This is an PPT of Data Structure. It include the following topic "BFS & DFS in Data Structure".

1. BFS AND DFS
Presented By:
Muskaan
MCA/25020/18

2. CONTENTS
 Introduction
 Types of graph Traversal
Depth-First Search
Breadth-First Search
Application of BFS and DFS

3. INTRODUCTION
Graph traversal is also known as graph search refers to the
process of visiting each vertex in a graph.
Such traversals are classified by the order in which the
vertices are visited. Tree traversal is a special case of graph
traversal.

4. DEPTH FIRST SEARCH
Depth-first search (DFS) is an algorithm for traversing
or searching tree or graph data structures.
DFS uses stack.

5. Depth-First Search
// recursive, preorder
void dfs (Node v) {
if (v == null)
return;
if (v not yet visited)
visit&mark(v); // visit node before adjacent nodes
for (each w adjacent to v)
if (w has not yet been visited)
dfs(w);
} // dfs

6. Example
0
7
1
5
4
3
2
6
Policy: Visit adjacent nodes in increasing index order

7. DFS: Start with Node 5
0
7
1
5
4
3
2
6
5 1 0 3 2 7 6 4

8. DFS: Start with Node 5
0
7
1
5
4
3
2
6
5
Push 5

9. DFS: Start with Node 5
0
7
1
5
4
3
2
6
Pop/Visit/Mark 5
5

10. DFS: Start with Node 5
0
7
1
5
4
3
2
6
1
2
5
Push 2, Push 1

11. DFS: Start with Node 5
0
7
1
5
4
3
2
6
2
Pop/Visit/Mark 1
5 1

12. DFS: Start with Node 5
0
7
1
5
4
3
2
6
0
4
2
5 1
Push 4, Push 0

13. DFS: Start with Node 5
0
7
1
5
4
3
2
6
4
2
5 1 0
Pop/Visit/Mark 0

14. DFS: Start with Node 5
0
7
1
5
4
3
2
6
3
7
4
2
Push 7, Push 3
5 1 0

15. DFS: Start with Node 5
0
7
1
5
4
3
2
6
7
4
2
5 1 0 3
Pop/Visit/Mark 3

16. DFS: Start with Node 5
0
7
1
5
4
3
2
6
7
4
2
5 1 0 3
2 is already in stack

17. DFS: Start with Node 5
0
7
1
5
4
3
2
6
7
4
2
Pop/Mark/Visit 7
5 1 0 3 7

18. DFS: Start with Node 5
0
7
1
5
4
3
2
6
6
4
2
5 1 0 3 7
Push 6

19. DFS: Start with Node 5
0
7
1
5
4
3
2
6
4
2
5 1 0 3 7 6
Pop/Mark/Visit 6

20. DFS: Start with Node 5
0
7
1
5
4
3
2
6
2
Pop/Mark/Visit 4
5 1 0 3 7 6 4

21. DFS: Start with Node 5
0
7
1
5
4
3
2
6
Pop/Mark/Visit 2
5 1 0 3 7 6 4 2

22. DFS: Start with Node 5
0
7
1
5
4
3
2
6
Done
5 1 0 3 7 6 4 2

23. BREADTH FIRST SEARCH
Breadth-first search (BFS) is an algorithm for traversing or
searching tree or graph data structures.
It uses queue.

24. Breadth-First Search
// non-recursive, preorder, breadth-first search
void bfs (Node v) {
if (v == null)
return;
enqueue(v);
while (queue is not empty) {
dequeue(v);
if (v has not yet been visited)
mark&visit(v);
for (each w adjacent to v)
if (w has not yet been visited && has not been queued)
enqueue(w);
} // while
} // bfs

25. BFS: Start with Node 5
7
1
5
4
3
2
6
0

26. BFS: Start with Node 5
7
1
5
4
3
2
6
0
5

27. BFS: Node one-away
7
1
5
4
3
2
6
0
5
5 1 2

28. BFS: Visit 1 and add its adjacent
nodes
7
1
5
4
3
2
6
0
5 1
05 1 2 4

29. BFS: Visit 2 and add its adjacent
nodes
7
1
5
4
3
2
6
0
5 1 2
05 1 2 4

30. BFS: Visit 0 and add its adjacent
nodes
7
1
5
4
3
2
6
0
5 1 2 0
05 1 2 4 3 7

31. BFS: Visit 4 and add its adjacent
nodes
7
1
5
4
3
2
6
0
5 1 2 0 4
05 1 2 4 3 7

32. BFS: Visit 3 and add its adjacent
nodes
7
1
5
4
3
2
6
0
5 1 2 0 4 3
5 1 2 0 4 3 7

33. BFS: Visit 7 and add its adjacent
nodes
7
1
5
4
3
2
6
0
5 1 2 0 4 3 7
5 1 2 0 4 3 7 6

34. BFS: Visit 6 and add its adjacent
nodes
7
1
5
4
3
2
6
0
5 1 2 0 4 3 7 6
5 1 2 0 4 3 7 6

35. BFS Traversal Result
7
1
5
4
3
2
6
5 1 2 0 4 3 7 6
0

36. Applications of BFS
•
•
•
Computing Distances
Checking for cycles in a graph
Reachability: Given a graph G and vertices x and y, determine if there
exists a path from x to y.

37. Applications of DFS
• Checking for Biconnected Graph: A graph is biconnected if removal of
any vertex does not affect connectivity of the other vertices. Used to
test if network is robust to failure of certain nodes. A single DFS
traversal algorithm.