def double_factorial_recursive(n: int) -> int: """ Compute double factorial using recursive method. Recursion can be costly for large numbers. To learn about the theory behind this algorithm: https://en.wikipedia.org/wiki/Double_factorial >>> from math import prod >>> all(double_factorial_recursive(i) == prod(range(i, 0, -2)) for i in range(20)) True >>> double_factorial_recursive(0.1) Traceback (most recent call last): ... ValueError: double_factorial_recursive() only accepts integral values >>> double_factorial_recursive(-1) Traceback (most recent call last): ... ValueError: double_factorial_recursive() not defined for negative values """ if not isinstance(n, int): raise ValueError("double_factorial_recursive() only accepts integral values") if n < 0: raise ValueError("double_factorial_recursive() not defined for negative values") return 1 if n <= 1 else n * double_factorial_recursive(n - 2) def double_factorial_iterative(num: int) -> int: """ Compute double factorial using iterative method. To learn about the theory behind this algorithm: https://en.wikipedia.org/wiki/Double_factorial >>> from math import prod >>> all(double_factorial_iterative(i) == prod(range(i, 0, -2)) for i in range(20)) True >>> double_factorial_iterative(0.1) Traceback (most recent call last): ... ValueError: double_factorial_iterative() only accepts integral values >>> double_factorial_iterative(-1) Traceback (most recent call last): ... ValueError: double_factorial_iterative() not defined for negative values """ if not isinstance(num, int): raise ValueError("double_factorial_iterative() only accepts integral values") if num < 0: raise ValueError("double_factorial_iterative() not defined for negative values") value = 1 for i in range(num, 0, -2): value *= i return value if __name__ == "__main__": import doctest doctest.testmod()