What is the space complexity of DFS using a recursive approach?

What is the space complexity of DFS using a recursive approach?

Step 1: Understand what DFS (Depth-First Search) is. It is a method for exploring nodes and edges of a graph or tree.
Step 2: Recognize that DFS can be implemented using recursion, which means the function calls itself to explore deeper into the graph.
Step 3: When a function is called in recursion, it uses a part of the computer's memory called the call stack.
Step 4: Each time the DFS function calls itself, a new layer is added to the call stack.
Step 5: The maximum depth of the call stack corresponds to the maximum number of nodes that can be on the stack at one time.
Step 6: In the worst case, the maximum depth of the call stack is equal to the number of vertices (V) in the graph.
Step 7: Therefore, the space used by the call stack in the recursive DFS is proportional to the number of vertices.
Step 8: This leads us to conclude that the space complexity of DFS using a recursive approach is O(V).

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