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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()

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