What is the space complexity of BFS and DFS?

What is the space complexity of BFS and DFS?

The space complexity of BFS (Breadth-First Search) is O(V), where V is the number of vertices. This is because BFS stores all the vertices in the queue at the same time. In contrast, DFS (Depth-First Search) has a space complexity of O(h), where h is the maximum height of the tree or graph, as it only needs to store the nodes in the current path.

Why does BFS use O(V) space?

BFS uses O(V) space because it needs to keep track of all the vertices in the queue at once, especially in the worst-case scenario where the last level of the tree or graph is fully populated.

What about the space complexity of iterative DFS?

Iterative DFS also has a space complexity of O(h), similar to recursive DFS, where h is the maximum depth of the search. It uses a stack to keep track of the nodes.

Can you explain how the space complexity affects performance?

Yes, space complexity can significantly affect performance, especially in large graphs. High space usage can lead to memory overflow or slow down the algorithm due to excessive memory allocation.