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# mid2solns - CMPS 101 Summer 2009 Midterm Exam 2 Solutions...

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CMPS 101 Summer 2009 Midterm Exam 2 Solutions 1. (20 Points) Let G be a directed graph. Determine whether, at any point during a Depth First Search of G , there can exist an edge of the following kind. No justification is required. (See last page for DFS pseudocode.) a. (4 points) A tree edge which joins a gray vertex to a black vertex. Yes b. (4 Points) A tree edge which joins a black vertex to a white vertex. No c. (4 Points) A back edge which joins a black vertex to a gray vertex. Yes d. (4 Points) A forward edge which joins a white vertex to a gray vertex. No e. (4 Points) A cross edge which joins a gray vertex to a white vertex. No 2. (20 Points) Trace Depth First Search (DFS) on the directed graph G below. Process the vertices in numerical order in line 5 of DFS, and line 3 of DFS-VISIT. (See the last page for DFS pseudocode.) 1 4 7 2 5 8 9 3 6 10 a. (5 Points) Fill in the following table of discovery and finish times. Draw the depth-first forest. Vertex

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mid2solns - CMPS 101 Summer 2009 Midterm Exam 2 Solutions...

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