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2.3-3 Use mathematical induction to show that when n is an exact power of 2, the solu- tion of the recurrence T(n) = = {²₁7(1/2) 2T (n/2) is T(n) = n lgn. if n = 2, +n if n = 2k, for k > 1

2.3-3 Use mathematical induction to show that when n is an exact power of 2, the solu- tion of the recurrence T(n) = = {²₁7(1/2) 2T (n/2) is T(n) = n lgn. if n = 2, +n if n = 2k, for k > 1

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2.3-3 Use mathematical induction to show that when n is an exact power of 2, the solu- tion of the recurrence T(n): = 2 if n = 2, 2T (n/2) +n if n = 2k, for k > 1 is T(n) = n lgn.
Transcribed Image Text:2.3-3 Use mathematical induction to show that when n is an exact power of 2, the solu- tion of the recurrence T(n): = 2 if n = 2, 2T (n/2) +n if n = 2k, for k > 1 is T(n) = n lgn.
2.3-4 We can express insertion sort as a recursive procedure as follows. In order to sort A[1..n], we recursively sort A[1. . n − 1] and then insert A[n] into the sorted array A[1 . . n − 1]. Write a recurrence for the running time of this recursive version of insertion sort.
Transcribed Image Text:2.3-4 We can express insertion sort as a recursive procedure as follows. In order to sort A[1..n], we recursively sort A[1. . n − 1] and then insert A[n] into the sorted array A[1 . . n − 1]. Write a recurrence for the running time of this recursive version of insertion sort.
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