The document explores graph traversal algorithms, particularly breadth-first search (BFS) and depth-first search (DFS), detailing their methods and applications. BFS examines nodes level by level using a queue, while DFS explores deeper from the initial node using a stack. Key differences include memory usage and speed, with BFS being slower and requiring more memory compared to DFS.

1. Understanding Graph Traversal
Algorithms: A Deep Dive into BFS
and DFS
Graph
Traversal
Algorithm

2. Graph Traversal
Algorithm
Traversing the graph means examining all
the nodes and vertices of the graph. There
are two standard methods by using which,
we can traverse the graphs.
• Breadth First Search (BFS) - BFS
traversing the graph from root node
and explores all the nearest nodes and
by process explore all the unexplored
nodes until it finds the goal.
• Depth First Search (DFS) - DFS
algorithm starts with the initial node of
the graph, and then goes to deeper
and deeper until we find the goal node
or the node which has no children.

3. DIFFERENCE BETWEEN BFS
AND DFS
Breadth First Search (BFS) Depth First Search (DFS)
BFS use queue data structure
to store un-explored nodes.
Uses stack data structure to
store un-explored nodes.
BFS is slower and require
more memory.
DFS is faster and require less
memory.
Shortest path, GPS navigation
systems are real-time
applications of BFS
Topological sorting, path
finding are real-time
applications of DFS

4. Graph Solving
We will apply BFS and DFS on this graph

5. BFS
1
2 4
4 5
5 3
3
ф
Q:
Q:
Q:
Q:
Q:
Q: Visited:
Visited:
Visited:
Visited:
Visited:
Visited:
ф
1
1,2
1,2,4
1,2,4,5
1,2,4,5,3
Here 1,2,4,5,3 are the Traversal order for the graph

6. DFS
S Visited:
Visited:
Visited:
Visited:
Visited:
Visited:
ф
1
1,4
1,4,3
1,4,3,2
1,4,3,2,5
1
4
2
3
2
ф
2
5
S
S
S
S
S
Here 1,4,3,2,5 are the Traversal order for the graph

7. Thanks