We have already had a recurrence relation of an algorithm, which is T (n) = 4T (n/2) + n log n. We know T (1) ≤c. (a) express it as T (n) = O(f (n)), by using the iteration method. (b) Prove, by using mathematical induction, that the iteration rule you have observed in 4(a) is correct and you have solved the recurrence relation correctly. [Hint: You can write out the general form of T (n) at the iteration step t, and prove 3 that this form is correct for any iteration step t by using mathematical induction. Then by finding out the eventual number of t and substituting it into your general form of T (n), you get the O(·) notation of T (n).]

We have already had a recurrence relation of an algorithm, which is T (n) = 4T (n/2) + n log n. We know T (1) ≤c. (a) express it as T (n) = O(f (n)), by using the iteration method. (b) Prove, by using mathematical induction, that the iteration rule you have observed in 4(a) is correct and you have solved the recurrence relation correctly. [Hint: You can write out the general form of T (n) at the iteration step t, and prove 3 that this form is correct for any iteration step t by using mathematical induction. Then by finding out the eventual number of t and substituting it into your general form of T (n), you get the O(·) notation of T (n).]

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter15: Recursion

Section: Chapter Questions

Problem 18SA

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