2003_spring_exam1Key

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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

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.

Page1 / 3

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online