dm-lec22-recur-p - So far Recurrence Relations Chapter 7...

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Recurrence Relations Chapter 7 p (7.1 Introduction) ctober 30, 2009 October 30, 2009 So far … ets Sets • Logic, Proof • Functions, Sequences, Relations lgorithms Algorithms • (Number theory) • Counting Methods Pigeonhole Principle … Pigeonhole Principle jinah@cs.kaist.ac.kr CS204 Discrete Math (Fall 2009) 2 sequence { C n } 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 19796 C n A special type of function in which the domain consists of a set of consecutive integers. – D = {0,1,2,3,4,5,6,7,8,9,10} –C 0 = 1, C 1 =1, C 2 = 2, … , C 10 = 19796, … , C n = ? n0123 4 5 6 7 8 9 1 0 4 2 32 29 430 862 6796 jinah@cs.kaist.ac.kr CS204 Discrete Math (Fall 2009) 3 C n 1 1 2 5 14 42 132 429 1430 4862 16796 Recurrence Relations • Advanced Counting Technique ecursion • Recursion • Recursive algorithms i d t h l t i f b l f i i t – Provide the solution of a problem of size n in terms of the solutions of one or more instances of the ame problem of smaller size same problem of smaller size – To analyze its complexity btain a recurrence relation hat expresses the number of Obta a ecu e ce e at o t at e p esses t e u be o operations required to solve a problem of size n in terms of the number of operations required to solve the problem for one or more instances of smaller size.
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This note was uploaded on 02/04/2010 for the course COMPUTER S Cs206 taught by Professor Unkown during the Spring '08 term at Korea Advanced Institute of Science and Technology.

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dm-lec22-recur-p - So far Recurrence Relations Chapter 7...

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