BFS vs. DFS

Breadth-First Search (BFS) and Depth-First Search (DFS) are fundamental graph traversal algorithms with different exploration strategies and trade-offs. BFS explores nodes level by level from a starting node, using a queue, which guarantees the shortest path (in terms of number of edges) in unweighted graphs but requires more memory to store the frontier. 

DFS, in contrast, explores as far as possible along one branch before backtracking, using a stack or recursion; it is more memory-efficient in many cases but does not guarantee the shortest path. BFS is typically preferred for shortest-path and level-order problems, while DFS is better suited for tasks such as cycle detection, topological sorting, and exploring all possible paths.

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