Tables 1.2 - BFS Algorithm Pattern BFS(G,s) Precondition: G...

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Unformatted text preview: BFS Algorithm Pattern BFS(G,s) Precondition: G is a graph, s is a vertex in G Postcondition: all vertices in G reachable from s have been visited for each vertex u V [G] color[u] BLACK //initialize vertex colour[s] RED Q.enqueue(s ) while Q u Q.dequeue() for each v Adj[u ] //explore edge (u,v ) if color[v ] = BLACK colour[v] RED Q.enqueue(v ) colour [u ] GRAY CSE 2011 Prof. J. Elder - 121 - Last Updated: 4/1/10 10:16 AM BFS Example A undiscovered A discovered (on Queue) A finished unexplored edge A L1 B discovery edge C E D F cross edge L0 L1 L0 A B C E CSE 2011 Prof. J. Elder L1 D F A B C E - 122 - D F Last Updated: 4/1/10 10:16 AM BFS Example (cont.) L0 L1 L0 A B C E L0 L1 D F L0 C E CSE 2011 Prof. J. Elder B L2 A B L2 L1 L1 D - 123 - C E D F A B L2 F A C E D F Last Updated: 4/1/10 10:16 AM BFS Example (cont.) L0 L1 L0 L1 A B L2 C E L1 D B L2 F A C E D F A B L2 L0 C E CSE 2011 Prof. J. Elder D F - 124 - Last Updated: 4/1/10 10:16 AM Properties Notation Gs: connected component of s A Property 1 BFS(G, s) visits all the vertices and edges of Gs B C D Property 2 E The discovery edges labeled by BFS(G, s) form a spanning tree Ts of Gs L0 Property 3 For each vertex v in Li The path of Ts from s to v has i edges Every path from s to v in Gs has at least i edges CSE 2011 Prof. J. Elder - 125 - L1 A B L2 F C E D F Last Updated: 4/1/10 10:16 AM ...
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Tables 1.2 - BFS Algorithm Pattern BFS(G,s) Precondition: G...

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