feat: This function uses the tail-recursive form of the Euclidean algorithm to calculate

Author: Acuspeedster

maths/gcd_of_n_numbers.py

@@ -1,6 +1,7 @@
 """
 Gcd of N Numbers
 Reference: https://en.wikipedia.org/wiki/Greatest_common_divisor
+Reference for tail recursion: https://www.geeksforgeeks.org/tail-recursion/
 """
 
 from collections import Counter
@@ -104,6 +105,51 @@ def get_greatest_common_divisor(*numbers: int) -> int:
         mult *= m
     return mult
 
+def gcd_tail_recursive(a: int, b: int) -> int:
+    """
+    Calculate the Greatest Common Divisor (GCD) using a tail-recursive approach.
+
+    This function uses the tail-recursive form of the Euclidean algorithm to calculate
+    the GCD of two integers `a` and `b`. The GCD is the largest integer that divides both
+    `a` and `b` without leaving a remainder.
+
+    Tail recursion is a form of recursion where the recursive call is the last operation
+    in the function. In languages that support tail call optimization, this allows the
+    function to be optimized by reusing the current function's stack frame for the
+    next call. Python, however, does not support tail call optimization, but using this
+    style can still help structure the recursion for better clarity.
+
+    Args:
+        a (int): The first integer.
+        b (int): The second integer.
+
+    Returns:
+        int: The greatest common divisor of `a` and `b`.
+
+    Raises:
+        ValueError: If both `a` and `b` are zero, as the GCD is not defined for this case.
+
+    Example:
+        >>> gcd_tail_recursive(24, 40)
+        8
+        >>> gcd_tail_recursive(11, 37)
+        1
+        >>> gcd_tail_recursive(0, 5)
+        5
+        >>> gcd_tail_recursive(5, 0)
+        5
+        >>> gcd_tail_recursive(0, 0)
+        ValueError: GCD is not defined for both a and b being zero.
+
+    Notes:
+        - gcd(a, 0) = abs(a)
+        - gcd(0, b) = abs(b)
+        - gcd(0, 0) is undefined.
+    """
+    if b == 0:
+        return abs(a)
+    return gcd_tail_recursive(b, a % b)
 
 if __name__ == "__main__":
     print(get_greatest_common_divisor(18, 45))  # 9
+    print(gcd_tail_recursive(23, 37))  # 1