What are the time complexities of BFS and DFS?

What are the time complexities of BFS and DFS?

BFS (Breadth-First Search) has a time complexity of O(V + E), while DFS (Depth-First Search) also has a time complexity of O(V + E), where V is the number of vertices and E is the number of edges.

Can you explain why both have the same time complexity?

Sure! Both algorithms explore all vertices and edges in the graph. BFS explores level by level, while DFS goes deep into one branch before backtracking, but they both end up visiting every vertex and edge.

Are there scenarios where one is preferred over the other?

Yes, BFS is preferred for finding the shortest path in unweighted graphs, while DFS is often used for tasks like topological sorting or solving puzzles.

What about their space complexities?

BFS has a space complexity of O(V) due to the queue used for storing nodes, while DFS has a space complexity of O(h), where h is the maximum height of the tree, due to the recursion stack.