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![3
Depth-First Search
• Maintains several fields for each vV
• Like BFS, colors the vertices to indicate their
states. Each vertex is
– Initially white,
– grayed when discovered,
– blackened when finished
• Like BFS, records discovery of a white v during
scanning Adj[u] by [v] u
Md. Shafiuzzaman](https://image.slidesharecdn.com/dfs-190921162554/75/Depth-First-Search-3-2048.jpg)
![29
Depth-First Search
DFS(G)
for each uV do
color[u] white
[u] NIL
time 0
for each uV do
if color[u] white then
DFS-VISIT(G, u)
DFS-VISIT(G, u)
color[u] gray
d[u] time time 1
for each v Adj[u] do
if color[v] white then
[v] u
DFS-VISIT(G, v)
color[u] black
f[u] time time 1
Md. Shafiuzzaman](https://image.slidesharecdn.com/dfs-190921162554/75/Depth-First-Search-29-2048.jpg)
![30
Depth-First Search
• Running time: (VE)
• Initialization loop in DFS : (V)
• Main loop in DFS: (V) exclusive of time to execute
calls to DFS-VISIT
• DFS-VISIT is called exactly once for each vV since
– DFS-VISIT is invoked only on white vertices and
– DFS-VISIT(G, u) immediately colors u as gray
• For loop of DFS-VISIT(G, u) is executed |Adj[u]| time
• Since |Adj[u]| E, total cost of executing loop of
DFS-VISIT is (E)
Md. Shafiuzzaman](https://image.slidesharecdn.com/dfs-190921162554/75/Depth-First-Search-30-2048.jpg)
![3
Depth-First Search
• Maintains several fields for each vV
• Like BFS, colors the vertices to indicate their
states. Each vertex is
– Initially white,
– grayed when discovered,
– blackened when finished
• Like BFS, records discovery of a white v during
scanning Adj[u] by [v] u
Md. Shafiuzzaman](https://crownmelresort.com/image.slidesharecdn.com/dfs-190921162554/75/Depth-First-Search-3-2048.jpg)
![29
Depth-First Search
DFS(G)
for each uV do
color[u] white
[u] NIL
time 0
for each uV do
if color[u] white then
DFS-VISIT(G, u)
DFS-VISIT(G, u)
color[u] gray
d[u] time time 1
for each v Adj[u] do
if color[v] white then
[v] u
DFS-VISIT(G, v)
color[u] black
f[u] time time 1
Md. Shafiuzzaman](https://crownmelresort.com/image.slidesharecdn.com/dfs-190921162554/75/Depth-First-Search-29-2048.jpg)
![30
Depth-First Search
• Running time: (VE)
• Initialization loop in DFS : (V)
• Main loop in DFS: (V) exclusive of time to execute
calls to DFS-VISIT
• DFS-VISIT is called exactly once for each vV since
– DFS-VISIT is invoked only on white vertices and
– DFS-VISIT(G, u) immediately colors u as gray
• For loop of DFS-VISIT(G, u) is executed |Adj[u]| time
• Since |Adj[u]| E, total cost of executing loop of
DFS-VISIT is (E)
Md. Shafiuzzaman](https://crownmelresort.com/image.slidesharecdn.com/dfs-190921162554/75/Depth-First-Search-30-2048.jpg)
Uploaded byMd. Shafiuzzaman Hira
Depth-First Search
This document discusses depth-first search (DFS), a graph search algorithm that explores edges deeper whenever possible. It uses a LIFO queue and colors vertices as white, gray, or black to track the search process. DFS recursively visits unexplored neighbor vertices, coloring them gray before exploring their edges. The running time is O(V+E) as DFS calls itself once per vertex and explores each edge once.
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More from Md. Shafiuzzaman Hira
Depth-First Search
- 1. Graph Searching: Depth-First Search Preparedby Md. Shafiuzzaman Lecturer, Dept. of CSE, JUST
- 2. 2 Depth-First Search • GraphG(V, E) directed or undirected • Adjacency list representation • Goal: Systematically explore every vertex and every edge • Idea: search deeper whenever possible – Using a LIFO queue (Stack; FIFO queue used in BFS) Md. Shafiuzzaman
- 3. 3 Depth-First Search • Maintainsseveral fields for each vV • Like BFS, colors the vertices to indicate their states. Each vertex is – Initially white, – grayed when discovered, – blackened when finished • Like BFS, records discovery of a white v during scanning Adj[u] by [v] u Md. Shafiuzzaman
- 4. 4 Depth-First Search: Example xy z s t w v u Md. Shafiuzzaman
- 5. 5 Depth-First Search: Example xy z s t w v u 1 Md. Shafiuzzaman
- 6. 6 Depth-First Search: Example xy z s t w v u 1 2 Md. Shafiuzzaman
- 7. 7 Depth-First Search: Example xy z s t w v u 1 2 3 Md. Shafiuzzaman
- 8. 8 Depth-First Search: Example xy z s t w v u 1 2 3 Md. Shafiuzzaman
- 9. 9 Depth-First Search: Example xy z s t w v u 1 2 3 4 Md. Shafiuzzaman
- 10. 10 Depth-First Search: Example xy z s t w v u 1 2 3 4 5 Md. Shafiuzzaman
- 11. 11 Depth-First Search: Example xy z s t w v u 1 2 3 4 5 Md. Shafiuzzaman
- 12. 12 Depth-First Search: Example xy z s t w v u 1 2 3 4 5 6 Md. Shafiuzzaman
- 13. 13 Depth-First Search: Example xy z s t w v u 1 2 3 4 5 6 7 Md. Shafiuzzaman
- 14. 14 Depth-First Search: Example xy z s t w v u 1 2 3 4 5 6 7 8 Md. Shafiuzzaman
- 15. 15 Depth-First Search: Example xy z s t w v u 1 2 3 4 5 6 7 8 Md. Shafiuzzaman
- 16. 16 Depth-First Search: Example xy z s t w v u 1 2 3 4 5 6 7 8 9 Md. Shafiuzzaman
- 17. 17 Depth-First Search: Example xy z s t w v u 1 2 3 4 5 6 7 8 9 Md. Shafiuzzaman
- 18. 18 Depth-First Search: Example xy z s t w v u 1 2 3 4 5 6 7 8 9 10 Md. Shafiuzzaman
- 19. 19 Depth-First Search: Example xy z s t w v u 1 2 3 4 5 6 7 9 10 8 11 Md. Shafiuzzaman
- 20. 20 Depth-First Search: Example xy z s t w v u 2 3 4 5 6 7 9 10 8 111 12 Md. Shafiuzzaman
- 21. 21 Depth-First Search: Example xy z s t w v u 2 3 4 5 6 7 9 10 8 111 12 13 Md. Shafiuzzaman
- 22. 22 Depth-First Search: Example xy z s t w v u 2 3 4 5 6 7 9 10 8 111 12 13 Md. Shafiuzzaman
- 23. 23 Depth-First Search: Example xy z s t w v u 2 3 4 5 6 7 9 10 8 111 12 13 Md. Shafiuzzaman
- 24. 24 Depth-First Search: Example xy z s t w v u 2 3 4 5 6 7 9 10 8 111 12 13 14 Md. Shafiuzzaman
- 25. 25 Depth-First Search: Example xy z s t w v u 2 3 4 5 6 7 9 10 8 111 12 13 14 Md. Shafiuzzaman
- 26. 26 Depth-First Search: Example xy z s t w v u 2 3 4 5 6 7 9 10 8 111 12 13 14 15 Md. Shafiuzzaman
- 27. 27 Depth-First Search: Example xy z s t w v u 2 3 4 5 6 7 9 10 8 111 12 14 15 13 16 Md. Shafiuzzaman
- 28. 28 Depth-First Search: Example xy z s t w v u 2 3 4 5 6 7 9 10 8 111 12 14 15 13 16 x y z s t w v u 2 3 4 5 6 7 9 10 8 111 12 14 15 13 16 DFS(G) terminated Depth-first forest (DFF) Md. Shafiuzzaman
- 29. 29 Depth-First Search DFS(G) for eachuV do color[u] white [u] NIL time 0 for each uV do if color[u] white then DFS-VISIT(G, u) DFS-VISIT(G, u) color[u] gray d[u] time time 1 for each v Adj[u] do if color[v] white then [v] u DFS-VISIT(G, v) color[u] black f[u] time time 1 Md. Shafiuzzaman
- 30. 30 Depth-First Search • Runningtime: (VE) • Initialization loop in DFS : (V) • Main loop in DFS: (V) exclusive of time to execute calls to DFS-VISIT • DFS-VISIT is called exactly once for each vV since – DFS-VISIT is invoked only on white vertices and – DFS-VISIT(G, u) immediately colors u as gray • For loop of DFS-VISIT(G, u) is executed |Adj[u]| time • Since |Adj[u]| E, total cost of executing loop of DFS-VISIT is (E) Md. Shafiuzzaman