What is the space complexity of a recursive function that uses a stack to perfor

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Question: What is the space complexity of a recursive function that uses a stack to perform depth-first search on a graph?

Options:

Correct Answer: O(n)

Solution:

The space complexity is O(n) due to the maximum depth of the recursion stack in the worst case.

What is the space complexity of a recursive function that uses a stack to perform depth-first search on a graph?

What is the space complexity of a recursive function that uses a stack to perform depth-first search on a graph?

Step 1: Understand what space complexity means. It refers to the amount of memory space required by an algorithm as a function of the input size.
Step 2: Recognize that a recursive function uses a call stack to keep track of function calls.
Step 3: In a depth-first search (DFS) on a graph, the function may go as deep as the number of nodes in the longest path from the starting node to a leaf node.
Step 4: The maximum depth of the recursion stack corresponds to the maximum number of function calls that can be active at the same time.
Step 5: In the worst case, this maximum depth can be equal to the number of nodes in the graph, which we denote as 'n'.
Step 6: Therefore, the space used by the recursion stack in the worst case is O(n).

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