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Unformatted text preview: Solution to Homework 8 Com S 311 Apr 1, 2003 1 Exercise 22.11 (P. 538, 4 points, grader: Yu Cao) The running result of DFS(3) is displayed as following: Table 1: The d and V ertex d 1 N ull N ull 2 3 4 3 N ull 4 2 5 5 1 3 6 1 3 2 Exercise 22.26 (P. 539, 6 points, grader: Yu Cao) 1. we can apply BFS to solve this problem. In order to apply the BFS algorithms, we need to configure a graph. Suppose the wrestlers as the vertices of the graph. Suppose the rivalry between two wrestlers as the edge of the graph. 2. Once we generate a graph to represent the relation among wrestlers, we convert this problem into a bipartite graph problem. 3. The algorithms is listed as following: Start from one of the vertex, run BFS from this vertex. 1&#13; 4&#13; 5&#13; 2&#13; 3&#13; 6&#13; Figure 1: BFS tree 1 During the running procedure of BFS, check the node in each level. If there are both Good guy and Bad guy in the same level. We can say its impossible to designate some of the wrestlers as good guys and the remainder as bad guys such that each rivalry is between a good guy and a bad guy. Otherwise its possible. 3 Prolbem 22.27 (8 points, grader: Fangcheng Tang) Solution: Run BFS on any node s in the graph, remembering the node u discovered last. Run BFS from u remembering the node v discovered last . ( u, v ) is the diameter of the tree. Correctness: let a and b be any two nodes such that ( a, b ) is the diameter of the tree.There is unique path from a to b . Let t be the first node on that path discovered by BFS....
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