EECS 3101 York University Instructor: Andy Mirzaian MACHINE MODEL AND TIMING ANALYSIS NOTATION Introduction This course has two major goals. (1) To teach certain fundamental combinatorial (as opposed to numerical) algorithms. (2) To teach general techniques for the design and analysis of algorithms. The first question to address is “What is analysis of algorithms?”. We […]
UG OS (202) Practice Midterm Exam Page 1 Name________________ This practice midterm is DEFINITELY MUCH TOO LONG. The real midterm will be shorter. Homework problems are also possible. PLEASE WRITE YOUR NAME AND ANSWERS ON ALL 8 QUESTION SHEETS. You may use the backs of the question sheets to continue your answers. You may also
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EECS 3101 York University Instructor: Andy Mirzaian RECURRENCE RELATIONS In this lecture note we study some basic recurrence relations. These equations arise in the analysis of algorithms, among other things. We consider the following: 1. Divide-&-Conquer Recurrences and the Master Theorem. 2. Full History Recurrences. 3. The Guess-then-Verify Technique. 4. The Variable Substitution Method. There
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Notes on Better Master Theorems for DivideandConquer Recurrences Intro duction Divideandconquer recurrences are ubiquitous known for solving recurrences such as in the analysis of algorithms Many metho ds are Tom Mathematics Laboratory for Leighton Department and Computer Science Massachusetts Institute of Technology Cambridge Massachusetts Octob er Abstract Techniques Computer Science known
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EECS 3101 Prof. Andy Mirzaian STUDY MATERIAL: • [CLRS] Appendix A, chapter 4 • Lecture Note 3 2 Summations: 𝑛 𝑓𝑖 =𝑓1+𝑓2+⋯+𝑓𝑛=Θ(?) 𝑖=1 𝑛 2𝑖=Θ 𝑛2𝑛 𝑖=1 Recurrence Relations: 𝑇𝑛−1+𝑓(𝑛) ∀𝑛≥1 𝑛 𝑇𝑛=0 ∀𝑛 -1 f(n) = n: f(n) = n2: f(n) = nd: 1 + 2 + ··· + n 12 + 22 +
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2/26/2018 Practice Midterm Answers Practice Midterm Answers My answers are somewhat short, I would expect yours to be a little more detailed, but NOT very much more detailed. 1A. Draw the process state diagram from the notes. This diagram contains nodes (i.e. circles) labeled with the possible states for a process. It also contains arcs
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EECS 3101 Prof. Andy Mirzaian Welcome to the beautiful and wonderful world of algorithms! 2 STUDY MATERIAL: • [CLRS] chapter 1 • Lecture Note 1 NOTE: • Material covered in lecture slides are as self contained as possible and may not necessarily follow the text book format. 3 Origin of the word Algorithm =
EECS 3101 York University Instructor: Andy Mirzaian LOWER BOUND FOR COMPARISON-BASED SORTING In this handout we consider the question: How efficiently can we sort? Such questions (deter- mining how to best carry out a task) are among the most difficult and intellectually challenging problems of theoretical computer science. It is generally much more difficult to
EECS 3101 Prof. Andy Mirzaian STUDY MATERIAL: • [CLRS] chapters 6, 7, 8, 9 • Lecture Notes 5, 6 2 TOPICS The Sorting Problem Some general facts QuickSort HeapSort, Heaps, Priority Queues Sorting Lower Bound Special Purpose Sorting Algorithms The Selection Problem Lower Bound Techniques Prune-&-Search
EECS 3101 Prof. Andy Mirzaian STUDY MATERIAL: • [CLRS] chapters 2, 4.1-2, 12.1, 31.1-2, 33.4 • Lecture Note 4 2 TOPICS The algorithm design process: Central Tools: Iteration & Recursion Partial correctness: Assertions Termination: Measure of Progress Iterative Algorithms: Loop Invariant Incremental Method Recursive Algorithms: Recursive Pre- & Post- Condition & strong
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