""" Greatest Common Divisor. Wikipedia reference: https://en.wikipedia.org/wiki/Greatest_common_divisor gcd(a, b) = gcd(a, -b) = gcd(-a, b) = gcd(-a, -b) by definition of divisibility """ def greatest_common_divisor(a: int, b: int) -> int: """ Calculate Greatest Common Divisor (GCD). >>> greatest_common_divisor(24, 40) 8 >>> greatest_common_divisor(1, 1) 1 >>> greatest_common_divisor(1, 800) 1 >>> greatest_common_divisor(11, 37) 1 >>> greatest_common_divisor(3, 5) 1 >>> greatest_common_divisor(16, 4) 4 >>> greatest_common_divisor(-3, 9) 3 >>> greatest_common_divisor(9, -3) 3 >>> greatest_common_divisor(3, -9) 3 >>> greatest_common_divisor(-3, -9) 3 """ return abs(b) if a == 0 else greatest_common_divisor(b % a, a) def gcd_by_iterative(x: int, y: int) -> int: """ Below method is more memory efficient because it does not create additional stack frames for recursive functions calls (as done in the above method). >>> gcd_by_iterative(24, 40) 8 >>> greatest_common_divisor(24, 40) == gcd_by_iterative(24, 40) True >>> gcd_by_iterative(-3, -9) 3 >>> gcd_by_iterative(3, -9) 3 >>> gcd_by_iterative(1, -800) 1 >>> gcd_by_iterative(11, 37) 1 """ while y: # --> when y=0 then loop will terminate and return x as final GCD. x, y = y, x % y return abs(x) def main(): """ Call Greatest Common Divisor function. """ try: nums = input("Enter two integers separated by comma (,): ").split(",") num_1 = int(nums[0]) num_2 = int(nums[1]) print( f"greatest_common_divisor({num_1}, {num_2}) = " f"{greatest_common_divisor(num_1, num_2)}" ) print(f"By iterative gcd({num_1}, {num_2}) = {gcd_by_iterative(num_1, num_2)}") except (IndexError, UnboundLocalError, ValueError): print("Wrong input") if __name__ == "__main__": main()