mirror of
https://github.com/TheAlgorithms/Python.git
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a6831c898a
* add type hints to math/gcd * add doctest * math/gcd - run black formatter * math/gcd: remove manual doctest * add correction to gcd of negative numbers * add more doctest in iterative gcd
78 lines
2.0 KiB
Python
78 lines
2.0 KiB
Python
"""
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Greatest Common Divisor.
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Wikipedia reference: https://en.wikipedia.org/wiki/Greatest_common_divisor
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gcd(a, b) = gcd(a, -b) = gcd(-a, b) = gcd(-a, -b) by definition of divisibility
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"""
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def greatest_common_divisor(a: int, b: int) -> int:
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"""
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Calculate Greatest Common Divisor (GCD).
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>>> greatest_common_divisor(24, 40)
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8
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>>> greatest_common_divisor(1, 1)
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1
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>>> greatest_common_divisor(1, 800)
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1
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>>> greatest_common_divisor(11, 37)
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1
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>>> greatest_common_divisor(3, 5)
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1
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>>> greatest_common_divisor(16, 4)
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4
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>>> greatest_common_divisor(-3, 9)
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3
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>>> greatest_common_divisor(9, -3)
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3
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>>> greatest_common_divisor(3, -9)
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3
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>>> greatest_common_divisor(-3, -9)
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3
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"""
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return abs(b) if a == 0 else greatest_common_divisor(b % a, a)
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def gcd_by_iterative(x: int, y: int) -> int:
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"""
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Below method is more memory efficient because it does not create additional
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stack frames for recursive functions calls (as done in the above method).
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>>> gcd_by_iterative(24, 40)
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8
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>>> greatest_common_divisor(24, 40) == gcd_by_iterative(24, 40)
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True
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>>> gcd_by_iterative(-3, -9)
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3
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>>> gcd_by_iterative(3, -9)
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3
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>>> gcd_by_iterative(1, -800)
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1
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>>> gcd_by_iterative(11, 37)
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1
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"""
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while y: # --> when y=0 then loop will terminate and return x as final GCD.
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x, y = y, x % y
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return abs(x)
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def main():
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"""
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Call Greatest Common Divisor function.
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"""
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try:
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nums = input("Enter two integers separated by comma (,): ").split(",")
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num_1 = int(nums[0])
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num_2 = int(nums[1])
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print(
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f"greatest_common_divisor({num_1}, {num_2}) = "
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f"{greatest_common_divisor(num_1, num_2)}"
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)
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print(f"By iterative gcd({num_1}, {num_2}) = {gcd_by_iterative(num_1, num_2)}")
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except (IndexError, UnboundLocalError, ValueError):
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print("Wrong input")
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if __name__ == "__main__":
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main()
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