mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-30 16:31:08 +00:00
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
"""
|
|
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()
|