2003_spring_exam1Key - Q1. You are given recursive...

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Q1. You are given recursive CombineSort procedure that sorts input sequence A={ a 1, a 2… a n}. Find its recurrence relation T(n) and use it to calculate worst case complexity of this algorithm. (Note: Combine procedure has cn worst time complexity). Start = 1; Finish = n; BEGIN CombineSor t(A, Start, Finish) IF (Start < Finish) THEN Middle=(Start + Finish)/2; CombineSor t(A, Start, Middle); CombineSor t(A, Middle+1, Finish); Combin e(A, Start, Middle, Finish); END IF END BEGIN Answer: Unless you already got it, it is nothing but MergeSort. Recurrence relation is T(n) = 2T(n/2) + cn; n > 1 T(n) = a; n = 1 This relation can be solved by substitutions T(n) = 2(2T(n/4)+cn/2)+cn = 4(2T(n/8)+cn/4)+2cn = … 2 k T(1)+kcn = an+cn log n Hence T(n) = O(n log n) Q2. Water flows into Hoover dam at a variable rate throughout every month (i.e., 30 days: the tidal cycle) and water is released at a regular interval (once every month). You have the detailed water level data for a period of 30 consecutive days (not necessarily a calendar month, and not necessarily starting or ending with the time of releasing the water). Give an efficient algorithm to find out exactly when the water was released. (Assume
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This note was uploaded on 11/30/2011 for the course COT 5405 taught by Professor Ungor during the Fall '08 term at University of Florida.

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2003_spring_exam1Key - Q1. You are given recursive...

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