Lecture02 - Recurrence Relations Overview Recurrence...

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1 Recurrence Relations • Overview – Recurrence Relations • Techniques for solving them – Methods for generating a guess – Induction proofs – Master Theorem Where do recurrence relations come from? • Analysis of a divide and conquer algorithm – Towers of Hanoi, Merge Sort, Binary Search • Analysis of a combinatorial object This is the key analysis step I want you to master • Use small cases to check correctness of your recurrence relation The Towers of Hanoi
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2 What if we knew we could solve part of the problem? Assume we can move k (in this case, 4) different rings Can we do one better? Solved for one more!
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3 Recurrence Relations • Overview – Connection to recursive algorithms • Techniques for solving them – Methods for generating a guess – Induction proofs – Master Theorem Solving Recurrence Relations • No general, automatic procedure for solving recurrence relations is known. • There are methods for solving specific forms of recurrences • Links to some good sites with more info: – Wikipedia: http://en.wikipedia.org/wiki/Recurrence_relation – SUNY-SB web site: http://www.cs.sunysb.edu/~algorith/lectures- good/node3.html Some Solution Techniques Guess a solution and prove by induction.
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This note was uploaded on 07/25/2008 for the course CSE 830 taught by Professor Ofria during the Spring '08 term at Michigan State University.

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Lecture02 - Recurrence Relations Overview Recurrence...

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