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# HW4 - Assignment#4 CS/531 Due Date Mon Nov 7 2011...

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Assignment #4, CS/531 Due Date: Mon. Nov. 7, 2011 UNSUPPORTED SOLUTIONS RECEIVE NO CREDIT. Total points: 51 1 (7 pts). Maximum Contiguous Subsequence Sum Problem revisited. Let A [1 ..n ] be an array of numbers. The elements in A can be either positive or negative. We want to find the indices k, l so that the sum l i = k A [ i ] is maximum among all possible choices of k, l . For example if A = {− 3 , 12 , 6 , 10 , 5 , 2 } , the answer is k = 2 , l = 4, since A [2] + A [3] + A [4] = 12 + ( 6) + 10 = 16 is the maximum sum of all possible choices. This is exactly the problem 3 in HW2. However, this time you must describe an O ( n ) time algorithm for solving this problem. 2. (1 pt) Consider the graph G = ( V, E ) shown in Figure 1. The integers near an edge is its weight. Using Kruskal’s algorithm, compute the minimum spanning tree T 1 of G . List the edges of T 1 in the order they are added into T 1 . 5 3 2 6 4 7 1 8 6 3 4 2 a b c d e f h g Figure 1: Kruskal’s Algorithm. 3. (6 pts) For a given undirected, edge weighted graph G = ( V, E ), there might be more than one MST of G . This can happen if G has two edges e and e ′′ such that w ( e ) = w ( e ′′ ). In this case, when we run Kruskal algorithm on G , the edges e and e ′′ may be processed in different

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HW4 - Assignment#4 CS/531 Due Date Mon Nov 7 2011...

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