i think it help everyone.

1. Welcome To Our Presentation

2. Group Name : Quantative

3.  Depth First Search (DFS)
 Breadth First Search (BFS)
Topics

4. What is a graph?
1.Directed/Undirected
2.Weighted/Unweighted
3.Cyclic/Acyclic
A set of vertices and edges

5.  Breadth First Search (BFS)
Start several paths at a time, and advance in each one step at a time
The breadth-first search uses a FIFO queue.
 Depth First Search (DFS)
Once a possible path is found, continue the search until the end of the path
The Depth-first search uses a LIFO Stack.
Graph Traversal

6. How It Works?
1.Pick a source vertex S to start.
2.Discover the vertices that are adjacent to S.
Depth-first:
visit all neighbors of
a neighbor before
visiting your other
neighbors
Breadth First:
Pick each child of
S in turn and
discover their
vertices adjacent
to that child.
Done when all
children have been
discovered and
examined.

7. For a Graph G=(V, E) and n = |V| and m=|E|
When Adjacency List is used Complexity is O(m + n)
When Adjacency Matrix is used Scanning each row for
checking the connectivity of a Vertex is in order O(n).
So, Complexity is O(n2 )
DFS uses space O(|V|) in the worst case to store the
stack of vertices on the current search path as well as
the set of already-visited vertices.
Analysis of DFS

8. Example:

9. Depth-first search: Directed
graphs
 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.

10. DFS Example
Data Structure and Algorithm
source
vertex

11. DFS Example
Data Structure and Algorithm
1 | | |
|||
| |
source
vertex
d f

12. DFS Example
Data Structure and Algorithm
1 | | |
|||
2 | |
source
vertex
d f

13. DFS Example
Data Structure and Algorithm
1 | | |
||3 |
2 | |
source
vertex
d f

14. DFS Example
Data Structure and Algorithm
1 | | |
||3 | 4
2 | |
source
vertex
d f

15. DFS Example
Data Structure and Algorithm
1 | | |
|5 |3 | 4
2 | |
source
vertex
d f

16. DFS Example
Data Structure and Algorithm
1 | | |
|5 | 63 | 4
2 | |
source
vertex
d f

17. DFS Example
Data Structure and Algorithm
1 | | |
|5 | 63 | 4
2 | 7 |
source
vertex
d f

18. DFS Example
Data Structure and Algorithm
1 | 8 | |
|5 | 63 | 4
2 | 7 |
source
vertex
d f

19. DFS Example
Data Structure and Algorithm
1 | 8 | |
|5 | 63 | 4
2 | 7 9 |
source
vertex
d f

20. DFS Example
Data Structure and Algorithm
1 | 8 | |
|5 | 63 | 4
2 | 7 9 |10
source
vertex
d f

21. DFS Example
Data Structure and Algorithm
1 | 8 |11 |
|5 | 63 | 4
2 | 7 9 |10
source
vertex
d f

22. DFS Example
Data Structure and Algorithm
1 |12 8 |11 |
|5 | 63 | 4
2 | 7 9 |10
source
vertex
d f

23. DFS Example
Data Structure and Algorithm
1 |12 8 |11 13|
|5 | 63 | 4
2 | 7 9 |10
source
vertex
d f

24. DFS Example
Data Structure and Algorithm
1 |12 8 |11 13|
14|5 | 63 | 4
2 | 7 9 |10
source
vertex
d f

25. DFS Example
Data Structure and Algorithm
1 |12 8 |11 13|
14|155 | 63 | 4
2 | 7 9 |10
source
vertex
d f

26. DFS Example
Data Structure and Algorithm
1 |12 8 |11 13|16
14|155 | 63 | 4
2 | 7 9 |10
source
vertex
d f

27. Algorithm steps
Step:1
Push the root node in stack.
Step:2
Loop until stack is empty.
Step:3
Peek the node of the stack.
Step:4
If the node has unvisited child nodes get the
unvisited child node mark it has travers and push it
on stack.

28. Data
Structure
and
Algorithm
DFS: Algorithm
DFS(G)
 for each vertex u in V,
 color[u]=white; p[u]=NIL
 time=0;
 for each vertex u in V
 if (color[u]=white)
 DFS-VISIT(u)

29. Data
Structure
and
Algorithm
DFS-VISIT(u)
 color[u]=gray;
 time = time + 1;
 d[u] = time;
 for each v in Adj(u) do
 if (color[v] = white)
 p[v] = u;
 DFS-VISIT(v);
 color[u] = black;
 time = time + 1; f[u]= time;
DFS: Algorithm (Cont.)
source
vertex

30. BFS:
*Testing a graph for bipartitions
*To find the shortest path from a vertex s to
a vertex v in an un weighted graph
*To find the length of such a path
*To find out if a graph contains cycles
*To construct a BSF tree/forest from a graph
*Copying garbage collection
Applications

31. Applications
DFS:
* Finding connected components.
*Topological sorting.
*Finding the bridges of a graph.
*cycle Detecting
*Finding strongly connected components.
*Finding biconnectivity in graphs.