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math/greatest_common_divisor: add support for negative numbers (#2628)

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* 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
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Joyce 2020-10-29 00:17:26 -07:00 committed by GitHub
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maths/greatest_common_divisor.py
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@ -2,10 +2,12 @@
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, b):
def greatest_common_divisor(a: int, b: int) -> int:
"""
Calculate Greatest Common Divisor (GCD).
>>> greatest_common_divisor(24, 40)
@ -20,31 +22,44 @@ def greatest_common_divisor(a, b):
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 b if a == 0 else greatest_common_divisor(b % a, a)
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 use the stack (chunk of
memory). While above method is good, uses more memory for huge numbers because of the
recursive calls required to calculate the greatest common divisor.
"""
def gcd_by_iterative(x, y):
"""
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 x
return abs(x)
def main():
"""Call Greatest Common Divisor function."""
"""
Call Greatest Common Divisor function.
"""
try:
nums = input("Enter two integers separated by comma (,): ").split(",")
num_1 = int(nums[0])