What is the time and space complexity of depth-first search?

What is the time and space complexity of depth-first search?

The time complexity of depth-first search (DFS) is O(V + E), where V is the number of vertices and E is the number of edges. The space complexity is O(V) in the worst case due to the stack space used for recursion.

Can you explain why the time complexity is O(V + E)?

Sure! In DFS, each vertex is visited once, contributing O(V) to the time complexity. Each edge is also explored once, adding O(E). Thus, the total is O(V + E).

What about the space complexity in iterative DFS?

In iterative DFS, the space complexity remains O(V) because of the stack used to keep track of vertices. However, it can be less than O(V) in practice if the graph is sparse.

How does DFS compare to breadth-first search in terms of complexity?

Both DFS and BFS have the same time complexity of O(V + E). However, BFS has a higher space complexity of O(V) due to the queue used to store vertices.