hw5Fall2010 - the remainder as bad guys such that each...

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CMPS 101 Fall 2010 Homework Assignment 5 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 b. (1 Point) Let vertex w be the source c. (1 Point) Let vertex v be the source 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
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Unformatted text preview: 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.) 3. (1 Point) p.547: 22.3-1 Make a 3-by-3 chart with row and column labels WHITE, GRAY, and BLACK. In each cell ( , ) i j , indicate whether, at any point during a depth-first search of a directed graph, there can be an edge from a vertex of color i to a vertex of color j . For each possible edge, indicate what types it can be. 4. (1 Point) p.547: 22.3-2 Show how depth-first search works on the graph of Figure 22.6 (p.548). Assume that the for loop of lines 5-7 of the DFS procedure considers the vertices in alphabetical order, and assume that each adjacency list is ordered alphabetically. Show the discover and finishing times for each vertex, and show the classification of each edge. 1...
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