14. Summer 2009 with Solutions

14. Summer 2009 with Solutions - CS570 Analysis of...

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CS570 Analysis of Algorithms Summer 2009 Exam I Name: _____________________ Student ID: _________________ Maximum Received Problem 1 20 Problem 2 10 Problem 3 10 Problem 4 20 Problem 5 15 Problem 6 10 Problem 7 15 Total 100 https://www.coursehero.com/file/13299131/14-Summer-2009-with-Solutionspdf/ This study resource was shared via CourseHero.com
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2 hr exam Close book and notes 1) 20 pts Mark the following statements as TRUE or FALSE . No need to provide any justification. [ TRUE/FALSE ] T An array with following sequence of terms [20, 15, 18, 7, 9, 5, 12, 3, 6, 2] is a max- heap. [ TRUE/FALSE ] T Complexity of the following shortest path algorithms are the same: - Find shortest path between S and T - Find shortest path between S and all other points in the graph [ TRUE/FALSE ] T In an undirected weighted graph with distinct edge weights, both the lightest and the second lightest edge are in the MST. [ TRUE/FALSE ] F Dijkstra’s algorithm works correctly on graphs with negative-cost edges, as long as there are no negative-cost cycles in the graph. [ TRUE/FALSE ] T Not all recurrence relations can be solved by Master theorem. [ TRUE/FALSE ] F Mergesort does not need any additional memory space other than that held by the array being sorted. [ TRUE/FALSE ] T An algorithm with a complexity of O(n 2 ) could run faster than one with complexity of O(n) for a given problem. [ TRUE/FALSE ] F There are at least 2 distinct solutions to the stable matching problem--one that is preferred by men and one that is preferred by women. [ TRUE/FALSE ] F A divide and conquer algorithm has a minimum complexity of O(n log n) since the height of the recursion tree is always O(log n) . [ TRUE/FALSE ] T Stable matching algorithm presented in class is based on the greedy technique. https://www.coursehero.com/file/13299131/14-Summer-2009-with-Solutionspdf/ This study resource was shared via CourseHero.com
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2) 10 pts a) Arrange the following in the increasing order of asymptotic growth. Identify any ties. lg n 10 , 3 n , lg n 2n , 3n 2 , lg n lg n , 10 lg n , n lg n , n lg n If lg is log2 (convention), lg n 10 < lg n 2n < lg n 2n = n lg n < 3n 2 < 10 lg n < n lg n < 3 n If lg is log10 (from ISO specification) lg n 10 < lg n 2n < 10 lg n < lg n 2n = n lg n < 3n 2 < n lg n < 3 n b) Analyze the complexity of the following loops: i- x = 0 for i=1 to n x= x + lg n end for O(n) ii- x=0 for i=1 to n for j=1 to lg n x = x * lg n endfor endfor O(nlogn) iii- x = 0 k = “some constant” for i=1 to max (n, k) x= x + lg n end for O(n) iv- x=0 k = “some constant” for i=1 to min(n, k) for j=1 to lg n x = x * lg n endfor endfor O(logn) https://www.coursehero.com/file/13299131/14-Summer-2009-with-Solutionspdf/ This study resource was shared via CourseHero.com
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