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15.082 and 6.855J

15.082 and 6.855J. Breadth First Search. 4. 4. 2. 2. 8. 8. 1. 1. 5. 5. 7. 7. 9. 9. 3. 3. 6. 6. 1. 1. next. Initialize. 1. 1. Unmark all nodes in N; Mark node s. pred(1) = 0 next := 1 order(next) = 1 LIST:= {1}. LIST. 4. 2. 8. 1. 5. 7. 9. 3. 6. 1.

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15.082 and 6.855J

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  1. 15.082 and 6.855J Breadth First Search Breadth first search animation

  2. 4 4 2 2 8 8 1 1 5 5 7 7 9 9 3 3 6 6 1 1 next Initialize 1 1 Unmark all nodes in N; Mark node s pred(1) = 0 next := 1order(next) = 1 LIST:= {1} LIST Breadth first search animation

  3. 4 2 8 1 5 7 9 3 6 1 next Select a node i in LIST 1 1 1 In breadth first search, i is the first node in LIST LIST 1 Breadth first search animation

  4. If node i is incident to an admissible arc… 2 4 2 2 8 1 1 1 1 5 7 Mark Node j pred(j) := i Select an admissible arc (i,j) Next := Next + 1 order(j) := next add j to LIST 9 3 6 LIST 1 2 1 2 next Breadth first search animation

  5. If node i is incident to an admissible arc… 2 4 2 2 8 1 1 1 1 5 5 7 3 Mark Node j pred(j) := i Select an admissible arc (i,j) Next := Next + 1 order(j) := next add j to LIST 9 3 6 LIST 1 2 5 2 3 next Breadth first search animation

  6. If node i is incident to an admissible arc… 2 4 2 2 8 1 1 1 1 5 5 7 3 Next := Next + 1 order(j) := next add j to LIST Mark Node j pred(j) := i Select an admissible arc (i,j) 9 3 3 6 4 LIST 1 2 5 3 2 4 3 next Breadth first search animation

  7. If node i is not incident to an admissible arc… 2 4 2 2 8 1 1 1 1 1 5 5 7 3 9 Delete node i from LIST 3 3 6 4 LIST 1 2 5 3 2 4 3 next Breadth first search animation

  8. Select Node i 2 4 2 2 2 8 1 1 1 1 1 5 5 7 3 9 The first node on LIST becomes node i 3 3 6 4 LIST 1 2 5 3 2 3 4 next Breadth first search animation

  9. If node i is incident to an admissible arc… 5 2 4 4 2 2 2 8 1 1 1 5 5 7 3 Select an admissible arc (i,j) Mark Node j pred(j) := i Next := Next + 1 order(j) := next add j to LIST 9 3 3 6 4 LIST 1 2 5 3 4 4 3 2 5 next Breadth first search animation

  10. If node i is not incident to an admissible arc… 5 2 4 4 2 2 2 2 8 1 1 1 5 5 7 3 Delete node i from LIST 9 3 3 6 4 LIST 1 2 5 3 4 3 4 2 5 next Breadth first search animation

  11. Select a node 5 2 4 4 2 2 2 8 1 1 1 5 5 5 7 3 The first node on LIST becomes node i 9 3 3 6 4 LIST 1 2 5 3 4 3 4 2 5 next Breadth first search animation

  12. If node i is incident to an admissible arc… 5 2 4 4 2 2 2 8 1 1 1 5 5 5 7 3 Select an admissible arc (i,j) Next := Next + 1 order(j) := next add j to LIST Mark Node j pred(j) := i 9 3 3 6 6 4 6 LIST 1 2 5 3 4 6 3 4 6 2 5 next Breadth first search animation

  13. If node i is not incident to an admissible arc… 5 2 4 4 2 2 2 8 1 1 1 5 5 5 5 7 3 Delete node i from LIST 9 3 3 6 6 4 6 LIST 1 2 5 3 4 6 6 2 4 3 5 next Breadth first search animation

  14. Select node 3 5 2 4 4 2 2 2 8 1 1 1 5 5 5 5 7 3 node 3 is not incident to any admissible arcs delete node 3 from LIST 9 3 3 3 3 6 6 4 6 LIST 1 2 5 3 4 6 5 6 4 2 3 next Breadth first search animation

  15. Select a node 5 2 4 4 4 2 2 8 1 1 1 5 5 7 3 i : = 4 9 3 3 6 6 4 6 LIST 1 2 5 3 4 6 3 4 2 5 6 next Breadth first search animation

  16. If node i is incident to an admissible arc… 5 2 4 4 4 7 2 2 8 8 1 1 1 5 5 7 3 Mark Node j pred(j) := i Next := Next + 1 order(j) := next add j to LIST Select an admissible arc (i,j) 9 3 3 6 6 4 6 LIST 1 2 5 3 4 6 8 3 5 4 7 2 6 next Breadth first search animation

  17. If node i is not incident to an admissible arc… 5 2 4 4 4 4 7 2 2 8 8 1 1 1 5 5 7 3 Delete node i from LIST 9 3 3 6 6 4 6 LIST 1 2 5 3 4 6 8 7 3 5 4 2 6 next Breadth first search animation

  18. Select node i 5 2 4 4 7 2 2 8 8 1 1 1 5 5 7 3 i := 6 9 3 3 6 6 6 4 6 LIST 1 2 5 3 4 6 8 7 2 5 4 3 6 next Breadth first search animation

  19. If node i is incident to an admissible arc… 5 2 4 4 7 2 2 8 8 1 8 1 1 5 5 7 7 3 Next := Next + 1 order(j) := next add j to LIST Mark Node j pred(j) := i Select an admissible arc (i,j) 9 3 3 6 6 6 4 6 LIST 1 2 5 3 4 6 8 7 7 5 4 8 3 2 6 next Breadth first search animation

  20. If node i is incident to an admissible arc… 5 2 4 4 7 2 2 8 8 1 8 1 1 5 5 7 7 3 Next := Next + 1 order(j) := next add j to LIST Select an admissible arc (i,j) Mark Node j pred(j) := i 9 9 3 3 6 6 6 4 9 6 LIST 1 2 5 3 4 6 8 7 9 6 5 4 9 3 8 2 7 next Breadth first search animation

  21. If node i is not incident to an admissible arc… 5 2 4 4 7 2 2 8 8 1 8 1 1 5 5 7 7 3 Delete node i from LIST 9 9 3 3 6 6 6 6 4 9 6 LIST 1 2 5 3 4 6 8 7 9 6 5 4 3 8 2 9 7 next Breadth first search animation

  22. Select node 8 5 2 4 4 7 2 2 8 8 8 8 1 8 1 1 5 5 7 7 3 node 8 is not incident to an admissible arc; delete it from LIST 9 9 3 3 6 6 6 6 4 9 6 LIST 1 2 5 3 4 6 8 7 9 7 5 4 3 8 2 9 6 next Breadth first search animation

  23. Select node 7 5 2 4 4 7 2 2 8 8 1 8 1 1 5 5 7 7 7 7 3 node 7 is not incident to an admissible arc; delete it from LIST 9 9 3 3 6 6 6 6 4 9 6 LIST 1 2 5 3 4 6 8 7 9 6 7 5 4 3 8 2 9 next Breadth first search animation

  24. Select node 9 5 2 4 4 7 2 2 8 8 1 8 1 1 5 5 7 7 3 node 9 is not incident to an admissible arc; delete it from LIST 9 9 9 9 3 3 6 6 6 6 4 9 6 LIST 1 2 5 3 4 6 8 7 9 9 3 6 7 2 5 4 8 next Breadth first search animation

  25. THE END Breadth first search animation

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