The answer
Yes, every recursive function call allocates memory on the system's Call Stack to store local variables and return addresses.
Space Complexity of the Call Stack in Recursion
Does recursion use extra memory?
More FAQs in Space Complexity of the Call Stack in Recursion
The space complexity is equal to the maximum depth of the recursion tree at any given time.
Although it makes O(2^N) total calls, the maximum depth of the tree at any one time is N. Therefore, the space complexity is O(N).
A loop executes within a single function frame, continuously reusing the same O(1) memory space for its variables, avoiding the Call Stack buildup entirely.
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