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Depth-First Search Algorithm

b. d. a. c. d. d. a. b. b. e. a. ·. ·. ·. ·. ·. ·. ·. ·. ·. ·. ·. a. a. e. d. b. c. Depth-First Search Algorithm. dfs ( a ) a .marked  1 print a for each ( a , u)  E if (u.mark != 1) dfs (u). dfs(“a”). a. ·. b. ·. c. ·. d. ·.

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Depth-First Search Algorithm

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  1. b d a c d d a b b e a · · · · · · · · · · · a a e d b c Depth-First Search Algorithm dfs ( a ) a.marked  1 print a for each (a, u)  E if (u.mark != 1) dfs (u) dfs(“a”) .... a · b · c · d · e · EE 5301 - VLSI Design Automation I

  2. e a d a c d d b a b b · · · · · · · · · · · a e d b c Depth-First Search Algorithm dfs ( a ) a.marked  1 print a for each (a, u)  E if (b.mark != 1) dfs (b) dfs(“a”) .... dfs(“b”) .... u=b a a · b · c · d · e · EE 5301 - VLSI Design Automation I

  3. d a c d d b a e b a b · · · · · · · · · · · a e d b c Depth-First Search Algorithm dfs ( b ) b.marked  1 print b for each (b, u)  E if (u.mark != 1) dfs (u) dfs(“a”) .... dfs(“b”) .... a b a · b · c · d · e · EE 5301 - VLSI Design Automation I

  4. e a d a c d d b a b b · · · · · · · · · · · a e d b c Depth-First Search Algorithm dfs ( b ) b.marked  1 print b for each (b, u)  E if (a.mark != 1) dfs (a) dfs(“a”) .... dfs(“b”) .... u=a a b a · b · c · d · e · EE 5301 - VLSI Design Automation I

  5. c d a e b b d a d a b · · · · · · · · · · · a e d b c Depth-First Search Algorithm dfs ( b ) b.marked  1 print b for each (b, u)  E if (d.mark != 1) dfs (d) dfs(“a”) .... dfs(“b”) .... dfs(“d”) .... u=d a b a · b · c · d · e · EE 5301 - VLSI Design Automation I

  6. e a d a c d d b a b b · · · · · · · · · · · a e d b c Depth-First Search Algorithm dfs ( d ) d.marked  1 print d for each (d, u)  E if (u.mark != 1) dfs (u) dfs(“a”) .... dfs(“b”) .... dfs(“d”) .... a b d a · b · c · d · e · EE 5301 - VLSI Design Automation I

  7. c a a d b b d d b a e · · · · · · · · · · · a e d b c Depth-First Search Algorithm dfs ( d ) d.marked  1 print d for each (d, u)  E if (e.mark != 1) dfs (e) dfs(“a”) .... dfs(“b”) .... dfs(“d”) .... u=e dfs(“e”) .... a b d a · b · c · d · e · EE 5301 - VLSI Design Automation I

  8. c d a e b b d a d a b · · · · · · · · · · · a e d b c Depth-First Search Algorithm dfs ( e ) e.marked  1 print e for each (e, u)  E if (u.mark != 1) dfs (u) dfs(“a”) .... dfs(“b”) .... dfs(“d”) .... dfs(“e”) .... a b d e a · b · c · d · e · EE 5301 - VLSI Design Automation I

  9. c a a d b b d d b a e · · · · · · · · · · · a e d b c Depth-First Search Algorithm dfs ( e ) e.marked  1 print e for each (e, u)  E if (d.mark != 1) dfs (u) dfs(“a”) .... dfs(“b”) .... dfs(“d”) .... u=d dfs(“e”) .... a b d e a · b · c · d · e · EE 5301 - VLSI Design Automation I

  10. c d a e b b d a d a b · · · · · · · · · · · a e d b c Depth-First Search Algorithm dfs ( e ) e.marked  1 print e for each (e, u)  E if (u.mark != 1) dfs (u) dfs(“a”) .... dfs(“b”) .... dfs(“d”) .... dfs(“e”) .... a b d e a · b · c · d · e · EE 5301 - VLSI Design Automation I

  11. c d a e b b d a d a b · · · · · · · · · · · a e d b c Depth-First Search Algorithm dfs ( d ) d.marked  1 print d for each (d, u)  E if (b.mark != 1) dfs (b) dfs(“a”) .... dfs(“b”) .... dfs(“d”) .... u=b,a a b d e a · b · c · d · e · EE 5301 - VLSI Design Automation I

  12. e a d a c d d b a b b · · · · · · · · · · · a e d b c Depth-First Search Algorithm dfs ( d ) d.marked  1 print d for each (d, u)  E if (u.mark != 1) dfs (u) dfs(“a”) .... dfs(“b”) .... dfs(“d”) .... a b d e a · b · c · d · e · EE 5301 - VLSI Design Automation I

  13. d a c d d b a e b a b · · · · · · · · · · · a e d b c Depth-First Search Algorithm dfs ( b ) b.marked  1 print b for each (b, u)  E if (u.mark != 1) dfs (u) dfs(“a”) .... dfs(“b”) .... a b d e a · b · c · d · e · EE 5301 - VLSI Design Automation I

  14. d a c d d b a e b a b · · · · · · · · · · · a e d b c Depth-First Search Algorithm dfs ( a ) a.marked  1 print a for each (a, u)  E if (d.mark != 1) dfs (d) dfs(“a”) .... u=d a b d e a · b · c · d · e · EE 5301 - VLSI Design Automation I

  15. b d a c e d d b a a b · · · · · · · · · · · a e d b c Depth-First Search Algorithm dfs ( a ) a.marked  1 print a for each (a, u)  E if (c.mark != 1) dfs (c) dfs(“a”) .... dfs(“c”) .... u=c a b d e a · b · c · d · e · EE 5301 - VLSI Design Automation I

  16. d a c d d b a e b a b · · · · · · · · · · · a e d b c Depth-First Search Algorithm dfs ( c ) c.marked  1 print c for each (c, u)  E if (u.mark != 1) dfs (u) dfs(“a”) .... dfs(“c”) .... a b d e c a · b · c · d · e · EE 5301 - VLSI Design Automation I

  17. e a d a c d d b a b b · · · · · · · · · · · a e d b c Depth-First Search Algorithm dfs ( c ) c.marked  1 print c for each (c, u)  E if (a.mark != 1) dfs (a) dfs(“a”) .... dfs(“c”) .... u=a a b d e c a · b · c · d · e · EE 5301 - VLSI Design Automation I

  18. d a c d d b a e b a b · · · · · · · · · · · a e d b c Depth-First Search Algorithm dfs ( c ) c.marked  1 print c for each (c, u)  E if (u.mark != 1) dfs (u) dfs(“a”) .... dfs(“c”) .... a b d e c a · b · c · d · e · EE 5301 - VLSI Design Automation I

  19. d d a c b e b b a a d · · · · · · · · · · · a e d b c Depth-First Search Algorithm dfs ( a ) a.marked  1 print a for each (a, u)  E if (u.mark != 1) dfs (u) dfs(“a”) .... a b d e c a · b · c · d · e · EE 5301 - VLSI Design Automation I

  20. Dijkstra’s Algorithm - an example u0 0 8 v5 v1 10   16 13 6 9   v6 v7 7 11 17   v2 v4 14 5  Edges examined v3 EE 5301 - VLSI Design Automation I

  21. Dijkstra’s Algorithm - an example u0 0 8 v5 v1 10  8 16 13 6 9   v6 v7 7 11 17 13 16 v2 v4 14 5   updated, min picked v3 EE 5301 - VLSI Design Automation I

  22. Dijkstra’s Algorithm - an example u0 0 8 v5 v1 10  8 16 13 6 9   v6 v7 7 11 17 13 16 v2 v4 14 5  S Augmented v3 EE 5301 - VLSI Design Automation I

  23. Dijkstra’s Algorithm - an example u0 0 8 v5 v1 10  8 16 13 6 9   v6 v7 7 11 17 13 16 v2 v4 14 5  Edges examined v3 EE 5301 - VLSI Design Automation I

  24. Dijkstra’s Algorithm - an example u0 0 8 v5 v1 10 18 8 16 13 6 9   v6 v7 7 11 17 13 15 v2 v4 14 5 25  updated, min picked v3 EE 5301 - VLSI Design Automation I

  25. Dijkstra’s Algorithm - an example u0 0 8 v5 v1 10 18 8 16 13 6 9   v6 v7 7 11 17 13 15 v2 v4 14 5 25 S Augmented v3 EE 5301 - VLSI Design Automation I

  26. Dijkstra’s Algorithm - an example u0 0 8 v5 v1 10 18 8 16 13 6 9   v6 v7 7 11 17 13 15 v2 v4 14 5 25 Edges examined v3 EE 5301 - VLSI Design Automation I

  27. Dijkstra’s Algorithm - an example u0 0 8 v5 v1 10 18 8 16 13 6 9   v6 v7 7 11 17 13 15 v2 v4 14 5 25  updated, min picked v3 EE 5301 - VLSI Design Automation I

  28. Dijkstra’s Algorithm - an example u0 0 8 v5 v1 10 18 8 16 13 6 9   v6 v7 7 11 17 13 15 v2 v4 14 5 25 S augmented v3 EE 5301 - VLSI Design Automation I

  29. Dijkstra’s Algorithm - an example u0 0 8 v5 v1 10 18 8 16 13 6 9   v6 v7 7 11 17 13 15 v2 v4 14 5 25 Edges examined v3 EE 5301 - VLSI Design Automation I

  30. Dijkstra’s Algorithm - an example u0 0 8 v5 v1 10 18 8 16 13 6 9   v6 v7 7 11 17 13 15 v2 v4 14 5 20  updated, min picked v3 EE 5301 - VLSI Design Automation I

  31. Dijkstra’s Algorithm - an example u0 0 8 v5 v1 10 18 8 16 13 6 9   v6 v7 7 11 17 13 15 v2 v4 14 5 20 S augmented v3 EE 5301 - VLSI Design Automation I

  32. Dijkstra’s Algorithm - an example u0 0 8 v5 v1 10 18 8 16 13 6 9   v6 v7 7 11 17 13 15 v2 v4 14 5 20 Edges examined v3 EE 5301 - VLSI Design Automation I

  33. Dijkstra’s Algorithm - an example u0 0 8 v5 v1 10 18 8 16 13 6 9   v6 v7 7 11 17 13 15 v2 v4 14 5 20  updated, min picked v3 EE 5301 - VLSI Design Automation I

  34. Dijkstra’s Algorithm - an example u0 0 8 v5 v1 10 18 8 16 13 6 9   v6 v7 7 11 17 13 15 v2 v4 14 5 20 S augmented v3 EE 5301 - VLSI Design Automation I

  35. Prim’s Algorithm Example 2 v2 1 5 2 v3 4 2 v5 v1 3 1 3 v4 S = {v1} Node v1 v2 v3 v4 v5  - 2 4 3   - v1 v1v1- EE 5301 - VLSI Design Automation I

  36. Prim’s Algorithm Example 2 v2 1 5 2 v3 4 2 v5 v1 3 1 3 v4 S = {v1} Node v1v2 v3 v4 v5  - 2 4 3   - v1 v1v1 - EE 5301 - VLSI Design Automation I

  37. Prim’s Algorithm Example 2 v2 1 5 2 v3 4 2 v5 v1 3 1 3 v4 S = {v1, v2} Node v1 v2 v3 v4 v5  - 2 4 3   - v1 v1v1 - EE 5301 - VLSI Design Automation I

  38. Prim’s Algorithm Example 2 v2 1 5 2 v3 4 2 v5 v1 3 1 3 v4 S = {v1, v2} Node v1 v2 v3 v4 v5  - 2 1 25  - v1v2v2 v2 EE 5301 - VLSI Design Automation I

  39. Prim’s Algorithm Example 2 v2 1 5 2 v3 4 2 v5 v1 3 1 3 v4 S = {v1, v2} Node v1 v2v3 v4 v5  - 21 25  - v1 v2v2 v2 EE 5301 - VLSI Design Automation I

  40. Prim’s Algorithm Example 2 v2 1 5 2 v3 4 2 v5 v1 3 1 3 v4 S = {v1, v2, v3} Node v1 v2v3 v4 v5  - 21 2 5  - v1 v2v2 v2 EE 5301 - VLSI Design Automation I

  41. Prim’s Algorithm Example 2 v2 1 5 2 v3 4 2 v5 v1 3 1 3 v4 S = {v1, v2, v3} Node v1 v2v3 v4 v5  - 21 12  - v1 v2v3v3 EE 5301 - VLSI Design Automation I

  42. Prim’s Algorithm Example 2 v2 1 5 2 v3 4 2 v5 v1 3 1 3 v4 S = {v1, v2, v3} Node v1 v2v3v4 v5  - 2112  - v1 v2v3 v3 EE 5301 - VLSI Design Automation I

  43. Prim’s Algorithm Example 2 v2 1 5 2 v3 4 2 v5 v1 3 1 3 v4 S = {v1, v2, v3, v4} Node v1 v2v3v4 v5  - 211 2  - v1 v2v3 v3 EE 5301 - VLSI Design Automation I

  44. Prim’s Algorithm Example 2 v2 1 5 2 v3 4 2 v5 v1 3 1 3 v4 S = {v1, v2, v3, v4} Node v1 v2v3v4 v5  - 211 2  - v1 v2v3 v3 EE 5301 - VLSI Design Automation I

  45. Prim’s Algorithm Example 2 v2 1 5 2 v3 4 2 v5 v1 3 1 3 v4 S = {v1, v2, v3, v4, v5} Node v1 v2v3v4v5  - 211 2  - v1 v2v3 v3 EE 5301 - VLSI Design Automation I

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