What is the algorithm complexity of DFS and BFS?

What is the algorithm complexity of DFS and BFS?

DFS (Depth-First Search) has a time complexity of O(V + E), while BFS (Breadth-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 complexity?

Certainly! Both algorithms explore all vertices and edges in the graph. DFS goes deep into a branch before backtracking, while BFS explores all neighbors at the present depth before moving on. Hence, they both traverse the entire graph.

Are there scenarios where one is preferred over the other?

Yes, DFS is often preferred for problems involving pathfinding in deep graphs or when memory is limited, while BFS is better for finding the shortest path in unweighted graphs.

What about their space complexity?

DFS has a space complexity of O(h) where h is the maximum height of the tree, while BFS has a space complexity of O(V) since it stores all the nodes at the current level.