mathdatech/Python
1
0
Fork 0
mirror of https://github.com/TheAlgorithms/Python.git synced 2024-11-23 21:11:08 +00:00
Code Issues Packages Projects Releases Wiki Activity

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

Browse Source 
* 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
This commit is contained in:
Joyce 2020-10-29 00:17:26 -07:00 committed by GitHub
parent 99adac0eb1
commit a6831c898a
No known key found for this signature in database
GPG Key ID: 4AEE18F83AFDEB23
1 changed files with 27 additions and 12 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

39
maths/greatest_common_divisor.py
View File

@ -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)
"""
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):
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 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])