What is the space complexity of DFS in the worst case?

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Question: What is the space complexity of DFS in the worst case?

Options:

Correct Answer: O(V)

Solution:

The space complexity of DFS in the worst case is O(V) due to the stack used for recursion or explicit stack storage.

What is the space complexity of DFS in the worst case?

What is the space complexity of DFS in the worst case?

Step 1: Understand what DFS (Depth-First Search) is. It is an algorithm used to explore nodes and edges of a graph or tree.
Step 2: Recognize that DFS can be implemented using recursion or an explicit stack.
Step 3: Identify that in the worst case, DFS may need to explore all vertices (V) in the graph.
Step 4: Realize that the maximum depth of the recursion or the maximum size of the stack will be equal to the number of vertices (V) in the graph.
Step 5: Conclude that the space used by the stack (either from recursion or explicit stack) is proportional to the number of vertices.
Step 6: Therefore, the space complexity of DFS in the worst case is O(V).

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