What is the time complexity of BFS and DFS?

What is the time complexity of BFS and DFS?

The time complexity of Breadth-First Search (BFS) is O(V + E), where V is the number of vertices and E is the number of edges. For Depth-First Search (DFS), the time complexity is also O(V + E). Both algorithms explore all vertices and edges in the graph.

Can you explain why both have the same time complexity?

Certainly! Both BFS and DFS traverse every vertex and edge in the graph. In the worst case, they visit all V vertices and E edges, leading to the same time complexity of O(V + E). However, their approaches to traversal differ.

What about their space complexity?

The space complexity for BFS is O(V) due to the queue used to store the vertices. For DFS, it can be O(V) in the worst case if implemented using recursion, as the call stack can grow with the depth of the graph.

Which one is better for searching in a tree?

It depends on the specific use case. BFS is better for finding the shortest path in an unweighted tree, while DFS can be more memory efficient and is often faster for deep trees.