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Alyce Brady CS 510: Computer Algorithms

Depth-First Graph Traversal Algorithm. Alyce Brady CS 510: Computer Algorithms. Search: Look for a given node stop when node found, even if not all nodes were visited Traversal: Always visit all nodes. Search vs Traversal. Similar to Depth-first Traversal of a Binary Tree

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Alyce Brady CS 510: Computer Algorithms

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  1. Depth-First Graph Traversal Algorithm Alyce Brady CS 510: Computer Algorithms

  2. Search: Look for a given node stop when node found, even if not all nodes were visited Traversal: Always visit all nodes Search vs Traversal

  3. Similar to Depth-first Traversal of a Binary Tree Choose a starting vertex Do a depth-first search on each adjacent vertex Depth-first Search

  4. depth-first-search mark vertex as visited for each adjacent vertex if unvisited do a depth-first search on adjacent vertex Pseudo-Code forDepth-First Search

  5. Depth-First Search A B C D E F G

  6. Depth-First Search v A B C D E F G A

  7. Depth-First Search v A B C D E F G A

  8. Depth-First Search v A v B C D E F G A B

  9. Depth-First Search v A v B C D E F G A B

  10. Depth-First Search v A v B C D E F G A B

  11. Depth-First Search v A v B C v D E F G A B D

  12. Depth-First Search v A v B C v D E F G A B D

  13. Depth-First Search v A v B C v D E F G A B D

  14. Depth-First Search v A v B C v v D E F G A B D E

  15. Depth-First Search v A v B C v v D E F G A B D E

  16. Depth-First Search v A v B C v v D E F G A B D E

  17. Depth-First Search v A v B C v D E F G A B D E

  18. Depth-First Search v A v B C v v D E F G A B D E

  19. Depth-First Search v A v B C v v D E F G A B D E

  20. Depth-First Search v A v B C v v D E F G A B D E

  21. Depth-First Search v A v B C v v D E F G v A B D E F

  22. Depth-First Search v A v B C v v D E F G v A B D E F

  23. Depth-First Search v A v B C v v D E F G v A B D E F

  24. Depth-First Search v A v v B C v v D E F G v A B D E F C

  25. Depth-First Search v A v v B C v v D E F G v A B D E F C

  26. Depth-First Search v A v v B C v v D E F G v A B D E F C

  27. Depth-First Search v A v v B C v v D E F G v A B D E F C

  28. Depth-First Search v A v v B C v v v D E F G v A B D E F C G

  29. Depth-First Search v A v v B C v v v D E F G v A B D E F C G

  30. Depth-First Search v A v v B C v v v D E F G v A B D E F C G

  31. Depth-First Search v A v v B C v v v D E F G v A B D E F C G

  32. Depth-First Search v A v v B C v v v D E F G v A B D E F C G

  33. Depth-First Search v A v v B C v v v D E F G v A B D E F C G

  34. Depth-First Search v A v v B C v v v D E F G v A B D E F C G

  35. Depth-First Search v A v v B C v v v D E F G v A B D E F C G

  36. Depth-First Search A B C D E F G A B D E F C G

  37. Was this a true search? How would we make it a true search? Was this a true traversal? How would we make it a true traversal?

  38. Time Complexity Adjacency Lists Each node is marked visited once Each node is checked for each incoming edge O (v + e) Adjacency Matrix Have to check all entries in matrix: O(n2) Time and Space Complexityfor Depth-First Search

  39. Space Complexity Stack to handle nodes as they are explored Worst case: all nodes put on stack (if graph is linear) O(n) Time and Space Complexityfor Depth-First Search

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