Depth First Search(DFS)

1. Depth First Search
1
By-Ashish Ranjan

2. 2
Depth First Search (DFS)
• The DFS algorithm is a recursive
algorithm that uses the idea of
backtracking.
• It involves exhaustive searches of all
the nodes by going ahead, if
possible, else by backtracking.
• This recursive nature of DFS can be
implemented using stacks.

3. 3
The basic idea is as follows:
• Pick a starting node and push all its adjacent nodes into
a stack.
• Pop a node from stack to select the next node to visit
and push all its adjacent nodes into a stack.
• Repeat this process until the stack is empty. However,
ensure that the nodes that are visited are marked.
• This will prevent you from visiting the same node more
than once.
• If you do not mark the nodes that are visited and you
visit the same node more than once, you may end up in
an infinite loop.

4. 4
Adjacency Lists
A: F G
B: A H
C: A D
D: C F
E: C D G
F: E:
G: :
H: B:
I: H:
F
A
B C G
D
E
H
I

5. 5
F
A
B C G
D
E
H
I
dfs(A)
A-F A-G
Function call stack:

6. 6
F
A
B C G
D
E
H
I
dfs(A)
A-F A-G
Function call stack:
visit(F)
F-E

7. 7
F
A
B C G
D
E
H
I
dfs(A)
A-F A-G
Function call stack:
dfs(F)
F-E
dfs(E)
E-C E-D E-G

8. 8
F
A
B C G
D
E
H
I
dfs(A)
A-F A-G
Function call stack:
dfs(F)
F-E
dfs(E)
E-C E-D E-G
dfs(C)
C-A C-D

9. 9
F
A
B C G
D
E
H
I
dfs(A)
A-F A-G
Function call stack:
dfs(F)
F-E
dfs(E)
E-C E-D E-G
dfs(C)
C-A C-D

10. 10
F
A
B C G
D
E
H
I
dfs(A)
A-F A-G
Function call stack:
dfs(F)
F-E
dfs(E)
E-C E-D E-G
dfs(C)
C-A C-D
dfs(D)
D-C D-F

11. 11
F
A
B C G
D
E
H
I
dfs(A)
A-F A-G
Function call stack:
dfs(F)
F-E
dfs(E)
E-C E-D E-G
dfs(C)
C-A C-D
dfs(D)
D-C D-F

12. 12
F
A
B C G
D
E
H
I
dfs(A)
A-F A-G
Function call stack:
dfs(F)
F-E
dfs(E)
E-C E-D E-G
dfs(C)
C-A C-D
dfs(D)
D-C D-F

13. 13
F
A
B C G
D
E
H
I
dfs(A)
A-F A-G
Function call stack:
dfs(F)
F-E
dfs(E)
E-C E-D E-G
dfs(C)
C-A C-D

14. 14
F
A
B C G
D
E
H
I
dfs(A)
A-F A-G
Function call stack:
dfs(F)
F-E
dfs(E)
E-C E-D E-G

15. 15
F
A
B C G
D
E
H
I
dfs(A)
A-F A-G
Function call stack:
dfs(F)
F-E
dfs(E)
E-C E-D E-G

16. 16
F
A
B C G
D
E
H
I
dfs(A)
A-F A-G
Function call stack:
dfs(F)
F-E
dfs(E)
E-C E-D E-G
dfs(G)

17. 17
F
A
B C G
D
E
H
I
dfs(A)
A-F A-G
Function call stack:
dfs(F)
F-E
dfs(E)
E-C E-D E-G

18. 18
F
A
B C G
D
E
H
I
dfs(A)
A-F A-G
Function call stack:
dfs(F)
F-E

19. 19
F
A
B C G
D
E
H
I
dfs(A)
A-F A-G
Function call stack:

20. 20
F
A
B C G
D
E
H
I
dfs(A)
A-F A-G
Function call stack:

21. 21
F
A
B C G
D
E
H
I
Nodes reachable from A: A, C, D, E, F, G