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DFS & BFS Graph
The document discusses depth-first search (DFS) and breadth-first search (BFS) graph traversal algorithms. It provides details on how DFS uses a stack to search deeper in the graph first by exploring edges from the most recently discovered vertex. BFS uses a queue to search outward from the starting node to neighboring nodes first before searching further. An example of DFS running on a graph is shown with each step of the algorithm.
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DFS & BFS Graph
- 1. Identity MD.MAHFUZUL YAMIN ID:141-15-3429 SEC:F DEPARTMENT OFCSE DAFFODIL INTERNATIONAL UNIVERSITY
- 2. Topic Depth-First Search Think Stack Breadth-FirstSearch Think Queue
- 3. Depth-First Search Search“deeper” in the graph whenever possible Edges are explored out of the most recently discovered vertex v that still has unexplored edges • After all edges of v have been explored, the search “backtracks” from the parent of v • The process continues until all vertices reachable from the original source have been discovered • If undiscovered vertices remain, choose one of them as a new source and repeat the search from that vertex • DFS creates a “depth-first forest” 1 2 5 4 3
- 4. Depth-first search: Directedgraphs The algorithm is essentially the same as for undirected graphs, the difference residing in the interpretation of the word "adjacent". In a directed graph, node w is adjacent to node v if the directed edge (v, w) exists. If (v, w) exists but (w, v) does not, then w is adjacent to v but v is not adjacent to w. With this change of interpretation the procedures dfs and search apply equally well in the case of a directed graph.
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- 6. DFS Example 1 || | ||| | | source vertex d f
- 7. DFS Example 1 || | ||| 2 | | source vertex d f
- 8. DFS Example 1 || | ||3 | 2 | | source vertex d f
- 9. DFS Example 1 || | ||3 | 4 2 | | source vertex d f
- 10. DFS Example 1 || | |5 |3 | 4 2 | | source vertex d f
- 11. DFS Example 1 || | |5 | 63 | 4 2 | | source vertex d f
- 12. DFS Example 1 || | |5 | 63 | 4 2 | 7 | source vertex d f
- 13. DFS Example 1 |8 | | |5 | 63 | 4 2 | 7 | source vertex d f
- 14. DFS Example 1 |8 | | |5 | 63 | 4 2 | 7 9 | source vertex d f
- 15. DFS Example 1 |8 | | |5 | 63 | 4 2 | 7 9 |10 source vertex d f
- 16. DFS Example 1 |8 |11 | |5 | 63 | 4 2 | 7 9 |10 source vertex d f
- 17. DFS Example 1 |128 |11 | |5 | 63 | 4 2 | 7 9 |10 source vertex d f
- 18. DFS Example 1 |128 |11 13| |5 | 63 | 4 2 | 7 9 |10 source vertex d f
- 19. DFS Example 1 |128 |11 13| 14|5 | 63 | 4 2 | 7 9 |10 source vertex d f
- 20. DFS Example 1 |128 |11 13| 14|155 | 63 | 4 2 | 7 9 |10 source vertex d f
- 21. DFS Example 1 |128 |11 13|16 14|155 | 63 | 4 2 | 7 9 |10 source vertex d f
- 22. All vertex arevisited
- 23. Breadth-first search 23 • Ingraph theory, breadth-first search (BFS) is a graph search algorithm that begins at the root node and explores all the neighboring nodes. • Then for each of those nearest nodes, it explores their unexplored neighbor nodes, and so on, until it finds the goal.
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- 25. BFS: Start withNode 5 7 1 5 4 3 2 6 5 1 2 0 4 3 7 6 0
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