def multiplicative_persistence(num: int) -> int: """ Return the persistence of a given number. https://en.wikipedia.org/wiki/Persistence_of_a_number >>> multiplicative_persistence(217) 2 >>> multiplicative_persistence(-1) Traceback (most recent call last): ... ValueError: multiplicative_persistence() does not accept negative values >>> multiplicative_persistence("long number") Traceback (most recent call last): ... ValueError: multiplicative_persistence() only accepts integral values """ if not isinstance(num, int): raise ValueError("multiplicative_persistence() only accepts integral values") if num < 0: raise ValueError("multiplicative_persistence() does not accept negative values") steps = 0 num_string = str(num) while len(num_string) != 1: numbers = [int(i) for i in num_string] total = 1 for i in range(0, len(numbers)): total *= numbers[i] num_string = str(total) steps += 1 return steps def additive_persistence(num: int) -> int: """ Return the persistence of a given number. https://en.wikipedia.org/wiki/Persistence_of_a_number >>> additive_persistence(199) 3 >>> additive_persistence(-1) Traceback (most recent call last): ... ValueError: additive_persistence() does not accept negative values >>> additive_persistence("long number") Traceback (most recent call last): ... ValueError: additive_persistence() only accepts integral values """ if not isinstance(num, int): raise ValueError("additive_persistence() only accepts integral values") if num < 0: raise ValueError("additive_persistence() does not accept negative values") steps = 0 num_string = str(num) while len(num_string) != 1: numbers = [int(i) for i in num_string] total = 0 for i in range(0, len(numbers)): total += numbers[i] num_string = str(total) steps += 1 return steps if __name__ == "__main__": import doctest doctest.testmod()