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Elementary Graph Algorithms

Understand Breadth-First Search (BFS) and Depth-First Search (DFS) with illustrative examples from Comp.122, Fall 2004 course materials.

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Elementary Graph Algorithms

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  1. Elementary Graph Algorithms Comp 122, Fall 2004

  2. white: undiscovered gray: discovered black: finished BFS(G,s) 1. for each vertex u in V[G] – {s} 2 docolor[u]  white 3 d[u]  4 [u]  null 5 color[s]  gray 6 d[s]  0 7 [s]  null 8 Q   9 enqueue(Q,s) 10 while Q   11 do u  dequeue(Q) 12 for each v in Adj[u] 13 doif color[v] = white 14 then color[v]  gray 15 d[v]  d[u] + 1 16 [v]  u 17 enqueue(Q,v) 18 color[u]  black Q: a queue of discovered vertices color[v]: color of v d[v]: distance from s to v [u]: predecessor of v Example: animation. Comp 122, Fall 2004

  3. Example (BFS) r s t u    0     v w y x Q: s 0 Comp 122, Fall 2004

  4. Example (BFS) r s t u   0 1    1 v w y x Q: w r 1 1 Comp 122, Fall 2004

  5. Example (BFS) r s t u 2  0 1  2  1 v w y x Q: r t x 1 2 2 Comp 122, Fall 2004

  6. Example (BFS) r s t u 2  0 1 2  2 1 v w y x Q: t x v 2 2 2 Comp 122, Fall 2004

  7. Example (BFS) r s t u 2 0 3 1 2  2 1 v w y x Q: x v u 2 2 3 Comp 122, Fall 2004

  8. Example (BFS) r s t u 2 0 3 1 2 3 2 1 v w y x Q: v u y 2 3 3 Comp 122, Fall 2004

  9. Example (BFS) r s t u 2 0 3 1 2 3 2 1 v w y x Q: u y 3 3 Comp 122, Fall 2004

  10. Example (BFS) r s t u 2 0 3 1 2 3 2 1 v w y x Q: y 3 Comp 122, Fall 2004

  11. Example (BFS) r s t u 2 0 3 1 2 3 2 1 v w y x Q: Comp 122, Fall 2004

  12. Example (BFS) r s t u 2 0 3 1 2 3 2 1 v w y x BFS Tree Comp 122, Fall 2004

  13. DFS DFS-Visit(u) color[u]  GRAY time  time + 1 d[u] time for each v  Adj[u] doifcolor[v] = WHITE then[v] u DFS-Visit(v) color[u]  BLACK time  time + 1 f[u]  time DFS(G) 1. for each vertex u  V[G] 2. docolor[u]  white 3. [u]  NULL 4. time 0 5. for each vertex u  V[G] 6. doifcolor[u] = white 7. then DFS-Visit(u) Uses a global timestamp time. Comp 122, Fall 2004

  14. Example (DFS) u v w 1/ x z y Comp 122, Fall 2004

  15. Example (DFS) u v w 2/ 1/ x z y Comp 122, Fall 2004

  16. Example (DFS) u v w 2/ 1/ 3/ x z y Comp 122, Fall 2004

  17. Example (DFS) u v w 2/ 1/ 3/ 4/ x z y Comp 122, Fall 2004

  18. Example (DFS) u v w 2/ 1/ B 3/ 4/ x z y Comp 122, Fall 2004

  19. Example (DFS) u v w 2/ 1/ B 3/ 4/5 x z y Comp 122, Fall 2004

  20. Example (DFS) u v w 2/ 1/ B 3/6 4/5 x z y Comp 122, Fall 2004

  21. Example (DFS) u v w 2/7 1/ B 3/6 4/5 x z y Comp 122, Fall 2004

  22. Example (DFS) u v w 2/7 1/ B F 3/6 4/5 x z y Comp 122, Fall 2004

  23. Example (DFS) u v w 2/7 1/8 B F 3/6 4/5 x z y Comp 122, Fall 2004

  24. Example (DFS) u v w 2/7 9/ 1/8 B F 3/6 4/5 x z y Comp 122, Fall 2004

  25. Example (DFS) u v w 2/7 9/ 1/8 B C F 3/6 4/5 x z y Comp 122, Fall 2004

  26. Example (DFS) u v w 2/7 9/ 1/8 B C F 3/6 4/5 10/ x z y Comp 122, Fall 2004

  27. Example (DFS) u v w 2/7 9/ 1/8 B C F 3/6 4/5 10/ B x z y Comp 122, Fall 2004

  28. Example (DFS) u v w 2/7 9/ 1/8 B C F 3/6 4/5 10/11 B x z y Comp 122, Fall 2004

  29. Example (DFS) u v w 2/7 9/12 1/8 B C F 3/6 4/5 10/11 B x z y Comp 122, Fall 2004

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