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Unformatted text preview: Design and Analysis of Algorithms CSE 101 Final Examination August 3, 2007 Time: 2 hours and 45 minutes Maximum Points: 40 NAME: Student ID: Answer the following questions: 1. 8 points Describe an efficient algorithm to find a directed path that has the maximum number of edges among all directed paths in a given directed acyclic graph G . Present the main ideas, write the pseudo- code. Determine the time complexity of your algorithm. 2. 10 points We are given a sequence of integers, say (5 , 3 , 6 , 3 , 7 , 3 , 11 , 4 , 9 , 5). We are asked to find its longest bitonic subsequence . A sequence b 1 , . . . , b k is bitonic if there is an 1 i k such that the sequence is strictly increasing up to b i and then it is strictly decreasing, that is, b 1 < b 2 < b i and b i > b i +1 > b k . If i = 1, the sequence degen- erates into a strictly decreasing sequence. If i = k , the sequence is a strictly increasing one. In other words, strictly increasing or decreasing sequences are also bitonic.sequences are also bitonic....
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This note was uploaded on 03/16/2010 for the course CSE 101 taught by Professor Staff during the Winter '08 term at UCSD.
- Winter '08