recursion.py

# Recursion — a function that calls itself to solve a problem
# by breaking it into smaller instances of the same problem.
#
# Factorial is the classic example:
#   n! = n × (n-1) × (n-2) × ... × 1
#   0! = 1  (base case)
#
# Both iterative and recursive versions produce the same result.
# The recursive version directly mirrors the mathematical definition.


# --- Iterative ---

def factorial_iterative(n):
    result = 1
    for x in range(1, n + 1):
        result *= x
    return result


# --- Recursive ---
# Base case:     n == 0 or n == 1 → return 1
# Recursive case: n! = n × (n-1)!

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


if __name__ == '__main__':
    while True:
        try:
            n = int(input('Enter a non-negative integer: '))
            if n < 0:
                raise ValueError
            break
        except ValueError:
            print('Incorrect input, try again.')

    print(f'{n}! = {factorial_iterative(n)}  (iterative)')
    print(f'{n}! = {factorial_recursive(n)}  (recursive)')