BFS &DFS

Both BFS and DFS visit every reachable vertex in O(V plus E) time with an adjacency list, but their exploration order changes what they naturally solve. BFS uses a queue and is the standard choice for minimum number of edges in an unweighted graph because it explores layers in increasing distance. DFS uses recursion or an explicit stack and is useful for connected components, topological-sort postorder, backtracking, and cycle detection with an in-progress state. Both require visited tracking on general graphs to avoid loops. Discuss space honestly: BFS can hold an entire frontier, O(V) in the worst case; recursive DFS uses O(h) call-stack space for depth h but can also be O(V) on a chain. For disconnected graphs, loop over every unvisited vertex. Test a cycle, a tree, isolated vertices, and a graph where the shallowest target path differs from the first deep path. Do not say DFS finds shortest paths merely because it eventually reaches the target.