What is the time and space complexity of Depth-First Search (DFS)?

What is the time and space complexity of Depth-First Search (DFS)?

The time complexity of 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), and each edge is explored once, contributing 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) due to the stack used to store the vertices. However, it can be more efficient in practice compared to recursive DFS.

Are there any scenarios where DFS is preferred over BFS?

Yes, DFS is preferred in scenarios where you need to explore all paths, such as in puzzle solving or when memory is limited, as it can be more space-efficient.