chap22-solutions

# chap22-solutions - Selected Solutions for Chapter 22...

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Selected Solutions for Chapter 22: Elementary Graph Algorithms Solution to Exercise 22.1-7 BB T .i; j / D X e 2 E b ie b T ej D X e 2 E b ie b je ± If i D j , then b ie b je D 1 (it is 1 ± 1 or . N 1/ ± . N 1/ ) whenever e enters or leaves vertex i , and 0 otherwise. ± If i ¤ j , then b ie b je D N 1 when e D .i; j / or e D .j; i/ , and 0 otherwise. Thus, BB T .i; j / D ( degree of i D in-degree C out-degree if i D j ; N . # of edges connecting i and j / if i ¤ j : Solution to Exercise 22.2-5 The correctness proof for the BFS algorithm shows that u: d D ı.s; u/ , and the algorithm doesn’t assume that the adjacency lists are in any particular order. In Figure 22.3, if t precedes x in Adj Œw± , we can get the breadth-first tree shown in the figure. But if x precedes t in Adj Œw± and u precedes y in Adj Œx± , we can get edge .x; u/ in the breadth-first tree. Solution to Exercise 22.3-12 The following pseudocode modifies the DFS and DFS-VISIT procedures to assign values to the cc attributes of vertices.

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22-2 Selected Solutions for Chapter 22: Elementary Graph Algorithms DFS .G/ for each vertex u 2 G: V u: color D WHITE u:± D NIL time D 0 counter D 0 for each vertex u 2 G: V if u: color == WHITE counter D counter C 1 DFS-VISIT .G; u; counter / DFS-VISIT .G; u;
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chap22-solutions - Selected Solutions for Chapter 22...

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