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Depth-First Search (DFS) ,[object Object],[object Object],[object Object],[object Object]

DFS Algorithm ,[object Object],[object Object],[object Object],u v w1 w2 w3

DFS Algorithm Flag all vertices as not visited Flag yourself as visited For unvisited neighbors, call RDFS(w) recursively We can also record the paths using pred[ ].

Example Adjacency List source Visited Table (T/F) Initialize visited table (all False) Initialize Pred to -1 Pred 2 4 3 5 1 7 6 9 8 0 0 1 2 3 4 5 6 7 8 9 F F F F F F F F F F - - - - - - - - - -

Example Adjacency List source Visited Table (T/F) Mark 2 as visited Pred RDFS( 2 ) Now visit RDFS(8) 2 4 3 5 1 7 6 9 8 0 0 1 2 3 4 5 6 7 8 9 F F T F F F F F F F - - - - - - - - - -

Example Adjacency List source Visited Table (T/F) Mark 8 as visited mark Pred[8] Pred RDFS( 2 ) RDFS(8) 2 is already visited, so visit RDFS(0) Recursive calls 2 4 3 5 1 7 6 9 8 0 0 1 2 3 4 5 6 7 8 9 F F T F F F F F T F - - - - - - - - 2 -

Example Adjacency List source Visited Table (T/F) Mark 0 as visited Mark Pred[0] Pred RDFS( 2 ) RDFS(8) RDFS(0) -> no unvisited neighbors, return to call RDFS(8) Recursive calls 2 4 3 5 1 7 6 9 8 0 0 1 2 3 4 5 6 7 8 9 T F T F F F F F T F 8 - - - - - - - 2 -

Example Adjacency List source Visited Table (T/F) Pred RDFS( 2 ) RDFS(8) Now visit 9 -> RDFS(9) Recursive calls Back to 8 2 4 3 5 1 7 6 9 8 0 0 1 2 3 4 5 6 7 8 9 T F T F F F F F T F 8 - - - - - - - 2 -

Example Adjacency List source Visited Table (T/F) Mark 9 as visited Mark Pred[9] Pred RDFS( 2 ) RDFS(8) RDFS(9) -> visit 1, RDFS(1) Recursive calls 2 4 3 5 1 7 6 9 8 0 0 1 2 3 4 5 6 7 8 9 T F T F F F F F T T 8 - - - - - - - 2 8

Example Adjacency List source Visited Table (T/F) Mark 1 as visited Mark Pred[1] Pred RDFS( 2 ) RDFS(8) RDFS(9) RDFS(1) visit RDFS(3) Recursive calls 2 4 3 5 1 7 6 9 8 0 0 1 2 3 4 5 6 7 8 9 T T T F F F F F T T 8 9 - - - - - - 2 8

Example Adjacency List source Visited Table (T/F) Mark 3 as visited Mark Pred[3] Pred RDFS( 2 ) RDFS(8) RDFS(9) RDFS(1) RDFS(3) visit RDFS(4) Recursive calls 2 4 3 5 1 7 6 9 8 0 0 1 2 3 4 5 6 7 8 9 T T T T F F F F T T 8 9 - 1 - - - - 2 8

Example RDFS( 2 ) RDFS(8) RDFS(9) RDFS(1) RDFS(3) RDFS(4)  STOP all of 4’s neighbors have been visited return back to call RDFS(3) Adjacency List source Visited Table (T/F) Mark 4 as visited Mark Pred[4] Pred Recursive calls 2 4 3 5 1 7 6 9 8 0 0 1 2 3 4 5 6 7 8 9 T T T T T F F F T T 8 9 - 1 3 - - - 2 8

Example Adjacency List source Visited Table (T/F) Pred RDFS( 2 ) RDFS(8) RDFS(9) RDFS(1) RDFS(3) visit 5 -> RDFS(5) Recursive calls Back to 3 2 4 3 5 1 7 6 9 8 0 0 1 2 3 4 5 6 7 8 9 T T T T T F F F T T 8 9 - 1 3 - - - 2 8

Example Adjacency List source Visited Table (T/F) Pred RDFS( 2 ) RDFS(8) RDFS(9) RDFS(1) RDFS(3) RDFS(5) 3 is already visited, so visit 6 -> RDFS(6) Recursive calls Mark 5 as visited Mark Pred[5] 2 4 3 5 1 7 6 9 8 0 0 1 2 3 4 5 6 7 8 9 T T T T T T F F T T 8 9 - 1 3 3 - - 2 8

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3. DFS Algorithm Flag all vertices as not visited Flag yourself as visited For unvisited neighbors, call RDFS(w) recursively We can also record the paths using pred[ ].

4. Example Adjacency List source Visited Table (T/F) Initialize visited table (all False) Initialize Pred to -1 Pred 2 4 3 5 1 7 6 9 8 0 0 1 2 3 4 5 6 7 8 9 F F F F F F F F F F - - - - - - - - - -

5. Example Adjacency List source Visited Table (T/F) Mark 2 as visited Pred RDFS( 2 ) Now visit RDFS(8) 2 4 3 5 1 7 6 9 8 0 0 1 2 3 4 5 6 7 8 9 F F T F F F F F F F - - - - - - - - - -

6. Example Adjacency List source Visited Table (T/F) Mark 8 as visited mark Pred[8] Pred RDFS( 2 ) RDFS(8) 2 is already visited, so visit RDFS(0) Recursive calls 2 4 3 5 1 7 6 9 8 0 0 1 2 3 4 5 6 7 8 9 F F T F F F F F T F - - - - - - - - 2 -

7. Example Adjacency List source Visited Table (T/F) Mark 0 as visited Mark Pred[0] Pred RDFS( 2 ) RDFS(8) RDFS(0) -> no unvisited neighbors, return to call RDFS(8) Recursive calls 2 4 3 5 1 7 6 9 8 0 0 1 2 3 4 5 6 7 8 9 T F T F F F F F T F 8 - - - - - - - 2 -

8. Example Adjacency List source Visited Table (T/F) Pred RDFS( 2 ) RDFS(8) Now visit 9 -> RDFS(9) Recursive calls Back to 8 2 4 3 5 1 7 6 9 8 0 0 1 2 3 4 5 6 7 8 9 T F T F F F F F T F 8 - - - - - - - 2 -

9. Example Adjacency List source Visited Table (T/F) Mark 9 as visited Mark Pred[9] Pred RDFS( 2 ) RDFS(8) RDFS(9) -> visit 1, RDFS(1) Recursive calls 2 4 3 5 1 7 6 9 8 0 0 1 2 3 4 5 6 7 8 9 T F T F F F F F T T 8 - - - - - - - 2 8

10. Example Adjacency List source Visited Table (T/F) Mark 1 as visited Mark Pred[1] Pred RDFS( 2 ) RDFS(8) RDFS(9) RDFS(1) visit RDFS(3) Recursive calls 2 4 3 5 1 7 6 9 8 0 0 1 2 3 4 5 6 7 8 9 T T T F F F F F T T 8 9 - - - - - - 2 8

11. Example Adjacency List source Visited Table (T/F) Mark 3 as visited Mark Pred[3] Pred RDFS( 2 ) RDFS(8) RDFS(9) RDFS(1) RDFS(3) visit RDFS(4) Recursive calls 2 4 3 5 1 7 6 9 8 0 0 1 2 3 4 5 6 7 8 9 T T T T F F F F T T 8 9 - 1 - - - - 2 8

12. Example RDFS( 2 ) RDFS(8) RDFS(9) RDFS(1) RDFS(3) RDFS(4)  STOP all of 4’s neighbors have been visited return back to call RDFS(3) Adjacency List source Visited Table (T/F) Mark 4 as visited Mark Pred[4] Pred Recursive calls 2 4 3 5 1 7 6 9 8 0 0 1 2 3 4 5 6 7 8 9 T T T T T F F F T T 8 9 - 1 3 - - - 2 8

13. Example Adjacency List source Visited Table (T/F) Pred RDFS( 2 ) RDFS(8) RDFS(9) RDFS(1) RDFS(3) visit 5 -> RDFS(5) Recursive calls Back to 3 2 4 3 5 1 7 6 9 8 0 0 1 2 3 4 5 6 7 8 9 T T T T T F F F T T 8 9 - 1 3 - - - 2 8

14. Example Adjacency List source Visited Table (T/F) Pred RDFS( 2 ) RDFS(8) RDFS(9) RDFS(1) RDFS(3) RDFS(5) 3 is already visited, so visit 6 -> RDFS(6) Recursive calls Mark 5 as visited Mark Pred[5] 2 4 3 5 1 7 6 9 8 0 0 1 2 3 4 5 6 7 8 9 T T T T T T F F T T 8 9 - 1 3 3 - - 2 8

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