This document discusses breadth-first search (BFS) and depth-first search (DFS) algorithms for traversing graphs. It provides examples of how BFS uses a queue to search all neighbors at the current level before moving to the next level, while DFS uses a stack and explores each branch as far as possible before backtracking. The document compares key differences between BFS and DFS such as their time and space complexities, usefulness for finding shortest paths, and whether queues or stacks are used. Application areas for each algorithm are also mentioned.

1. BIRLA INSTITUTE OF TECHNOLOGY,MESRA
JAIPUR CAMPUS
TOPIC:
DFS & BFS
PRESENTED BY:
SAJAN SINGH(MCA/25019/18)
MEGHAJ KUMAR MALLICK(MCA/25017/18)
MCA 2ND YEAR ,3RD SEMESTER

2. INTRODUCTION TO GRAPH
• A graph G is simply a set V of vertices/nodes and a
collection E of pairs of vertices from V, called
edges/arcs.
Vertices v={1,2,3,4,5}
Edges={ (1,4), (1,2), (2,3), (3,5),(4,3) }

8. GRAPH TRAVERSAL

9. BREATH FIRST SEARCH
 Search for all vertices that are directly reachable from
root(called level 1 vertices).
 After mark all these vertices visit all these vertices that
are directly reachable from level 1 vertices(called level2
vertices) and so on.
 In general k vertices are directly reachable from a level
k-1 vertices.

10. EXAMPLE : FOR BFS

11. MEMORY REPESENTATION

12. BFS ALGORITHM

13. BFS ALOGRITHM

14. BFS ANALYSIS

15. APPLICATION OF BFS
1. Peer to peer networks:
In peer to peer networks like BIT- Torrent, BFS
search is used to find all neighbor nodes.
2. Social Networking Websites :
In social networks, we can find people within a given
distance ‘k’ from a person using BFS till ‘k’ levels .
2. In Garbage Collection: BFS is used in copying
garbage collection

16. DEPTH FIRST SEARCH
 Depth-first search (DFS) is an algorithm for
traversing or searching tree or graph data structures.
The algorithm starts at the root node (selecting some
arbitrary node as the root node in the case of a graph)
and explores as far as possible along each branch
before backtracking.
 It use the stack data structure (FILO) as frontier.

17. DFS IMPLEMENTATION

18. DFS PROCEDURE
 Procedure dfs(s)
make all vertices in graph as not reached
invoke scan(s)
Procedure scan(s)
mark & visit s
for each neighbor w of s
if the neighbor is not reached
invoke scan(w)

20. BFS & DFS COMPARISON
BFS DFS
 BFS stands for Breadth First
Search.
 BFS can be done with the
help of QUEUE i.e. FIFO.
 In BSF time & space
complexity is lesser as there is
no need to do backtracking.
 BFS is slower than DFS.
 BFS requires more memory.
 It is useful in finding shortest
path
 DFS stands for Depth First
Search.
 DFS can be done using
STACK i.e. LIFO
 It has higher time & space
complexity due to
backtracking.
 DFS is faster than BFS
 DFS requires less memory.
 Not useful for shortest path.

21. EXAMPLE FOR COMPARISON
BFS DFS