created a recursion folder

recursions/...

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+

recursions/recursive_digit_sum.py

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