Some applications of graph theory include:

• Transportation. Besides airline routes, a global positioning system (GPS) can compute a driving
route from one location to another. An intersection is a vertex in this case, and a road connecting
one intersection to another is an edge. Graph algorithms can determine the best route, where best can
mean shortest traveling time, shortest distance (mileage), or fewest traffic hazards.

• Communication. A person uses a telephone to call another person. The caller and callee are vertices,
and the call that connects them is an edge.

• Games. A game such as chess or checkers involves moving a playing piece from one square to
another. Only certain moves are legal. When representing a game configuration as a graph, a vertex
represents a square, and an edge represents a legal move to another square (to occupy an empty square
or to capture an opponent’s piece).

On a larger scale, the complete board configuration (the locations of all the pieces for both players)
can be a vertex, and a legal move (edge) will result in a different board configuration (vertex). A
computer program can consider all valid moves from a particular board configuration many turns
ahead to determine the best current move for a player.

• Degree requirements. A university degree for a particular major requires a number of courses. Some
of the courses may have prerequisite courses; for example, typically a student wishing to enroll in a
second, more advanced computer programming course must first complete an introductory computer
programming course. In a prerequisite graph, every course is a vertex, and a directed edge connects
a course to its prerequisite course(s).

• Social media. A vertex represents a person, and an edge represents friendship, connecting one person
to another.

• Web. A web page is a vertex, and a hyperlink is an edge connecting one web page to another. The
content of the World Wide Web is an immense directed graph.

• Chemistry. Atoms comprise molecules. The vertices of a graph can model the atoms of a molecule,
and the graph’s edges can represent the bonds between the atoms.

16.2. IMPLEMENTING GRAPHS IN PYTHON 635

• Computer programming. A flowchart like the one shown in Figure 5.1 is a directed graph. Each
geometric shape is a vertex, and each arrow that connects one shape to another is an edge.

These examples are only a few of the many problem domains that mathematical graphs naturally model.
Graph algorithms are a significant resource to software developers faced with the task of tackling problems
in these areas and many others.

16.2 Implementing Graphs in Python

Python does not have a native graph data structure; however, we can easily model a mathematical graph in
Python using a dictionary and sets. The keys in the dictionary represent the vertices of the graph, and each
key maps to a set. The set contains the vertices adjacent to the key. Using this technique we can express the
graph in Figure 16.3 as

# Dictionary representing the graph of airline routes
routes = {

“ATL”: {“MIA”, “DCA”, “ORD”, “MCI”, “DFW”, “DEN”},
“MIA”: {“LGA”, “DCA”, “ATL”, “DFW”},
“DFW”: {“LAX”, “DEN”, “MCI”, “ORD”, “ATL”, “MIA”},
“LAX”: {“SFO”, “DEN”, “MCI”, “DFW”},
“DEN”: {“SFO”, “LAX”, “MCI”, “DFW”, “SEA”, “ATL”},
“SEA”: {“SFO”, “DEN”, “ORD”, “LGA”},
“MCI”: {“DEN”, “LAX”, “DFW”, “ATL”, “ORD”, “LGA”},
“ORD”: {“SEA”, “MCI”, “DFW”, “ATL”, “DCA”, “LGA”},
“DCA”: {“ORD”, “ATL”, “MIA”, “LGA”},
“LGA”: {“SEA”, “MCI”, “ORD”, “DCA”, “MIA”},
“SFO”: {“SEA”, “DEN”, “LAX”}

}

Given this representation we can print all the airports with a direct connection from ATL as

for airport in routes[“ATL”]:
print(airport)

Since a Python set holds the collection of adjacent airports, the statement above most likely will print the
airports out in a different order than they appear in the source code assigning routes. If in a particular
application the ordering of adjacent vertices is important, use a Python list instead of a set. For most
problems, however, a set is the preferred adjacency structure. Counterintuitively, the formal name for this
kind of graph representation is adjacency list (see https://en.wikipedia.org/wiki/Adjacency list),
where list as used here means an unordered collection, or set. Python reserves the name list for an ordered
linear collection.

16.3 Path Finding

Computer scientists and mathematicians have developed a number of algorithms that solve common prob-
lems in graph theory. One problem is finding a path from one vertex to another within a graph. From our
airline example graph in Figure 16.3, ATL–DEN–SFO–SEA represents a path from ATL to SEA. Another
path from ATL to SEA is ATL–MIA–DFW–MCI–LGA–ORD–SEA. Since no direct flight exists between ATL
and SFO, the sequence ATL–SFO–SEA is not a path in the Figure 16.3 graph.

https://en.wikipedia.org/wiki/Adjacency_list

16.3. PATH FINDING 636

Generally, shorter paths are desirable, as a shorter path usually translates into some kind of savings,
such as shorter travel time or less fuel consumed. Some graphs have values attached to each edge that
represent a cost such as time or distance, making some edges more expensive than others. We will keep
things simple here and treat all edges equally. This means one path is shorter than another path if it visits
fewer vertices. The length of a path is the number of edges used in the path, so the path length of ATL–MIA–
DFW–MCI–LGA–ORD–SEA is 6. So, while ATL–MIA–DFW–MCI–LGA–ORD–SEA surely gets a passenger
from from ATL to SEA, the path ATL–DEN–SFO–SEA is shorter. (Can you find an even shorter path from
ATL to SEA in Figure 16.3?)

Our goal is to find a shortest path from one vertex to another in a graph. Notice that we say a shortest
path rather than the shortest path, as several different paths may tie for the shortest length; for example,
consider the following paths from MIA to SFO:

MIA–ATL–DEN–SFO

MIA–DFW–LAX–SFO

MIA–DFW–DEN–SFO

MIA–LGA–SEA–SFO

All of these paths have length 3, and no path from MIA to SFO is shorter than 3. In general, there should be
no paths connecting two vertices shorter than a shortest path between the vertices.

In order to find a shortest path in a graph, the algorithm must traverse the graph. Graph traversal is
more complicated than list traversal. Traversing a list is easy: begin at the first element (index 0) and visit
each successive element (element at current index plus one), in order, until locating the desired element or
running out of elements to visit. A graph, however, is not a linear structure; it is a network of interconnected
elements, and an element (vertex) can have multiple successors (zero or more adjacent vertices). If our
traversal algorithm is not careful, it could, for example, begin at vertex ATL and follow the path ATL–DCA–
LGA–ORD–ATL. Such a path that begins and ends at the same vertex is known as a cycle. A naı̈ve algorithm
could continue the traversal following the exact same path as shown here:

ATL–DCA–LGA–ORD–ATL–DCA–LGA–ORD–ATL–DCA–LGA–ORD–ATL– · · ·

The algorithm effectively becomes stuck in the cycle, revisiting the same vertices over and over. Unable to
escape the cycle, the algorithm cannot visit any vertices outside of this cycle.

To avoid getting stuck in a cycle our traversal algorithm must have a way to remember which vertices
it has visited so it does not attempt to revisit them. Our path finding algorithm will add a visited vertex to a
dictionary. The vertex serves as a key, and its associated value will be the vertex that immediately precedes
it on a shortest path from the starting vertex to the destination vertex. During its traversal of the graph, the
algorithm will check this dictionary before attempting to visit a vertex. If the vertex is not in the dictionary,
the algorithm “visits” the vertex by adding it (with its predecessor on a shortest path) to the dictionary. If
the vertex is already present in the dictionary, the algorithm ignores the vertex and continues its traversal
through other available vertices in the graph.

The second problem for our path finding algorithm is not merely to find a path from the starting vertex
to the ending vertex but to find a shortest path. Remember that an algorithm cannot see the graph globally
as we can when we look at its visual representation. The algorithm must be clever in its choice of which
vertex to visit next as it traverses the graph. This choice is crucial because once the algorithm adds a vertex
to the dictionary of visited vertices it can never go back and revisit the vertex to determine if choosing a
different adjacent vertex would result in a shorter path. (As noted above, if it attempts to revisit a vertex,
the algorithm could get stuck in a cycle, retracing the same path over and over again.)

16.4. BREADTH-FIRST SEARCH 637

16.4 Breadth-first Search

There are a number path finding algorithms, and Listing 16.1 (airlineroute.py) uses one such algorithm,
breadth-first search (BFS), to compute a shortest path from one vertex to another (see https://en.
wikipedia.org/wiki/Breadth-first search). The BFS algorithm uses a queue to guide the algorithm’s
progress. A queue is a first-come, first-serve data structure. It is similar to a list, in that a queue is a linear
sequence of elements, and clients can add elements to, and remove elements from, the sequence. Unlike
with a list, however, element addition and removal in a queue is restricted: clients may remove only the
most recent element added to the queue. A queue thus works like a line of customers waiting at a checkout
counter in a store. The cashier serves the person at the front of the line first, and customers who are ready
to check out but not in line must join the end of the line and wait for their turn. Conceptually, we can place
items on the back of a queue only, and we can remove items only from the front of a queue.

Fortunately, the Python standard library offers a Queue class in a module named queue. Our imple-
mentation of the BFS algorithm will use a Queue object, and it will use three methods that the Queue class
provides:

• put places an element onto the rear of the queue,

• get serves an element from the front of the queue, and

• empty returns True is the queue is empty and False it contains any elements.

The put and get methods modify the queue, but the empty method does not disturb the contents, if any, of
a queue object.

We can practice with a Queue object in the interactive interpreter:

>>> from queue import Queue
>>> q = Queue()
>>> q.empty()
True
>>> q.put(34)
>>> q.empty()
False
>>> q.put(“Hello”)
>>> q.put(12)
>>> q.put([10, 20, 30])
>>> q.get()
34
>>> q.get()
‘Hello’
>>> q.get()
12
>>> q.empty()
False
>>> q.get()
[10, 20, 30]
>>> q.empty()
True

As you can see, what goes into the queue first comes out first, and what goes in last comes out last.

Just as a queue organizes the service of customers at a grocery checkout so that the cashier serves earlier

https://en.wikipedia.org/wiki/Breadth-first_search
https://en.wikipedia.org/wiki/Breadth-first_search

16.4. BREADTH-FIRST SEARCH 638

arrivals before later ones, the proper use of a queue ensures the BFS algorithm visits vertices in a graph in
an order that guarantees it will find a shortest path between two vertices. BFS proceeds as follows:

Inputs: A starting vertex and destination vertex within a graph.
Begin with an empty dictionary and an empty queue.
Add the starting vertex to the queue.
while the queue is not empty and the dictionary does not contain the destination vertex as a key:

Serve the next vertex, v, from the queue.
for each vertex w adjacent to v:

if w is not in the dictionary:
Add w to the queue.
Add key w with its value v to the dictionary.

Output: The dictionary with the keys consisting vertices reachable from the starting vertex;
the value of a key is the vertex that immediately precedes it on a shortest path from the starting vertex
to the destination vertex.

The first time through its while loop the BFS algorithm extracts the starting vertex from the queue. The
for loop then considers every vertex adjacent to the starting vertex. These adjacent vertices go into the
queue. Note that all of these vertices added to the queue are a distance of 1 away from the starting vertex
and record the starting vertex as their predecessor. On the second iteration of its while loop the algorithm
removes one vertex from the queue. This has to be one of the vertices it added on its first iteration—a vertex
adjacent to the starting vertex. Call this vertex v. The algorithm adds any nonvisited vertices adjacent to
v to the queue. Note that all these nonvisited vertices adjacent to v are a distance of 2 from the starting
vertex. Because it is using a queue the algorithm cannot visit these newly added vertices until it processes
the vertices added to the queue earlier. This means the algorithm visits all the vertices that are a distance
of 1 from the starting vertex before it attempts to visit any vertices at a distance of 2 away from the starting
vertex. Unless it encounters the destination vertex beforehand, the algorithm eventually will extract from
the queue a vertex at a distance of 2 from the starting vertex, adding all of that vertex’s unvisited vertices
(distance 3) to the back of the queue. Consequently, all distance 2 vertices will be ahead of distance 3
vertices in the queue, and so the algorithm visits all distance 2 vertices before visiting any distance 3 vertex.
The while loop continues until the queue is empty or the algorithm reaches the destination vertex. In
this way the algorithm visits all distance 1 vertices before any distance 2 vertex, all distance 2 vertices
before any distance 3 vertex, all distance 3 vertices before any distance 4 vertex, and so forth. Figure 16.5
illustrates with an example BFS traveral. The queue ensures that the next vertex visited in the while loop
is no farther away from the starting vertex than any other yet-to-be visited vertex. Expanding the search to
a more distant vertex only after all nearer vertices have been considered is the trick to discovering a shortest
path in the graph from the starting vertex to the destination vertex.

From the dictionary that this BFS algorithm produces we can construct a shortest path by following the
predecessor links back from the destination vertex as described in the following procedure:

Inputs: A starting vertex and destination vertex within a graph.
Begin with an empty path.
Use the BFS algorithm to compute the dictionary containing vertex predecessors on
a shortest path from the starting vertex to the destination vertex.
if the destination vertex is in the dictionary:

Add the destination vertex to the path.
Set v to be the destination vertex.

16.4. BREADTH-FIRST SEARCH 639

Figure 16.5 The numbers indicate a possible order in which BFS visits vertices starting at vertex ATL. Since
a Python program uses a dictionary to represent the graph, the exact order of the visitation is unpredictable,
even from one execution to the next on the same machine. What is predictable, however, is that BFS will
visit all vertices at a distance of n from the starting vertex before it visits any vertex at a distance greater
than or equal to n+ 1 from the starting vertex. For example, the shortest distance between ATL and DEN
is 1 and the shortest distance between ATL and LAX is 2; this means the number associated with DEN must
be less than the number associated with LAX. Consequently, BFS from ATL necessarily would visit DEN
before visiting LAX.

ATL

MIA

DCA

DFWLAX

SFO

DEN

MCI
ORD

LGASEA

4
2

8
9

16.4. BREADTH-FIRST SEARCH 640

while the starting vertex is not in the path:
Update v to be v’s predecessor from the dictionary.
Add v to the front of the path.

Output:The path that contains, in order, the vertices found on a shortest path from the starting
vertex to the destination vertex; an empty path indicates that the destination vertex is not reachable
from the starting vertex.

Listing 16.1 (airlineroute.py) implements the BFS and path building algorithms in Python. The bfs
function faithfully implements the breadth-first search traversal algorithm, building and returning a dictio-
nary containing vertices, each paired with its immediate predecessor on a shortest path from the starting
vertex. The find_path function implements the second algorithm from above that uses the result of bfs
to construct a list of vertices, in order, an a shortest path from from the starting vertex to the destination
vertex.

The graph processed by Listing 16.1 (airlineroute.py) is shown in Figure 16.6. This graph adds three
new airports to Figure 16.3: BNA, CHA, and CLT. These new vertices are interconnected to each other, but
they are not connected to any of the vertices from the original graph. (In the real world you can get from
CHA [Chattanooga, Tennessee], for example, to DEN, but this contrived graph illustrates the general case
where a path may not exist between two vertices in a graph.)

Listing 16.1: airlineroute.py

from queue import Queue

def bfs(graph, start_vertex, end_vertex):
“”” Performs a breadth-first traversal of graph originating

at start_vertex and ending when the traversal encounters
end_vertex. Builds and returns a dictionary with
vertices mapped to their immediate predecessors on the
breadth-first traversal. “””

# A dictionary of vertex predecessors encountered on a breadth-first
# traversal from start_vertex to end_vertex.
# The dictionary key is a vertex, and the associated value is
# the vertex that comes immediately before the key on a
# breadth-first traversal.
# This dictionary initially is empty, and we will add vertices as
# we “visit” them during the breadth-first traversal.
predecessor = {}

# Make an empty queue and insert the starting vertex
# The algorithm will extract and visit vertices from this queue
q = Queue()
q.put(start_vertex)

# Keep searching while the queue holds vertices yet to visit
# and we have yet to visit our destination vertex
while not q.empty() and end_vertex not in predecessor:

vertex = q.get() # Get vertex on the front of the queue
for adjacent_vertex in graph[vertex]: # Consider all adjacent vertices

# Has the predecessor of this vertex been established?
if adjacent_vertex not in predecessor:

16.4. BREADTH-FIRST SEARCH 641

q.put(adjacent_vertex) # Enqueue the vertex
# Register which vertex should come immediately before this
# one on a shortest path (this “visits” the vertex)
predecessor[adjacent_vertex] = vertex

# At this point we exited the while loop because either the queue was
# empty or the destination vertex now is in the predecessor dictionary
# (or both). If the queue is empty but the destination vertex is not in
# the predecessor dictionary, the destination vertex is unreachable from the
# starting vertex. If the queue is not empty but the destination vertex
# is in the predecessor dictionary, the path from the starting vertex to
# the destination vertex exists and excludes one or more vertices in
# the graph. If the queue is empty and the destination vertex is in the
# predecessor dictionary, the shortest path from the starting vertex to the
# destination vertex includes all vertices reachable from the starting
# vertex.
return predecessor

def find_path(graph, start_vertex, end_vertex):
“”” Builds a list of vertices in order along the shortest path

from a starting vertex to an ending vertex in a graph.
graph: The graph to traverse.
start_vertex: The starting vertex.
end_vertex: The vertex to locate. “””

# Compute predecessor of each vertex on a shortest path
# Call the bfs function to build the predecessor dictionary
predecessor = bfs(graph, start_vertex, end_vertex)

path = [] # Path initially empty

# Check that we were able to reach the destination vertex
if end_vertex in predecessor:

# Start at the end and work backwards
path = [end_vertex]
vertex = end_vertex
# Keep going until we get to the beginning of the path
while vertex != start_vertex:

# Get vertex that comes immediately before on a shortest path
vertex = predecessor[vertex]
# Prepend the predecessor vertex to the front of the path list
path = [vertex] + path

return path

def main():
“”” Tests the find_path function by searching for routes between airports. “””

# Dictionary representing the graph of airline routes
routes = {

16.4. BREADTH-FIRST SEARCH 642

Figure 16.6 An extention of the graph in Figure 16.2 that includes three extra vertices. None of the new
vertices connect to any the vertices in the original graph.

ATL

MIA

DCA

DFWLAX

SFO

DEN

MCI
ORD

LGASEA

CHA

CLTBNA

“DEN”: {“SFO”, “LAX”, “MCI”, “DFW”, “SEA”, “ATL”},
“SEA”: {“SFO”, “DEN”, “ORD”, “LGA”},
“MCI”: {“DEN”, “LAX”, “DFW”, “ATL”, “ORD”, “LGA”},
“ORD”: {“SEA”, “MCI”, “DFW”, “ATL”, “DCA”, “LGA”},
“DCA”: {“ORD”, “ATL”, “MIA”, “LGA”},
“LGA”: {“SEA”, “MCI”, “ORD”, “DCA”, “MIA”},
“SFO”: {“SEA”, “DEN”, “LAX”},
“CLT”: {“BNA”, “CHA”},
“BNA”: {“CLT”, “CHA”},
“CHA”: {“CLT”, “BNA”}

}

# Attempt to find a route from one airport to another
print(find_path(routes, “LAX”, “DCA”))
print(find_path(routes, “MIA”, “SFO”))
print(find_path(routes, “ATL”, “MIA”))
print(find_path(routes, “LGA”, “LGA”))
print(find_path(routes, “CLT”, “BNA”))
print(find_path(routes, “BNA”, “ATL”))

if __name__ == “__main__”:
main()

Listing 16.1 (airlineroute.py) prints

16.4. BREADTH-FIRST SEARCH 643

[‘LAX’, ‘MCI’, ‘ORD’, ‘DCA’]
[‘MIA’, ‘DFW’, ‘LAX’, ‘SFO’]
[‘ATL’, ‘MIA’]
[‘LGA’]
[‘CLT’, ‘BNA’]
[]

The final line of the program’s output prints an empty list indicating that no path exists from BNA to ATL. A
graph in which a path exists between any two vertices is known as a connected graph. The graph shown in
Figure 16.3 is a connected graph. A graph that is not connected, like Figure 16.6, is a disconnected graph.

Suppose we wish to determine if a graph is connected; that is, does there exist a path between any two
vertices in the graph? Given our bfs function from Listing 16.1 (airlineroute.py), the following function
would work:

def is_connected(G):
“”” G is a dictionary that represents a graph. “””
for v in G: # Examine each dictionary key (vertex)

for w in G: # Examine each dictionary key (vertex)
if v != w and w not in bfs(G, v, w):

return False # Vertex w not reachable from vertex v
return True # All vertices in G are reachable from any vertex in G

This function essentially attempts to find a path from all vertices to all other vertices (except from a vertex to
itself). While this code works, it is very inefficient. It performs a large amount of unnecessary work. As an
example, given the graph in Figure 16.3 the is_connected function will find a path between ATL and SFO
and also during its processing find a path between SFO and ATL. Since the graph is undirected, attempting to
find the reverse path is superfluous. If the number of vertices in the graph is n, the is_connected function
calls the bfs function n2− n times. (The n2 is the number of possibilities resulting from pairing every
vertex with every other vertex, and we subtract n so we do not count pairing a vertex with itself.) Using this
technique on a graph with 50 vertices produces 2,450 calls of bfs.

Section 15.4 showed how two different search algorithms both can be correct and yet perform dramati-
cally differently. If we make a minor tweak to bfs, we can rewrite the is_connected function so that it can
do its job with only one call to bfs. Listing 16.2 (checkconnected.py) extends Listing 16.1 (airlineroute.py)
by adding an is_connected function. It makes two small changes to the original bfs function:

• The start_vertex and end_vertex parameters now are optional (default to None).

• The function will choose an arbitrary starting vertex from the graph if the caller does not supply one.

If the caller omits the end_vertex parameter, the while loop within bfs will compute predecessors for all
reachable vertices within the graph. This is because end_vertex defaults to None, and the function never
adds the None key to its initially empty predecessor dictionary. If the caller omits both the start_vertex
and end_vertex, the function will choose an arbitrary starting vertex from the graph. Due to the nature of
default arguments, the caller has no way to omit only the start_vertex parameter (see Section 8.2).

Listing 16.2: checkconnected.py

from queue import Queue

def bfs(graph, start_vertex=None, end_vertex=None):

16.4. BREADTH-FIRST SEARCH 644

“”” Performs a breadth-first traversal of graph originating
at start_vertex and ending when the traversal encounters
end_vertex. If the end_vertex parameter is omitted, the
BFS continues to all vertices in the graph. If the
start_vertex parameter is omitted, the BFS begins with an
arbitrary vertex in the graph.
Builds and returns a dictionary with
vertices mapped to their immediate predecessors on the
breadth-first traversal. “””

if graph:
if not start_vertex: # Caller provided a starting vertex?

start_vertex = list(graph.keys())[0] # Grab an arbitrary vertex from the graph

#print(“Start vertex:”, start_vertex)

# Make an empty queue and insert the starting vertex
# The algorithm will extract and visit vertices from this queue
q = Queue()
q.put(start_vertex)

# Keep searching while the queue holds vertices yet to visit
# and we have yet to visit our destination vertex
while not q.empty() and end_vertex not in predecessor:

vertex = q.get() # Get vertex on the front of the queue
for adjacent_vertex in graph[vertex]: # Consider all adjacent vertices

# Has the predecessor of this vertex been established?
if adjacent_vertex not in predecessor:

16.5. DEPTH-FIRST SEARCH 648

>>> s.pop()
34
>>> len(s) <= 0 True As you can see, what goes onto the stack last comes out first, and what goes in fist comes out last. DFS proceeds as follows: Inputs: A starting vertex and destination vertex within a graph. Begin with an empty set and an empty stack. Push the starting vertex onto the stack. while the stack is not empty and the set does not contain the destination vertex: Pop the top vertex, v, from the stack. if v in not in the set: Add v to the set: for each vertex w adjacent to v: if w is not in the set: Push w onto the stack Output: The set containing vertices reachable from the starting vertex. The first time through its while loop the DFS algorithm extracts the starting vertex from the stack. Since the visited set begins empty, the algorithms adds the starting vertex to the set. It then will add all of the starting vertex’s adjacent vertices to the stack. On the second iteration of its while loop the algorithm removes from the stack the last vertex it added on the previous iteration, one adjacent to the starting vertex. Call this vertex v. The algorithm adds any nonvisited vertices adjacent to v to the stack. Because it uses a stack the algorithm will visit these newly added vertices before it visits any vertices it added to the stack earlier. This allows the algorithm to propagate to vertices farther away from the starting vertex before it considers closer vertices. Figure 16.7 illustrates one such DFS traversal. Listing 16.3 (dfs.py) implements the DFS algorithm. Listing 16.3: dfs.py def dfs(graph, start_vertex=None, end_vertex=None): """ Performs a depth-first traversal of graph originating at start_vertex and ending when the traversal encounters end_vertex. If the end_vertex parameter is omitted, the DFS continues to all vertices in the graph. If the start_vertex parameter is omitted, the DFS begins with an arbitrary vertex in the graph. Builds and returns a set of vertices discovered during the depth-first traversal. """ # A set of vertices encountered on a depth-first # traversal from start_vertex to end_vertex. # This set initially is empty, and we will add vertices as # we "visit" them during the depth-first traversal. visited = set() if graph: if not start_vertex: # Caller provided a starting vertex? ©2017 Richard L. Halterman Draft date: January 18, 2018 16.5. DEPTH-FIRST SEARCH 649 Figure 16.7 The numbers indicate a possible order in which DFS visits vertices starting at vertex ATL. Since a Python program uses a dictionary to represent the graph, the exact order of the visitation is unpredictable, even from one execution to the next on the same machine. What is predictable, however, is that the path traced by DFS will tend to move farther from the starting vertex before visiting all vertices closer to the starting vertex. Observe that this traversal visits MIA last, even though MIA is adjacent to the starting vertex. ATL MIA DCA DFWLAX SFO DEN MCI ORD LGASEA 1 4 2 5 3 6 7 8 9 10 11 ©2017 Richard L. Halterman Draft date: January 18, 2018 16.5. DEPTH-FIRST SEARCH 650 start_vertex = list(graph.keys())[0] # Grab an arbitrary vertex from the graph #print("Start vertex:", start_vertex) # Make an empty stack and insert the starting vertex # The algorithm will extract and visit vertices from this stack s = [] s.append(start_vertex) # Keep searching while the stack holds vertices yet to visit # and we have yet to visit our destination vertex while len(s) > 0 and end_vertex not in visited:

vertex = s.pop() # Get vertex on the top of the stack
if vertex not in visited:

visited.add(vertex) # Visit the vertex
for adjacent_vertex in graph[vertex]: # Consider all adjacent vertices

# Has the predecessor of this vertex been established?
if adjacent_vertex not in visited:

s.append(adjacent_vertex) # Push the vertex
# At this point we exited the while loop because either the stack was
# empty or the destination vertex now is in the visited set (or both).
# If the stack is empty but the destination vertex is not in
# the visited set, the destination vertex is unreachable from the
# starting vertex. If the stack is not empty but the destination vertex
# is in the visited set, the path from the starting vertex to
# the destination vertex exists and excludes one or more vertices in
# the graph. If the stack is empty and the destination vertex is in the
# visited set, the shortest path from the starting vertex to the
# destination vertex includes all vertices reachable from the starting
# vertex.

return visited

def dfs2(graph, start_vertex=None, end_vertex=None):
“”” Performs a depth-first traversal of graph originating

at start_vertex and ending when the traversal encounters
end_vertex. If the end_vertex parameter is omitted, the
DFS continues to all vertices in the graph. If the
start_vertex parameter is omitted, the DFS begins with an
arbitrary vertex in the graph. Builds and returns a set of
vertices discovered during the depth-first traversal. “””

# A set of vertices encountered on a depth-first
# traversal from start_vertex to end_vertex.
# This set initially is empty, and we will add vertices as
# we “visit” them during the depth-first traversal.
visited = set()

def dfs3(start_vertex, end_vertex):
visited.add(start_vertex)
for adjacent_vertex in graph[start_vertex]:

if adjacent_vertex not in visited and end_vertex not in visited:
dfs3(adjacent_vertex, end_vertex)

16.5. DEPTH-FIRST SEARCH 651

if graph:
if not start_vertex: # Caller provided a starting vertex?

start_vertex = list(graph.keys())[0] # Grab an arbitrary vertex from the graph
dfs3(start_vertex, end_vertex) # Build the visited set

return visited

def bfs(graph, start_vertex=None, end_vertex=None):
“”” Performs a breadth-first traversal of graph originating

at start_vertex and ending when the traversal encounters
end_vertex. If the end_vertex parameter is omitted, the
BFS continues to all vertices in the graph. If the
start_vertex parameter is omitted, the BFS begins with an
arbitrary vertex in the graph.
Builds and returns a dictionary with
vertices mapped to their immediate predecessors on the
breadth-first traversal. “””

if graph:
if not start_vertex: # Caller provided a starting vertex?

start_vertex = list(graph.keys())[0] # Grab an arbitrary vertex from the graph

#print(“Start vertex:”, start_vertex)

# Make an empty queue and insert the starting vertex
# The algorithm will extract and visit vertices from this queue
q = Queue()
q.put(start_vertex)

# Keep searching while the queue holds vertices yet to visit
# and we have yet to visit our destination vertex
while not q.empty() and end_vertex not in predecessor:

vertex = q.get() # Get vertex on the front of the queue
for adjacent_vertex in graph[vertex]: # Consider all adjacent vertices

# Has the predecessor of this vertex been established?
if adjacent_vertex not in predecessor:

q.put(adjacent_vertex) # Enqueue the vertex
# Register which vertex should come immediately before this
# one on a shortest path (this “visits” the vertex)
#print(adjacent_vertex, “<--", vertex) predecessor[adjacent_vertex] = vertex # At this point we exited the while loop because either the queue was # empty or the destination vertex now is in the predecessor dictionary # (or both). If the queue is empty but the destination vertex is not in ©2017 Richard L. Halterman Draft date: January 18, 2018 16.5. DEPTH-FIRST SEARCH 652 # the predecessor dictionary, the destination vertex is unreachable from the # starting vertex. If the queue is not empty but the destination vertex # is in the predecessor dictionary, the path from the starting vertex to # the destination vertex exists and excludes one or more vertices in # the graph. If the queue is empty and the destination vertex is in the # predecessor dictionary, the shortest path from the starting vertex to the # destination vertex includes all vertices reachable from the starting # vertex. return predecessor def find_path(graph, start_vertex, end_vertex): """ Builds a list of vertices in order along the shortest path from a starting vertex to an ending vertex in a graph. graph: The graph to traverse. start_vertex: The starting vertex. end_vertex: The vertex to locate. """ # Compute predecessor of each vertex on a shortest path # Call the bfs function to build the predecessor dictionary predecessor = bfs(graph, start_vertex, end_vertex) path = [] # Path initially empty # Check that we were able to reach the destination vertex if end_vertex in predecessor: # Start at the end and work backwards path = [end_vertex] vertex = end_vertex # Keep going until we get to the beginning of the path while vertex != start_vertex: # Get vertex that comes immediately before on a shortest path vertex = predecessor[vertex] # Prepend the predecessor vertex to the front of the path list path = [vertex] + path return path def is_connected(G): """ Returns True if G is a dictionary representing a connected graph; otherwise, returns False. A graph containing no vertices (and, therefore, no edges) is considered connected. """ # Use bfs to compute the predecessor of each vertex on a # shortest path from an arbitrary vertex within G. predecessor = dfs2(G) #predecessor = bfs(G) for vertex in G: if vertex not in predecessor: return False return True def is_connected2(G): ©2017 Richard L. Halterman Draft date: January 18, 2018 16.5. DEPTH-FIRST SEARCH 653 """ G is a dictionary that represents a graph. """ for v in G: # Examine each dictionary key (vertex) for w in G: # Examine each dictionary key (vertex) if v != w and w not in bfs(G, v, w): return False # Vertex w not reachable from vertex v return True # All vertices in G are reachable from any vertex in G def main(): """ Tests the find_path and is_connected functions. """ # Dictionary representing the graph of airline routes routes = { "ATL": {"MIA", "DCA", "ORD", "MCI", "DFW", "DEN"}, "MIA": {"LGA", "DCA", "ATL", "DFW"}, "DFW": {"LAX", "DEN", "MCI", "ORD", "ATL", "MIA"}, "LAX": {"SFO", "DEN", "MCI", "DFW"}, "DEN": {"SFO", "LAX", "MCI", "DFW", "SEA", "ATL"}, "SEA": {"SFO", "DEN", "ORD", "LGA"}, "MCI": {"DEN", "LAX", "DFW", "ATL", "ORD", "LGA"}, "ORD": {"SEA", "MCI", "DFW", "ATL", "DCA", "LGA"}, "DCA": {"ORD", "ATL", "MIA", "LGA"}, "LGA": {"SEA", "MCI", "ORD", "DCA", "MIA"}, "SFO": {"SEA", "DEN", "LAX"}, "CLT": {"BNA", "CHA"}, "BNA": {"CLT", "CHA"}, "CHA": {"CLT", "BNA"} } r1 = { "ATL": {"MIA", "DCA", "ORD", "MCI", "DFW", "DEN"}, "MIA": {"LGA", "DCA", "ATL", "DFW"}, "DFW": {"LAX", "DEN", "MCI", "ORD", "ATL", "MIA"}, "LAX": {"SFO", "DEN", "MCI", "DFW"}, "DEN": {"SFO", "LAX", "MCI", "DFW", "SEA", "ATL"}, "SEA": {"SFO", "DEN", "ORD", "LGA"}, "MCI": {"DEN", "LAX", "DFW", "ATL", "ORD", "LGA"}, "ORD": {"SEA", "MCI", "DFW", "ATL", "DCA", "LGA"}, "DCA": {"ORD", "ATL", "MIA", "LGA"}, "LGA": {"SEA", "MCI", "ORD", "DCA", "MIA"}, "SFO": {"SEA", "DEN", "LAX"} } r2 = { "CLT": {"BNA", "CHA"}, "BNA": {"CLT", "CHA"}, "CHA": {"CLT", "BNA"} } # Find shortest paths, as before print(find_path(routes, "LAX", "DCA")) print(find_path(routes, "MIA", "SFO")) print(find_path(routes, "ATL", "MIA")) print(find_path(routes, "LGA", "LGA")) ©2017 Richard L. Halterman Draft date: January 18, 2018 16.6. EXERCISES 654 print(find_path(routes, "CLT", "BNA")) print(find_path(routes, "BNA", "ATL")) # Check connectivity print("Connected: ", is_connected(routes), is_connected2(routes)) print("Connected: ", is_connected(r1), is_connected2(r1)) print("Connected: ", is_connected(r2), is_connected2(r2)) if __name__ == "__main__": main() Because of the way it works, DFS is not useful for finding the shortest path between to vertices. Many useful graph algorithms involve variations of BFS or DFS. 16.6 Exercises CAUTION! SECTION UNDER CONSTRUCTION Add item. ©2017 Richard L. Halterman Draft date: January 18, 2018 655 Index needs a relationship, 514 absolute value, 102 accessor methods, 467 accumulator, 117 actual, 167 adapter design pattern, 539 adjacency list, 635 adjacent vertices, 631 aggregate, 514 aggregation, 514 algorithm, 63 aliases, 188 aliasing, 354 aliasing, object, 334 arc, 631 ascending ordering of list elements, 567 associative array, 402 associative container, 398 attributes, 312 base case, 244 base class, 519 benchmarking, 190 BFS, 637 binary search, 584 block, 12 body, 72 Boolean, 69 breadth-first search, 637 buffering, 252 bugs, 59 callback function, 253, 469 calling code, 159 catch-all exception handler, 433, 446 catching an exception, 429 chained assignment, 52 class, 17, 311 class constructor, 323 class hierarchy, 527 class variables, 507 client, 312 client code, 159 closure, 275 code duplication, 223 code instrumentation, 604 comma-separated list, 21 command prompt, 368 commutative, 350 compiler, 2, 3 composition, 513 concatenation, 18 conditional expression, 100 connected graph, 643 context manager, 318 control codes, 32 cooperative multiple inheritance, 541 cycle in a graph, 636 data, 311 data persistence, 316 debugger, 4 decorator, 300 default argument, 238 default parameters, 238 definite loop, 121 delimit, 16 denominator, 323, 474 dependent function, 237 depth-first search, 647 derivative, 290 derived class, 519 design pattern, 539 DFS, 647 dictionary, 398 dictionary key, 398 differentiation, 290 digraph, 631 dir function, 165 direct base class, 525 directed graph, 631 directory function, 165 disconnected graph, 643 ©2017 Richard L. Halterman Draft date: January 18, 2018 INDEX 656 docstring, 212 documentation string, 212 double negative, 79 double underscore, 473 dunder, 473 EAFP, 429 easier to ask for forgiveness than permission, 429 edge, 631 elapsed time, 171 end keyword argument in print, 36 Eratosthenes, 366 escape symbol, 32 except block, 429 exception, 425 exception else block, 451 exception classes, common standard, 426 exception handling, 425 exception, re-raising, 448 exception, swallowing, 446 existential quantification, 417 expression, 15 external documentation, 212 factorial, 241 Fibonacci sequence, 245 fields, 312 files, 316 finally block, 453 floating-point numbers, 28 for statement, 122 formal, 167 formatting string, 39 function, 158 function definition, 194 function invocation, 194 function time.clock, 170 function time.sleep, 172 function call, 159 function coherence, 214 function composition, 207, 219 function definition parts, 194 function invocation, 159 functional composition, 34 functional decomposition, 194 functional independence, 237 functionally equivalent, 568 garbage, 336 garbage collection, 336 generalized unpacking, 396 generator, 280 generator comprehension, 374 generator expression, 374 get attribute, 505 getattr, 505 getters, 467 global variable, 233 graph, 631 graph theory, 631 handling an exception, 429 has a relationship, 514 hash tables, 402 hashing, 402 Hoare, C. A. R., 582 id function, 165 identifier, 26 identifiers beginning with two underscores, 473 if statement, 71 immutable, 209 in place list processing, 596 indefinite loop, 122 index, 315, 341 indirect base class, 525 inheritance, 518 inheritance hierarchy, 527 inheritance, single, 519 instance variable, 312 instance variable, object, 463 integer division, 46 internal documentation, 212 interpreter, 3, 4 is a, 524 key, 398, 399 keyword argument, 36 keyword arguments, 411 keywords, 27 lambda calculus, 274 lambda expression, 274 last-in, first out, 647 lazy list, 385 LBYL, 428 LCS, 621 len function, 345 length, 345 LIFO, 647 linear search, 584 list aliasing, 354 ©2017 Richard L. Halterman Draft date: January 18, 2018 INDEX 657 list comprehension, 370 list function, 348 list of lists, 375 list slicing, 358 local variables, 233 longest common subsequence, 621 look before you leap, 428 loop unrolling, 601 mathematical graph, 631 matrix, 375 member, object, 463 members, 312 memoization, 617 Mersenne Twister, 173 method call, 312 method resolution order, 547 method, object, 463 methods, 311 midpoint, 200 module, 159, 162 modules, 157, 248 modulus, 46 monolithic code, 193 MRO, 547 multiple inheritance, 540 multiplication table, 126 mutable, 344, 355 mutator methods, 467 name collision, 186 namespace, 186 namespace pollution, 187 nested, 84 nested loop, 126 newline, 32 node, 631 non-decreasing order of list elements, 567 None object reference, 336 numerator, 323, 474 numerical differentiation, 291 object aliasing, 334 object composition, 472 object oriented, 311 operations, 312 override, 519 Papert, Seymour, 179 partial application, 304 pass statement, 82 permutation, 131, 600 positional parameters, 39 predicate, 69, 417 private object members, 473 profiler, 4 pure function, 238 qualified name, 163 quantification, 415 queue, 637 Quicksort, 582 ragged array, 376 random access, 385 re-raising an exception, 448 read, eval, print loop, 16 recursive, 241 recursive case, 244 refactoring, 223 refactoring code, 223 reference counting, 336 regular expression, 429 relational operators, 70 remainder, 46 reserved words, 27 run-time errors, 56 run-time exceptions, 56 scripting languages, 4 selection sort, 576 sep keyword argument in print, 37 sequence, 621 set attribute, 505 set comprehension, 415 setattr, 505 setters, 467 short-circuit evaluation, 81 Sieve of Eratosthenes, 366 single inheritance, 519 slice assignment, 360 slicing, 358 stack, 439, 647 stack trace, 439 stack unwinding, 439 statement, 5 string, 16 string formatter, 40 stub, 497 subclass, 519 subscript, 341 subsequence, 621 ©2017 Richard L. Halterman Draft date: January 18, 2018 INDEX 658 super function, 519 superclass, 519 swallowing an exception, 446 symbolic differentiation, 291 syntactic sugar, 324 syntax error, 55 tab stop, 74 table, 376 tags, Tk, 514 terminal, 368 test runner, 562 test-driven development, 494 testing, 492 text files, 320 texttttry statement, 429 throw away variable, 381 throwing an exception, 429 times table, 126 Tk tags, 514 Tk toolkit, 326 tkinter, 326 token, 407 transitivity, 568 transitivity of class inhertiance, 525 translation phase, 55 try block, 429 tuple, 22 tuple assignment, 21 tuple unpacking, 201 Turtle graphics, 179 type, 17 UML, 527 unbound variable, 25 undefined variable, 25 underscore, beginning an identifier, 473 Unified Modeling Language, 527 unit testing, 558 universal quantification, 417 unpacking a tuple, 201 unwinding the stack, 439 value, 399 vertex, 631 while statement, 114 whitespace, 12 wrapper, 539 yield from, 606 yield statement, 281 ©2017 Richard L. Halterman Draft date: January 18, 2018 The Context of Software Development Software Development Tools Learning Programming with Python Writing a Python Program The Python Interactive Shell A Longer Python program Exercises Values and Variables Integer and String Values Variables and Assignment Identifiers Floating-point Numbers Control Codes within Strings User Input Controlling the print Function String Formatting Multi-line Strings Exercises Expressions and Arithmetic Expressions Mixed Type Expressions Operator Precedence and Associativity Formatting Expressions Comments Errors Syntax Errors Run-time Exceptions Logic Errors Arithmetic Examples More Arithmetic Operators Algorithms Exercises Conditional Execution Boolean Expressions Boolean Expressions The Simple if Statement The if/else Statement Compound Boolean Expressions The pass Statement Floating-point Equality Nested Conditionals Multi-way Decision Statements Multi-way Versus Sequential Conditionals Conditional Expressions Errors in Conditional Statements Logic Complexity Exercises Iteration The while Statement Definite Loops vs. Indefinite Loops The for Statement Nested Loops Abnormal Loop Termination The break statement The continue Statement while/else and for/else Infinite Loops Iteration Examples Computing Square Root Drawing a Tree Printing Prime Numbers Insisting on the Proper Input Exercises Using Functions Introduction to Using Functions Functions and Modules The Built-in Functions Standard Mathematical Functions time Functions Random Numbers System-specific Functions The eval and exec Functions Turtle Graphics Other Techniques for Importing Functions and Modules Exercises Writing Functions Function Basics Parameter Passing Documenting Functions Function Examples Better Organized Prime Generator Command Interpreter Restricted Input Better Die Rolling Simulator Tree Drawing Function Floating-point Equality Refactoring to Eliminate Code Duplication Custom Functions vs. Standard Functions Exercises More on Functions Global Variables Default Parameters Introduction to Recursion Making Functions Reusable Functions as Data Separating Concerns with Pluggable Modules Lambda Expressions Generators Local Function Definitions Decorators Partial Application Exercises Objects Using Objects String Objects File Objects Fraction Objects Turtle Graphics Objects Graphics with tkinter Objects Other Standard Python Objects Object Mutability and Aliasing Garbage Collection Exercises Lists Using Lists List Traversal Building Lists List Membership List Assignment and Equivalence List Bounds Slicing List Element Removal Lists and Functions List Methods Prime Generation with a List Command-line Arguments List Comprehensions Multidimensional Lists Summary of List Creation Techniques Lists vs. Generators Exercises Tuples, Dictionaries, and Sets Tuples Arbitrary Argument Lists Dictionaries Using Dictionaries Counting with Dictionaries Grouping with Dictionaries Keyword Arguments Sets Set Quantification with all and any Enumerating the Elements of a Data Structure Exercises Handling Exceptions Motivation Common Standard Exceptions Handling Exceptions Handling Multiple Exceptions The Catch-all Handler Catching Exception Objects Exception Handling Scope Raising Exceptions The try Statement's Optional else Block finally block Using Exceptions Wisely Exercises Custom Types Circle Objects Restricting Access to Members Rational Numbers Bank Account Objects Stopwatch Objects Traffic Light Objects Automated Testing Plotting Data Dynamic Content Class Variables Exercises Class Design: Composition and Inheritance Composition Class Inheritance Composition vs. Inheritance Multiple Inheritance Unit Testing Custom Exceptions Exercises Algorithm Quality Good Algorithms Versus Bad Algorithms Sorting Flexible Sorting Search Linear Search Binary Search Recursion Revisited List Permutations Randomly Permuting a List Reversing a List Memoization Exercises Representing Relationships with Graphs Introduction to Graphs Implementing Graphs in Python Path Finding Breadth-first Search Depth-first Search Exercises Index

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