程序代做CS代考 python cache interpreter CS 61A Structure and Interpretation of Computer Programs

CS 61A Structure and Interpretation of Computer Programs
Fall 2014
INSTRUCTIONS
Midterm 2
• You have 2 hours to complete the exam.
• The exam is closed book, closed notes, closed computer, closed calculator, except one hand-written 8.5” ⇥ 11”
crib sheet of your own creation and the 2 ocial 61A midterm study guides attached to the back of this exam.
• Mark your answers ON THE EXAM ITSELF. If you are not sure of your answer you may wish to provide a brief explanation.
Last name
First name
SID
Login
TA & section time
Name of the person to your left
Name of the person to your right
All the work on this exam is my own. (please sign)
For sta↵ use only
Q.1 Q.2 Q.3 Q.4 Q.5 Total /12 /14 /8 /8 /8 /50

2
Blank Page

1. (12 points) Class Hierarchy
For each row below, write the output displayed by the interactive Python interpreter when the expression is evaluated. Expressions are evaluated in order, and expressions may a↵ect later expressions.
Whenever the interpreter would report an error, write Error. You should include any lines displayed before an error. Reminder: The interactive interpreter displays the repr string of the value of a successfully evaluated expression, unless it is None. Assume that you have started Python 3 and executed the following:
class Worker: greeting = ’Sir’
def __init__(self): self.elf = Worker
def work(self):
return self.greeting + ’, I work’
def __repr__(self):
return Bourgeoisie.greeting
class Bourgeoisie(Worker): greeting = ’Peon’
def work(self):
print(Worker.work(self))
return ’My job is to gather wealth’ class Proletariat(Worker):
greeting = ’Comrade’ def work(self, other):
other.greeting = self.greeting + ’ ’ + other.greeting other.work() # for revolution
return other
= Worker ()
= Bourgeoisie ()
jack
john
jack.greeting = ’Maam’
3
Expression
5*5 1/0
Interactive Output
25
Error
Expression
Interactive Output
john.work()[10:]
Proletariat().work(john)
john.elf.work(john)
Worker().work()
jack
jack.work()

4
2. (14 points) Space
(a) (8 pt) Fill in the environment diagram that results from executing the code below until the entire program is finished, an error occurs, or all frames are filled. You may not need to use all of the spaces or frames.
A complete answer will:
• Add all missing names and parent annotations to all local frames. • Add all missing values created during execution.
• Show the return value for each local frame.
1 2 3 4 5 6 7 8 9
10 11 12 13
func locals(only) [parent=Global]
f1: ___________ [parent=____________]
Return Value
f2: ___________ [parent=____________]
Return Value
f3: ___________ [parent=____________]
Return Value
Global frame
locals
only 3
def locals(only):
def get(out):
nonlocal only
def only(one):
return lambda get: out
out = out + 1
return [out + 2]
out = get(-only)
return only
only = 3
earth = locals(only)
earth(4)(5)
f4: ___________ [parent=____________]
Return Value

(b) (6 pt) Fill in the blanks with the shortest possible expressions that complete the code in a way that results in the environment diagram shown. You can use only brackets, commas, colons, and the names luke, spock, and yoda. You *cannot* use integer literals, such as 0, in your answer! You also cannot call any built-in functions or invoke any methods by name.
2
list list 00
21
5
spock, yoda = 1, 2
!
!
luke = [______________________________________________________________________] !
!
yoda = 0
!
!
yoda = [______________________________________________________________________] !
! yoda.append(__________________________________________________________________)
Global frame spock 1 luke
yoda
list 012
list list 0120
2

6
3. (8 points) This One Goes to Eleven
(a) (4 pt) Fill in the blanks of the implementation of sixty_ones below, a function that takes a Link instance
representing a sequence of integers and returns the number of times that 6 and 1 appear consecutively.
def sixty_ones(s):
“””Return the number of times that 1 directly follows 6 in linked list s.
>>> once = Link(4, Link(6, Link(1, Link(6, Link(0, Link(1))))))
>>> twice = Link(1, Link(6, Link(1, once)))
>>> thrice = Link(6, twice)
>>> apply_to_all(sixty_ones, [Link.empty, once, twice, thrice])
[0, 1, 2, 3]
“””
if _________________________________________________________________:
return 0
elif _______________________________________________________________:
return 1 + _____________________________________________________: else:
return _________________________________________________________
(b) (4 pt) Fill in the blanks of the implementation of no_eleven below, a function that returns a list of all
distinct length-n lists of ones and sixes in which 1 and 1 do not appear consecutively. def no_eleven(n):
“””Return a list of lists of 1’s and 6’s that do not contain 1 after 1.
>>> no_eleven (2)
[[6, 6], [6, 1], [1, 6]]
>>> no_eleven (3)
[[6, 6, 6], [6, 6, 1], [6, 1, 6], [1, 6, 6], [1, 6, 1]] >>> no_eleven (4)[:4] # first half
[[6, 6, 6, 6], [6, 6, 6, 1], [6, 6, 1, 6], [6, 1, 6, 6]] >>> no_eleven (4)[4:] # second half
[[6, 1, 6, 1], [1, 6, 6, 6], [1, 6, 6, 1], [1, 6, 1, 6]] “””
if n == 0:
return _____________________________________________________________ elif n == 1:
return else:
a, b = return
_____________________________________________________________
no_eleven(___________________), no_eleven(___________________) [_________________ for s in a] + [_________________ for s in b]

4. (8 points) Tree Time
(a) (4 pt) A GrootTree g is a binary tree that has an attribute parent. Its parent is the GrootTree in which g is a branch. If a GrootTree instance is not a branch of any other GrootTree instance, then its parent is BinaryTree.empty.
BinaryTree.empty should not have a parent attribute. Assume that every GrootTree instance is a branch of at most one other GrootTree instance and not a branch of any other kind of tree.
Fill in the blanks below so that the parent attribute is set correctly. You may not need to use all of the lines. Indentation is allowed. You should not include any assert statements. Using your solution, the doctests for fib_groot should pass. The BinaryTree class appears on your study guide.
Hint: A picture of fib_groot(3) appears on the next page.
class GrootTree(BinaryTree):
“””A binary tree with a parent.”””
def __init__(self, entry, left=BinaryTree.empty, right=BinaryTree.empty): BinaryTree.__init__(self, entry, left, right)
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
def fib_groot(n):
“””Return a Fibonacci GrootTree.
>>> t = fib_groot (3)
>>> t.entry 2
>>> t.parent.is_empty True
>>> t.left.parent.entry 2
>>> t.right.left.parent.right.parent.entry 1
“””
if n == 0 or n == 1:
return GrootTree(n) else:
left, right = fib_groot(n-2), fib_groot(n-1)
return GrootTree(left.entry + right.entry, left, right)
7

8
(b) (4 pt) Fill in the blanks of the implementation of paths, a function that takes two arguments: a GrootTree instance g and a list s. It returns the number of paths through g whose entries are the elements of s. A path through a GrootTree can extend either to a branch or its parent.
You may assume that the GrootTree class is implemented correctly and that the list s is non-empty.
The two paths that have entries [2, 1, 2, 1, 0] in fib_groot(3) are shown below (left). The one path that has entries [2, 1, 0, 1, 0] is shown below (right).
Two paths for [2, 1, 2, 1, 0] One path for [2, 1, 0, 1, 0]
222
111111
010101
def paths(g, s):
“””The number of paths through g with entries s.
>>> t = fib_groot (3)
>>> paths(t, [1]) 0
>>> paths(t, [2])
1
>>> paths(t, [2, 1, 2, 1, 0]) 2
>>> paths(t, [2, 1, 0, 1, 0]) 1
>>> paths(t, [2, 1, 2, 1, 2, 1]) 8
“””
if g is BinaryTree.empty ________________________________________________: return 0
elif ____________________________________________________________________: return 1
else:
xs = [_______________________________________________________________]
return sum([ ___________________________________________ for x in xs])

5. (8 points) Abstraction and Growth
(a) (6 pt) Your project partner has invented an abstract representation of a sequence called a slinky, which uses a transition function to compute each element from the previous element. A slinky explicitly stores only those elements that cannot be computed by calling transition, using a starts dictionary. Each entry in starts is a pair of an index key and an element value. See the doctests for examples.
Help your partner fix this implementation by crossing out as many lines as possible, but leaving a program that passes the doctests. Do not change the doctests. The program continues onto the following page.
def length(slinky): return slinky [0]
def starts(slinky): return slinky [1]
def transition(slinky): return slinky [2]
def slinky(elements , transition):
“””Return a slinky containing elements.
>>> t = slinky([2, 4, 10, 20, 40], lambda x: 2*x)
>>> starts(t)
{0: 2, 2: 10}
>>> get(t, 3)
20
>>> r = slinky(range(3, 10), lambda x: x+1)
>>> length(r) 7
>>> starts(r)
{0: 3}
>>> get(r, 2) 5
>>> slinky([], abs)
[0, {}, ]
>>> slinky([5, 4, 3], abs)
[3, {0: 5, 1: 4, 2: 3}, ] “””
starts = {}
last = None
for e in elements [1:]:
for index in range(len(elements)):
if not e:
if index == 0:
return [0, {}, transition]
if last is None or e != transition(last):
if e == 0 or e != transition(last):
if index == 0 or elements[index] != transition(elements[index-1]):
starts[index] = elements[index] starts[index] = elements.pop(index) starts[e] = transition(last) starts[e] = last
last = e
return return return return
[len(starts), starts , transition] [len(elements), starts , transition] [len(starts), elements , transition] [len(elements), elements , transition]
9

10
def get(slinky, index):
“””Return the element at index of slinky.””” if index in starts(slinky):
return starts(slinky)[index] start = index
start = 0
f = transition(slinky)
while start not in starts(slinky): while not f(get(start)) == index:
start = start + 1
start = start – 1
value = starts(slinky)[start] value = starts(slinky)[0] value = starts(slinky)[index] while start < index: while value < index: value = f(value) value = value + 1 start = start + 1 start = start + index return value return f(value) (b) (2 pt) Circle the ⇥ expression below that describes the number of operations required to compute slinky(elements, transition), assuming that • n is the initial length of elements, • d is the final length of the starts dictionary created, • the transition function requires constant time, • the pop method of a list requires constant time, • the len function applied to a list requires linear time, • the len function applied to a range requires constant time, • adding or updating an entry in a dictionary requires constant time, • getting an element from a list by its index requires constant time, • creating a list requires time that is proportional to the length of the list. ⇥(1) ⇥(n) ⇥(d) ⇥(n2) ⇥(d2) ⇥(n · d) Scratch Paper 11 12 Scratch Paper CS 61A Midterm 1 Study Guide – Page 1 Import statement Name Value Assignment statement Code (left): Statements and expressions Red arrow points to next line.  Gray arrow points to the line just executed Binding Frames (right): A name is bound to a value In a frame, there is at most one binding per name 208 mul(add(2, mul(4, 6)), add(3, 5)) mul 26 8 add(2, mul(4, 6)) add(3, 5) add 2 24 mul(4, 6) mul 4 6 add 3 5 Pure Functions -2 abs(number): 2 2, 10 pow(x, y): Non-Pure Functions -2 print(...): display “-2” 1024 None Intrinsic name of function called Formal parameter bound to argument Local frame Return value is  not a binding! User-defined function Built-in function Defining: Formal parameter >>> def square( x ):
return mul(x, x)
(return statement) Call expression: square(2+2) operand: 2+2
argument: 4
operator: square function: func square(x)
Calling/Applying: 4 square( x ):
Argument Intrinsic name
return mul(x, x) 16 Return value
Compound statement
Clause

:

Suite
…
:
… 
…
!
2 boolean  contexts
def abs_value(x):
if x > 0: return x
elif x == 0: return 0
else:
return -x
1 statement, 3 clauses, 
3 headers,
3 suites,
2
A name evaluates to
the value bound to
that name in the
earliest frame of
the current 1 environment in which
that name is found.
2
Error
1
•An environment is a sequence of frames
•An environment for a non-nested function (no def within def) consists of one local frame, followed by the global frame
Evaluation rule for call expressions:
1.Evaluate the operator and operand subexpressions. 2.Apply the function that is the value of the operator
subexpression to the arguments that are the values of the operand subexpressions.
Applying user-defined functions:
1.Create a new local frame with the same parent as the function that was applied.
2.Bind the arguments to the function’s formal parameter names in that frame.
3.Execute the body of the function in the environment beginning at that frame.
Execution rule for def statements:
1.Create a new function value with the specified name, formal parameters, and function body.
2.Its parent is the first frame of the current environment. 3.Bind the name of the function to the function value in the
first frame of the current environment.
Execution rule for assignment statements:
1.Evaluate the expression(s) on the right of the equal sign. 2.Simultaneously bind the names on the left to those values,
in the first frame of the current environment.
Execution rule for conditional statements:
Each clause is considered in order.
1.Evaluate the header’s expression.
2.If it is a true value, execute the suite, then skip the remaining clauses in the statement.
Evaluation rule for or expressions:
1.Evaluate the subexpression .
2.If the result is a true value v, then the expression
evaluates to v.
3.Otherwise, the expression evaluates to the value of the
subexpression .
Evaluation rule for and expressions:
1.Evaluate the subexpression .
2.If the result is a false value v, then the expression
evaluates to v.
3.Otherwise, the expression evaluates to the value of the
subexpression .
Evaluation rule for not expressions:
1.Evaluate ; The value is True if the result is a false value, and False otherwise.
Execution rule for while statements:
1. Evaluate the header’s expression.
2. If it is a true value, execute the (whole) suite, then return to step 1.
B AB
A call expression and the body of the function being called are evaluated in different environments
1
A
2
1
def fib(n): hof.py
“””Compute the nth Fibonacci number, for N >= 1.”””
pred, curr = 0, 1 # Zeroth and first Fibonacci numbers
k = 1 # curr is the kth Fibonacci number return total
pred, curr = curr, pred + curr
k=k+1
def identity(k):
return curr return k
while k < n: def cube(k): return pow(k, 3) Function of a single argument (not called term) A formal parameter that will be bound to a function def summation(n, term): """Sum the first n terms of a sequence. >>> summation(5, cube)
225
“””
total, k = 0, 1 while k <= n: The cube function is passed as an argument value total, k = total + term(k), k + 1 return total The function bound to term gets called here 0+13 +23 +33 +43 +55 def pi_term(k): return 8 / (k * 4 − 3) / (k * 4 − 1) # Local function definitions; returning functions Def statement Body “y” is not found “y” is not found Return expression Higher-order function: A function that takes a function as an argument value or returns a function as a return value Nested def statements: Functions defined within other function bodies are bound to names in the local frame def make_adder(n): CS 61A Midterm 1 Study Guide – Page 2 square = lambda x,y: x * y Evaluates to a function.  square = lambda x: x * x VS def square(x): return x * x • Both create a function with the same domain, range, and behavior. • Both functions have as their parent the environment in which they were defined. • Both bind that function to the name square. • Only the def statement gives the function an intrinsic name. When a function is defined: A function No "return" keyword! with formal parameters x and y that returns the value of "x * y" Must be a single expression Can refer to names in the enclosing function A function that returns a function def make_adder(n): """Return a function that takes one argument k and returns k + n. ! The name add_three is bound to a function 1. Create a function value: func () 2. Its parent is the current frame. 
>>> add_three = make_adder(3)
>>> add_three(4) 7 
“””
def adder(k): return k + n
return adder
A local def statement
 
3. Bind to the function value in the current frame 
(which is the first frame of the current environment).
When a function is called:
1. Add a local frame, titled with the of the function being called.
2. Copy the parent of the function to the local frame: [parent=] 3. Bind the to the arguments in the local frame.
4. Execute the body of the function in the environment that starts with
the local frame.
•w
Is fact implemented correctly?
1. Verify the base case.
2. Treat fact as a functional abstraction!
3. Assume that fact(n-1) is correct.
4. Verify that fact(n) is correct,
assuming that fact(n-1) correct.
•Every user-defined function has a parent frame (often global) •The parent of a function is the frame in which it was defined •Every local frame has a parent
frame (often global)
•The parent of a frame is the
parent of the function called 3
2
1
A function’s signature has all the information to create a local frame
def curry2(f):!
“””Returns a function g such that g(x)(y) returns f(x, y).”””! def g(x):!
def h(y):!
return f(x, y)!
return h! return g
Anatomy of a recursive function:
• The def statement header is similar to other functions • Conditional statements check for base cases
• Base cases are evaluated without recursive calls
• Recursive cases are evaluated with recursive calls
def sum_digits(n):!
“””Return the sum of the digits of positive integer n.”””! if n < 10:! Currying: Transforming a multi-argument function into a single-argument, higher-order function. return n! else:! all_but_last, last = n // 10, n % 10! return sum_digits(all_but_last) + last • Each cascade frame is from a different call to cascade. • Until the Return value appears, that call has not completed. • Any statement can appear before or after the recursive call. • Recursive decomposition: finding simpler instances of a problem. • E.g., count_partitions(6, 4) • Explore two possibilities: •Useatleastone4 • Don't use any 4 • Solve two simpler problems: • count_partitions(2, 4) • count_partitions(6, 3) • Tree recursion often involves exploring different choices. from operator import floordiv, mod def count_partitions(n, m):! ifn==0:! return 1! elifn<0:! return 0! elif m == 0:! return 0! else:! with_m = count_partitions(n-m, m) ! without_m = count_partitions(n, m-1)! return with_m + without_m 1  12  123  1234  def 123  12  1 def inverse_cascade(n): grow(n) print(n) shrink(n) f_then_g(f, g, n): ifn:f(n) g(n) n: 0,1,2,3,4,5,6, 7, 8, fib(n): 0,1,1,2,3,5,8,13,21, def fib(n):! if n == 0:! return 0! elif n == 1:! return 1! else:! return fib(n-2) + fib(n-1) def divide_exact(n, d): """Return the quotient and remainder of dividing N by D. Multiple assignment  to two names Multiple return values, separated by commas ! >>> >>> q
q, r = divide_exact(2012, 10)
grow = lambda n: f_then_g(grow, print, n//10) shrink = lambda n: f_then_g(print, shrink, n//10)
201
>>> r
2
“””
return floordiv(n, d), mod(n, d)
Nested def

CS 61A Midterm 2 Study Guide — Page 1
Numeric types in Python:
List comprehensions:
[

for in if ]
Short version: [

for in ]
A combined expression that evaluates to a list using this
evaluation procedure:
1. Add a new frame with the current frame as its parent 2. Create an empty result list that is the value of the
expression
3. For each element in the iterable value of :
A. Bind to that element in the new frame from step 1 B. If evaluates to a true value, then add
List & dictionary mutation:
!
>>> type(2)
!
>>> type(1.5)
!
>>> type(1+1j)
Represents integers exactly
Represents real numbers approximately
>>> a = [10] >>> b = a >>> a == b True
>>> a.append(20) >>> a == b
True
>>> a
[10, 20]
>>> b [10, 20]
>>>a=[10] >>>b=[10] >>>a==b True
>>> b.append(20) >>> a
[10]
>>> b
[10, 20]
>>>a==b False
Functional pair implementation: def pair(x, y):
“””Return a functional pair.”””
the value of

to the result list apply_to_all(map_fn, s):
>>> nums = {‘I’: 1.0, ‘V’: 5, ‘X’: 10} >>> nums[‘X’]
10
>>> nums[‘I’] = 1
>>> nums[‘L’] = 50
>>> nums
{‘X’: 10, ‘L’: 50, ‘V’: 5, ‘I’: 1}
>>> sum(nums.values())
66
>>> dict([(3, 9), (4, 16), (5, 25)])
{3: 9, 4: 16, 5: 25}
>>> nums.get(‘A’, 0)
0
>>> nums.get(‘V’, 0)
5
>>> {x: x*x for x in range(3,6)}
{3: 9, 4: 16, 5: 25}
>>> suits = [‘coin’, ‘string’, ‘myriad’] >>> original_suits = suits
>>> suits.pop()
‘myriad’
>>> suits.remove(‘string’)
>>> suits.append(‘cup’)
>>> suits.extend([‘sword’, ‘club’])
>>> suits[2] = ‘spade’
>>> suits
[‘coin’, ‘cup’, ‘spade’, ‘club’]
>>> suits[0:2] = [‘heart’, ‘diamond’] >>> suits
[‘heart’, ‘diamond’, ‘spade’, ‘club’] >>> original_suits
[‘heart’, ‘diamond’, ‘spade’, ‘club’]
Identity:
is
evaluates to True if both and evaluate to the same object Equality:
==
evaluates to True if both and evaluate to equal values
Identical objects are always equal values
You can copy a list by calling the list constructor or slicing the list from the beginning to the end.
Constants: Constant terms do not affect the order of growth of a process
def get(index): if index == 0:
return x elif index == 1: return y
This function represents a pair
def
!
def
!
def
“””Apply map_fn to each element of s.
>>> apply_to_all(lambda x: x*3, range(5)) [0, 3,6,9,12]
“””
return [map_fn(x) for x in s]
keep_if(filter_fn, s):
“””List elements x of s for which filter_fn(x) is true.
0, 1, 2, 3, 4
λx: x*3
0, 3, 6, 9, 12
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
λx: x>5 6, 7, 8, 9
return get def select(p, i):
Constructor is a higher-order function
“””Return element i of pair p.”””
return p(i)
>>> p = pair(1, 2)
>>> select(p, 0) 1
>>> select(p, 1) 2
Lists:
Selector defers to the object itself
>>>
[6,
“””
keep_if(lambda x: x>5, range(10)) 7,8,9]
return [x for x in s if filter_fn(x)]
reduce(reduce_fn, s, initial):
“””Combine elements of s pairwise using reduce_fn,  
starting with initial.
“””
r= initial
for xins: pow 64 4
>>> digits = [1, 8, 2, 8] >>> len(digits)
16,777,216
4
>>> digits[3] 8
digits
r = reduce_fn(r, x) returnr
pow 4 3
>>> [2, 7] + digits * 2
[2, 7, 1, 8, 2, 8, 1, 8, 2, 8]
>>> pairs = [[10, 20], [30, 40]] >>> pairs[1]
reduce(pow, [1, 2, 3, 4], 2)
pow 2
pow 2 1
2
[30, 40]
>>> pairs[1][0] 30
pairs
Executing a for statement:
for in :
1. Evaluate the header , which must yield an iterable value (a sequence)
2. For each element in that sequence, in order:
A. Bind to that element in the current frame
B. Execute the
Unpacking in a  A sequence of  
for statement: fixed-length sequences
⇥(n) ⇥(500·n) ⇥( 1 ·n) 500
>>> >>>
>>> … … ! >>> 2
pairs=[[1, 2], [2, 2], [3, 2], [4, 4]] same_count = 0
A name for each element in a fixed-length sequence
for x, y in pairs: if x == y:
same_count = same_count + 1 same_count
Logarithms: The base of a logarithm does not affect the order of growth of a process
⇥(log2 n) ⇥(log10 n) ⇥(ln n)
Nesting: When an inner process is repeated for each step in an outer process,multiply the steps in the outer and inner processes to find the total number of steps
def overlap(a, b): count = 0
for item in a:
if item in b:
count += 1 return count
Outer: length of a
Inner: length of b
Type dispatching: Look up a cross-type implementation of an operation based on the types of its arguments
Type coercion: Look up a function for converting one type to another, then apply a type-specific implementation.
(bn )
⇥(n2 ) (n)
(log n) (1)
Exponential growth. Recursive fib takes
(n) steps, where = 1 + 5 1.61828 2
Incrementing the problem scales R(n) by a factor
Quadratic growth. E.g., overlap Incrementing n increases R(n) by the problem size n
Linear growth. E.g., factors or exp Logarithmic growth. E.g., exp_fast Doubling the problem only increments R(n) Constant. The problem size doesn’t matter
The parent frame contains the balance of withdraw
Every call decreases the same balance
>>> withdraw = make_withdraw(100) >>> withdraw(25)
75
>>> withdraw(25)
50
def make_withdraw(balance): def withdraw(amount): nonlocal balance
if amount > balance: return ‘No funds’
balance = balance – amount
return balance return withdraw
-2, -1, 0, 1,
…, -3,
2, 3, 4, …
If a and b are both length n,
then overlap takes ⇥(n2)steps
Lower-order terms: The fastest-growing part of the computation dominates the total
⇥(n2) ⇥(n2 +n) ⇥(n2 +500·n+log2 n+1000) Effect
Create a new binding from name “x” to number 2 in the first frame of the current environment
Re-bind name “x” to object 2 in the first frame of the current environment
Re-bind “x” to 2 in the first non-local frame of the current environment in which “x” is bound
SyntaxError: no binding for nonlocal ‘x’ found SyntaxError: name ‘x’ is parameter and nonlocal
range(-2, 2)
Length: ending value – starting value
Element selection: starting value + index
Status
x = 2
>>> list(range(-2, 2)) [-2, -1, 0, 1]
List constructor
•No nonlocal statement •”x” is not bound locally
•No nonlocal statement •”x” is bound locally •nonlocal x
•”x” is bound in a
non-local frame •nonlocal x
•”x” is not bound in a non-local frame
•nonlocal x
•”x” is bound in a  
non-local frame
•”x” also bound locally
!>>> list(range(4)) [0, 1, 2, 3]
Membership:
Range with a 0 starting value
Slicing:
Strings as sequences:
>>> city = ‘Berkeley’ >>> len(city)
8
>>> city[3]
‘k’
>>> ‘here’ in “Where’s Waldo?”
True
>>> 234 in [1, 2, 3, 4, 5] False
>>> [2, 3, 4] in [1, 2, 3, 4] False
>>> digits = [1, 8, 2, 8] >>> digits[0:2]
>>> 2 in digits
True
>>> 1828 not in digits True
[1, 8]
>>> digits[1:] [8, 2, 8]
Slicing creates a new object
[
[
R(n) = (f(n))
means that there are positive constants k1 and k2 such that k1 ·f(n)R(n)k2 ·f(n) for all n larger than some m

CS 61A Midterm 2 Study Guide — Page 2
Linked list data abstraction:
Python object system:
Idea: All bank accounts have a balance and an account holder;  
the Account class should add those attributes to each of its instances A new instance is >>> a = Account(‘Jim’)
empty = ’empty’
!
def link(first, rest):
return [first, rest] !
def first(s): return s[0]
!
def rest(s): return s[1]
!
def len_link(s): x = 0
while s != empty:
s, x = rest(s), x+1
return x !
def getitem_link(s, i): while i > 0:
s, i = rest(s), i – 1 return first(s)
!
def partitions(n, m):
“””Return a linked list of partitions of n using parts of up to m.
Each partition is a linked list.
“””
if n == 0:
returnlink(empty,empty) elif n < 0: return empty elif m == 0: return empty else: # Do I use at least one m? yes = partitions(n-m, m) no = partitions(n, m-1) add_m = lambda s: link(m, s) yes = apply_to_all_link(add_m, yes) return extend(yes, no) created by calling a >>> a.holder class ‘Jim’
>>> a.balance Whenaclassiscalled: 0
An account instance
1.A new instance of that class is created:
2.The __init__ method of the class is called with the new object as its first
argument (named self), along with any additional arguments provided in the call expression.
class Account:
def __init__(self, account_holder): self.balance = 0
self.holder = account_holder def deposit(self, amount):
self.balance = self.balance + amount
return self.balance bound to an instance of def withdraw(self, amount):
__init__ is called a constructor
self should always be
def extend(s, t):
assert is_link(s) and is_link(t) if s == empty:
return t else:
return link(first(s), extend(rest(s), t))
!
def apply_to_all_link(f, s): if s == empty:
return s else:
return link(f(first(s)), apply_to_all_link(f, rest(s)))
the Account class or a subclass of Account
if amount > self.balance: return ‘Insufficient funds’
self.balance = self.balance – amount return self.balance
>>> type(Account.deposit)
>>> type(a.deposit)
>>> Account.deposit(a, 5) 10
>>> a.deposit(2)
12
Dot expression
str and repr are both polymorphic; they apply to any object repr invokes a zero-argument method __repr__ on its argument
Account class attributes
Instance attributes of jim_account
>>> jim_account = Account(‘Jim’) >>> tom_account = Account(‘Tom’) >>> tom_account.interest
0.02
>>> jim_account.interest 0.02
>>> Account.interest = 0.04 >>> tom_account.interest 0.04
>>> jim_account.interest 0.04
Instance attributes of tom_account
>>> jim_account.interest = 0.08 >>> jim_account.interest
0.08
>>> tom_account.interest
0.04
>>> Account.interest = 0.05 >>> tom_account.interest 0.05
>>> jim_account.interest 0.08
Functioncall:all arguments within parentheses
Method invokation: One object before the dot and other arguments within parentheses
The can
The must be a
Evaluates to the value of the attribute looked up by in the object that is the value of the .
To evaluate a dot expression:
1. Evaluate the to the left of the dot, which yields
the object of the dot expression
2. is matched against the instance attributes of that object;
if an attribute with that name exists, its value is returned 3. If not, is looked up in the class, which yields a class
attribute value
4. That value is returned unless it is a function, in which case a
bound method is returned instead
Assignment statements with a dot expression on their left-hand side affect attributes for the object of that dot expression
• If the object is an instance, then assignment sets an instance attribute • If the object is a class, then assignment sets a class attribute
Call expression
A linked list is a pair
link(1, link(2, link(3, link(4, empty) 
represents the sequence
1 2 3 4
“empty” represents the empty list
.
be any valid Python expression. simple name.
The 0-indexed element of the pair is the first element of the linked list
The 1-indexed element of the pair is the rest of the linked list
The result of calling repr on a value is what Python prints in an interactive session
The result of calling str on a value is   what Python prints using the print function
>>> 12e12 12000000000000.0
>>> print(repr(12e12)) 12000000000000.0
>>> print(today) 2014-10-13
>>> today.__repr__() ‘datetime.date(2014, 10, 13)’
class Link: Some zero empty=() lengthsequence
>>> today.__str__() ‘2014-10-13’
def __init__(self, first, rest=empty): self.first = first
self.rest = rest
def __getitem__(self, i): if i == 0:
return self.first else:
return self.rest[i-1] def __len__(self):
return 1 + len(self.rest)
Yes, this call is recursive
class CheckingAccount(Account):
“””A bank account that charges for withdrawals.””” withdraw_fee = 1
interest = 0.01
def withdraw(self, amount):
return Account.withdraw(self, amount + self.withdraw_fee) or
>>> ch = CheckingAccount(‘Tom’) # Calls Account.__init__ >>> ch.interest # Found in CheckingAccount
0.01
>>> ch.deposit(20) # Found in Account
20
>>> ch.withdraw(5) # Found in CheckingAccount 14
class Tree:
def __init__(self, entry, branches=()):
self.entry = entry
for branch in branches:
assert isinstance(branch, Tree) self.branches = list(branches)
Built-in isinstance function: returns True if branch has a class that is or inherits from Tree
class BinaryTree(Tree):
empty = Tree(None)
empty.is_empty = True
def __init__(self, entry, left=empty, right=empty): 1
To look up a name in a class:
2. Otherwise, look up the name in the base class, if there is one.
Tree.__init__(self, entry, (left, right))
self.is_empty = False @property
def left(self):
return self.branches[0] t = Bin(3, Bin(1),
@property
def right(self): returnself.branches[1]
E
9
E: An empty tree
Bin = BinaryTree
Bin(7, Bin(5),
11
3
7 E 5
E E E
return super().withdraw(
Bin(9, Bin.empty, Bin(11))))E E
amount + self.withdraw_fee)
1. If it names an attribute in the class, return the attribute value.
balance: 0 holder: ‘Jim’
Memoization:
def memo(f): cache = {}
def memoized(n):
if n not in cache:
cache[n] = f(n) return cache[n]
return memoized
interest: 0.02 0.04 0.05 (withdraw, deposit, __init__)
balance: 0 holder: ‘Jim’ interest: 0.08
balance: 0 holder: ‘Tom’
Sequence abstraction special names:
__getitem__ Element selection [] __len__ Built-in len function

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