BFS and DFS transversal algorithmsanshdh
- 1. BFS and DFS: Graph Traversal Algorithms Today, we'll dive into two fundamental graph traversal algorithms: Breadth-First Search (BFS) and Depth-First Search (DFS).
- 2. Fundamentals of BFS and DFS BFS BFS explores a graph level by level. It starts at a source node and visits all its immediate neighbors, then their neighbors, and so on. DFS DFS explores a graph by going as deep as possible along a branch before backtracking. It starts at a source node and visits its first neighbor, then its neighbor's first neighbor, and so on, until it reaches a dead end.
- 3. Choosing the Right Search Algorithm BFS Ideal for finding the shortest path, like in a maze or network routing. DFS Useful for detecting cycles, topological sorting, and finding connected components in a graph.
- 4. Algorithmic Implementation BFS Implementation BFS uses a queue to store nodes to be visited, ensuring level-by-level exploration. DFS Implementation DFS employs a stack to track the order of visited nodes, enabling depth-first traversal.
- 5. Time and Space Complexity: BFS vs. DFS O(V+E) Time The time complexity of both BFS and DFS is typically O(V+E), where V is the number of vertices and E is the number of edges in the graph. O(V) Space The space complexity of both BFS and DFS is typically O(V), as they need to store the visited nodes.