get_recursive_digit_sum.py

"""
We define super digit of an integer x using the following rules:
- If x has only 1 digit, then its super digit is x.
- Otherwise, the super digit of x is equal to the super digit of the digit-sum of x.
    Here, digit-sum of a number is defined as the sum of its digits.
You are given two numbers n and k. You have to calculate the super digit of P.
P is created when number n is concatenated k times.
"""


def get_recursive_digit_sum(number, repeats):
    """
    Returns the super digit of a number that is created
    by concatenating number repeats times
    """

    number_superdigit = __get_recursive_digit_sum(number)
    return __get_recursive_digit_sum(str(number_superdigit) * repeats)


def __get_recursive_digit_sum(number):
    if len(number) < 1:
        return 0
    if len(number) < 2:
        return int(number)

    digit_sum = 0
    for digit in number:
        digit_sum += int(digit)
    return __get_recursive_digit_sum(str(digit_sum))