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Comprehensive Analysis of Breadth-First Search (BFS) Algorithm for Shortest Path

DESCRIPTION

This document provides an in-depth exploration of the Breadth-First Search (BFS) algorithm, focusing on its application in finding the shortest path in a graph. It outlines the algorithm's operational mechanics, detailing each step involving discovery and processing of graph nodes. The BFS approach is illustrated with sequential state transitions, highlighting the queue management and node exploration process. Sample paths and discovered nodes are presented to deepen understanding, making this resource valuable for learners and practitioners of graph theory.

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Comprehensive Analysis of Breadth-First Search (BFS) Algorithm for Shortest Path

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Presentation Transcript

  1. Breadth First Search 2 4 8 s 5 7 3 6 9

  2. Breadth First Search Shortest pathfrom s 1 2 2 4 8 0 s 5 7 3 6 9 Undiscovered Queue: s Discovered Top of queue Finished

  3. Breadth First Search 1 2 4 8 0 s 5 7 3 3 6 9 1 Undiscovered Queue: s 2 Discovered Top of queue Finished

  4. Breadth First Search 1 2 4 8 0 5 s 5 7 1 3 6 9 1 Undiscovered Queue: s 2 3 Discovered Top of queue Finished

  5. Breadth First Search 1 2 4 8 0 s 5 7 1 3 6 9 1 Undiscovered Queue: 2 3 5 Discovered Top of queue Finished

  6. Breadth First Search 1 2 2 4 4 8 0 s 5 7 1 3 6 9 1 Undiscovered Queue: 2 3 5 Discovered Top of queue Finished

  7. Breadth First Search 1 2 2 4 8 5 already discovered:don't enqueue 0 s 5 7 1 3 6 9 1 Undiscovered Queue: 2 3 5 4 Discovered Top of queue Finished

  8. Breadth First Search 1 2 2 4 8 0 s 5 7 1 3 6 9 1 Undiscovered Queue: 2 3 5 4 Discovered Top of queue Finished

  9. Breadth First Search 1 2 2 4 8 0 s 5 7 1 3 6 9 1 Undiscovered Queue: 3 5 4 Discovered Top of queue Finished

  10. Breadth First Search 1 2 2 4 8 0 s 5 7 1 3 6 6 9 1 2 Undiscovered Queue: 3 5 4 Discovered Top of queue Finished

  11. Breadth First Search 1 2 2 4 8 0 s 5 7 1 3 6 9 1 2 Undiscovered Queue: 3 5 4 6 Discovered Top of queue Finished

  12. Breadth First Search 1 2 2 4 8 0 s 5 7 1 3 6 9 1 2 Undiscovered Queue: 5 4 6 Discovered Top of queue Finished

  13. Breadth First Search 1 2 2 4 8 0 s 5 7 1 3 6 9 1 2 Undiscovered Queue: 5 4 6 Discovered Top of queue Finished

  14. Breadth First Search 1 2 2 4 8 0 s 5 7 1 3 6 9 1 2 Undiscovered Queue: 4 6 Discovered Top of queue Finished

  15. Breadth First Search 1 2 3 2 4 8 8 0 s 5 7 1 3 6 9 1 2 Undiscovered Queue: 4 6 Discovered Top of queue Finished

  16. Breadth First Search 1 2 3 2 4 8 0 s 5 7 1 3 6 9 1 2 Undiscovered Queue: 4 6 8 Discovered Top of queue Finished

  17. Breadth First Search 1 2 3 2 4 8 0 7 s 5 7 1 3 3 6 9 1 2 Undiscovered Queue: 6 8 Discovered Top of queue Finished

  18. Breadth First Search 1 2 3 2 4 8 0 s 5 7 1 3 3 6 9 9 3 1 2 Undiscovered Queue: 6 8 7 Discovered Top of queue Finished

  19. Breadth First Search 1 2 3 2 4 8 0 s 5 7 1 3 3 6 9 3 1 2 Undiscovered Queue: 6 8 7 9 Discovered Top of queue Finished

  20. Breadth First Search 1 2 3 2 4 8 0 s 5 7 1 3 3 6 9 3 1 2 Undiscovered Queue: 8 7 9 Discovered Top of queue Finished

  21. Breadth First Search 1 2 3 2 4 8 0 s 5 7 1 3 3 6 9 3 1 2 Undiscovered Queue: 7 9 Discovered Top of queue Finished

  22. Breadth First Search 1 2 3 2 4 8 0 s 5 7 1 3 3 6 9 3 1 2 Undiscovered Queue: 7 9 Discovered Top of queue Finished

  23. Breadth First Search 1 2 3 2 4 8 0 s 5 7 1 3 3 6 9 3 1 2 Undiscovered Queue: 7 9 Discovered Top of queue Finished

  24. Breadth First Search 1 2 3 2 4 8 0 s 5 7 1 3 3 6 9 3 1 2 Undiscovered Queue: 7 9 Discovered Top of queue Finished

  25. Breadth First Search 1 2 3 2 4 8 0 s 5 7 1 3 3 6 9 3 1 2 Undiscovered Queue: 9 Discovered Top of queue Finished

  26. Breadth First Search 1 2 3 2 4 8 0 s 5 7 1 3 3 6 9 3 1 2 Undiscovered Queue: 9 Discovered Top of queue Finished

  27. Breadth First Search 1 2 3 2 4 8 0 s 5 7 1 3 3 6 9 3 1 2 Undiscovered Queue: 9 Discovered Top of queue Finished

  28. Breadth First Search 1 2 3 2 4 8 0 s 5 7 1 3 3 6 9 3 1 2 Undiscovered Queue: Discovered Top of queue Finished

  29. Breadth First Search 1 2 3 2 4 8 0 s 5 7 1 3 3 6 9 3 1 2 Level Graph

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