Graphs 1.8 - DFS Algorithm with Discovery and Finish Times...

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Unformatted text preview: DFS Algorithm with Discovery and Finish Times DFS-Visit (u) Precondition: vertex u is undiscovered Postcondition: all vertices reachable from u have been processed colour[u ] RED time time + 1 d[u] time for each v Adj[u ] //explore edge (u,v ) if color[v ] = BLACK DFS-Visit(v ) colour [u ] GRAY time time + 1 f [u ] time CSE 2011 Prof. J. Elder - 36 - Last Updated: 4/1/10 10:16 AM Other Variants of Depth-First Search The DFS Pattern can also be used to Compute a forest of spanning trees (one for each call to DFSvisit) encoded in a predecessor list [u] Label edges in the graph according to their role in the search (see textbook) Tree edges, traversed to an undiscovered vertex Forward edges, traversed to a descendent vertex on the current spanning tree Back edges, traversed to an ancestor vertex on the current spanning tree Cross edges, traversed to a vertex that has already been discovered, but is not an ancestor or a descendent CSE 2011 Prof. J. Elder - 37 - Last Updated: 4/1/10 10:16 AM Example DFS on Directed Graph CSE 2011 Prof. J. Elder - 38 - Last Updated: 4/1/10 10:16 AM DFS Note: Stack is Last-In First-Out (LIFO) s / b / a d / f / e / / g / c Found Not Handled Stack <node,# edges> f d / j / / i / h m / / k CSE 2011 Prof. J. Elder l - 39 - / Last Updated: 4/1/10 10:16 AM Found Not Handled Stack <node,# edges> DFS s 1/ b / a d / e / f / g / c / / j / / i / s,0 h m / / k CSE 2011 Prof. J. Elder l - 40 - / Last Updated: 4/1/10 10:16 AM ...
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Graphs 1.8 - DFS Algorithm with Discovery and Finish Times...

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