Problem Statement
Compare Breadth-First Search and Depth-First Search. When would you use each algorithm?
Explanation
Breadth-First Search and Depth-First Search are fundamental graph traversal algorithms with different exploration strategies and use cases.
BFS explores the graph level by level, visiting all neighbors of a vertex before moving to the next level. It uses a queue data structure to maintain the order of vertices to visit. Starting from a source vertex, BFS visits all vertices at distance 1, then all at distance 2, and so on. Time complexity is O of V plus E and space complexity is O of V for the queue and visited array. BFS guarantees finding the shortest path in unweighted graphs.
DFS explores the graph by going as deep as possible along each branch before backtracking. It uses a stack explicitly or implicitly through recursion. Starting from a source vertex, DFS explores one neighbor completely before exploring other neighbors. Time complexity is O of V plus E and space complexity is O of V for the recursion stack or explicit stack in worst case. DFS is more memory efficient for deep graphs.
Use BFS when you need to find the shortest path in an unweighted graph, when you want to find all vertices within a given distance, for level-order traversal of trees, in social networking applications to find people within a certain degree of connection, and when you want to find connected components. BFS is also useful in web crawlers for breadth-first exploration and in GPS navigation for finding nearby locations.
Use DFS when you need to detect cycles in a graph, for topological sorting in directed acyclic graphs, to find strongly connected components, when checking if a path exists between two vertices, in maze and puzzle solving where you want to explore all possibilities, and when memory is limited as DFS typically uses less memory than BFS. DFS is also used in game tree evaluation, finding articulation points and bridges in graphs, and solving constraint satisfaction problems.
A key difference is that BFS finds the shortest path and explores nearest vertices first making it suitable for level-wise processing, while DFS explores deeper before going wide making it suitable for exhaustive search and backtracking scenarios. BFS uses more memory storing entire levels while DFS memory grows with depth. Choose based on whether you need shortest paths or deep exploration.