What is the space complexity of Depth-First Search (DFS) in the worst case?

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Question: What is the space complexity of Depth-First Search (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 space used for recursion or the explicit stack.

What is the space complexity of Depth-First Search (DFS) in the worst case?

What is the space complexity of Depth-First Search (DFS) in the worst case?

Step 1: Understand what Depth-First Search (DFS) 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 in the graph.
Step 5: Conclude that the space used for 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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