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

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Question: What is the space complexity of a recursive function that uses stack space?

Options:

Correct Answer: O(n)

Solution:

The space complexity of a recursive function is O(n) due to the stack space used for each recursive call.

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

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

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 calls itself multiple times. Each time it calls itself, it uses some memory space.
Step 3: Identify that each recursive call adds a new layer to the call stack. This stack keeps track of all the active function calls.
Step 4: Determine how many times the function can call itself before reaching a base case. This is usually related to the size of the input, n.
Step 5: Conclude that if the function can call itself n times, the total stack space used will be proportional to n.
Step 6: Therefore, the space complexity of the recursive function is O(n), where n is the maximum depth of the recursion.

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