BFS vs DFS: Which has better space complexity?

What is the difference in space complexity between BFS and DFS?

BFS (Breadth-First Search) typically has a space complexity of O(b^d), where b is the branching factor and d is the depth of the shallowest solution. In contrast, DFS (Depth-First Search) has a space complexity of O(d), where d is the maximum depth of the search tree.

Why does BFS have higher space complexity?

BFS stores all nodes at the current level before moving to the next level, which can lead to a large number of nodes being stored in memory, especially in wide trees.

Are there scenarios where DFS is more space-efficient?

Yes, in scenarios where the solution is deep and the branching factor is low, DFS can be more space-efficient since it only needs to store nodes along the current path.

Can you give an example of a problem where BFS is preferred despite its space complexity?

Certainly! BFS is preferred in finding the shortest path in unweighted graphs, as it explores all possible paths level by level.