Understanding Breadth First Search (BFS) Algorithm

Dive into the fundamentals of Breadth First Search (BFS), a versatile graph traversal algorithm used in computer science. This presentation explores how BFS systematically explores nodes level by level, making it ideal for finding the shortest path in unweighted graphs, solving puzzles, and more. Learn its step-by-step process, implementation in code, and real-world applications through clear examples and visuals. Perfect for students, developers, and anyone interested in mastering algorithmic problem-solving.

1. Topic:- Breadth First Search ( BFS ) Presented By:- Name:- Sadanand Kumar Reg:- 220101120034 Branch – B.tech (CSE) 6 th Sem Guided By :- A ss t. P rof . Manswini Padhy Mathematical Problem Solving

2. Contents Introduction What is BFS? Applications of BFS Algorithm Time Complexity of BFS Algorithm Space Complexity of BFS Algorithm Example Of BFS Conclusion

3. Introduction The BFS algorithm, or Breadth-First Search algorithm, is a fundamental graph traversal technique widely used in computer science. It is used to find the shortest path in unweighted graphs, making it ideal for various real-world applications like network broadcasting and web crawling.

4. What is BFS? Breadth-first search (BFS) is an algorithm for searching a tree data structure for a node that satisfies a given property. It starts at the tree root and explores all nodes at the present depth prior to moving on to the nodes at the next depth level.

5. Applications of BFS Algorithm Shortest Path in Unweighted Graphs: BFS is used to find the shortest path between two nodes in an unweighted graph. Web Crawlers: BFS is used by web crawlers to explore web pages level by level. Social Networking Sites: BFS helps in finding the shortest path between users, such as degrees of separation. Broadcasting in Networks: BFS is used to send information (like a broadcast message) to all nodes in a network. Finding Connected Components: BFS helps in identifying all connected components in an undirected graph. Cycle Detection: BFS can be used to detect cycles in an undirected graph. Peer-to-Peer Networks: BFS is used to find all nodes within a certain number of hops in P2P networks. Solving Puzzles: BFS can be used to find the shortest solution in puzzles like the Rubik's Cube or the shortest path in a maze.

6. Time Complexity of BFS Algorithm The time complexity of BFS is O(V + E). Space Complexity of BFS Algorithm The space complexity of BFS algorithm is O(V).

7. A B G F E D C Example Of BFS

8. Conclusion Breadth-First Search (BFS) is a versatile and powerful algorithm that excels in scenarios requiring exhaustive exploration and shortest-path solutions in unweighted graphs. Its level-by-level traversal makes it ideal for applications like social network analysis, shortest-path navigation, web crawling, and game state exploration. While it offers guaranteed optimality in terms of steps and simplicity in implementation, BFS’s efficiency depends on the graph’s structure, with its O(V + E) time complexity and significant memory demands due to queue storage. As a fundamental tool in computer science and AI, BFS continues to underpin solutions to both theoretical and practical problems, balancing thoroughness with systematic precision.

9. THANK YOU