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

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Recurrence Relations Chapter 7 (7.1 Introduction) October 30, 2009 So far … • Sets Sets Logic, Proof Functions, Sequences, Relations • Algorithms Algorithms (Number theory) Counting Methods – … Pigeonhole Principle … Pigeonhole Principle [email protected] CS204 Discrete Math (Fall 2009) 2 sequence { C } { C n } 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 19796 C A i l t f f ti i hi h th d i 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 = ? n 0 1 2 3 4 5 6 7 8 9 10 C 1 1 2 5 14 42 132 429 1430 4862 16796 [email protected] CS204 Discrete Math (Fall 2009) 3 n Recurrence Relations Advanced Counting Technique • Recursion Recursive algorithms P id th l ti f bl 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 same problem of smaller size – To analyze its complexity Obtain a recurrence relation that expresses the number of 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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dm-lec22-recur-p - So far Recurrence Relations Chapter...

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