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58 lines
1.8 KiB
Python
58 lines
1.8 KiB
Python
"""
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The super digit problem is defined as follows:
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Given an integer n represented as a string and an integer k,
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the goal is to find the super digit of the number formed by concatenating
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the integer n k times.
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The super digit of a number is defined recursively:
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- If the number has only one digit, that digit is the super digit.
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- Otherwise, the super digit is the super digit of the sum of its digits.
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For example, for n = "9875" and k = 4, the concatenated number is:
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super_digit(9875987598759875), which can be reduced by summing its digits.
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"""
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from __future__ import annotations
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def super_digit(n_str: str, repetitions: int) -> int:
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"""
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Computes the super digit of a number formed by concatenating n_str repetitions times.
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Parameters:
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n_str (str): The string representation of the integer.
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repetitions (int): The number of times to concatenate n_str.
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Returns:
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int: The super digit of the concatenated number.
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>>> super_digit("148", 3)
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3
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>>> super_digit("9875", 4)
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8
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>>> super_digit("123", 3)
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9
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"""
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# Calculate the initial sum of the digits in n_str
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digit_sum = sum(int(digit) for digit in n_str)
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# Multiply the sum by repetitions
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total_sum = digit_sum * repetitions
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# Recursive function to find the super digit
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while total_sum >= 10:
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total_sum = sum(int(digit) for digit in str(total_sum))
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return total_sum
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if __name__ == '__main__':
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# Read input and split it into n_str and repetitions
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first_multiple_input = input().rstrip().split()
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n_str = first_multiple_input[0] # n as a string
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repetitions = int(first_multiple_input[1]) # repetitions as an integer
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# Call the super_digit function and print the result
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result = super_digit(n_str, repetitions)
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print(result)
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