Factorial (Recursive)

factorial(0) = 1, otherwise factorial(n) = n * factorial(n - 1). The smallest example of recursion with a single base case, used to visualise the call stack growing on descent and shrinking on unwind.

Algorithm

Canonical input n = 5 gives factorial(5) = 120. The replay shows six descent frames and five unwind frames (11 total).

Basic Implementation

basic.py

def factorial(n):
    if n == 0:
        return 1
    return n * factorial(n - 1)

result = factorial(5)
print(result)

Complexity

Time: O(n)
Space: O(n) call stack

Implementation notes

Python: no need to raise the recursion limit at this depth.
The replay shows the call-stack contents on each frame and the computed n * factorial(n-1) value on each unwind, matching the lesson spec.

descend then unwind Each non-base call awaits the result of the next call, then multiplies.