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# hw5solns - CMPS 101 Summer 2009 Homework Assignment 5...

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1 CMPS 101 Summer 2009 Homework Assignment 5 Solutions 1. (3 Points) p. 538: 22.2-2 Show the d and π values that result from running breadth-first search on the undirected graph below using the following vertices as source. For each source, show the order in which vertices are added to the Queue, and show the state of the BFS tree after execution completes. Assume adjacency lists are processed in alphabetical order. r s t u v w x y a. (1 Point) Let vertex u be the source Solution: vertex adjacency list d π r s v 4 s s r w 3 w t u w x 1 u u t x y 0 nil v r 5 r w s t x 2 t x t u w y 1 u y u x 1 u Queue: u t x y w s r v BFS Tree u t x y w s r v b. (1 Point) Let vertex w be the source Solution: vertex adjacency list d π r s v 2 s s r w 1 w t u w x 1 w u t x y 2 t v r 3 r w s t x 0 nil x t u w y 1 w y u x 2 x Queue: w s t x r u y v BFS Tree w s t x r u y v

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2 c. (1 Point) Let vertex v be the source Solution: vertex adjacency list d π r s v 1 v s r w 2 r t u w x 4 w u t x y 5 t v r 0 nil w s t x 3 s x t u w y 4 w y u x 5 x Queue: v r s w t x u y BFS Tree v r s w t x u y 2. (1 Point) p. 538: 22.2-6 There are two types of professional wrestlers: “good guys” and “bad guys.” Between any pair of professional wrestlers, there may or may not be a rivalry. Suppose we have n professional wrestlers and we have a list of r pairs of wrestlers for which there are rivalries. Give an ( ) O n r + -time algorithm that determines whether it is possible 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. If it is possible to perform such a designation, your algorithm should produce it. (Hint: figure out how to use BFS to solve this problem.) Solution: Let the n wrestlers be the vertices of an undirected graph in which two vertices are joined by an edge if and only if there is a rivalry between the corresponding wrestlers. The question asks whether it is possible to partition the vertex set into two subsets Good and Bad such that all edges join Good vertices to Bad vertices. Such a graph is called bipartite . More precisely, an undirected graph ) , ( E V G = is called bipartite if its vertex set V can be partitioned into two subsets
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hw5solns - CMPS 101 Summer 2009 Homework Assignment 5...

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