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

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

Options:

Correct Answer: O(n)

Solution:

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

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

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

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. Each time it calls itself, it adds a new layer to the stack.
Step 3: Identify the maximum depth of the recursion. This is how many times the function can call itself before reaching a base case.
Step 4: Realize that each function call uses some space in memory (for parameters, local variables, etc.).
Step 5: If the maximum depth of recursion is 'n', then the stack will have 'n' function calls at its deepest point.
Step 6: Conclude that the space used by the stack is proportional to the maximum depth, which is O(n).

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