mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-12-05 02:40:16 +00:00
cecf43d648
* Pyupgrade to Python 3.9
* updating DIRECTORY.md
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
86 lines
2.0 KiB
Python
86 lines
2.0 KiB
Python
"""
|
|
Extended Euclidean Algorithm.
|
|
|
|
Finds 2 numbers a and b such that it satisfies
|
|
the equation am + bn = gcd(m, n) (a.k.a Bezout's Identity)
|
|
|
|
https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm
|
|
"""
|
|
|
|
# @Author: S. Sharma <silentcat>
|
|
# @Date: 2019-02-25T12:08:53-06:00
|
|
# @Email: silentcat@protonmail.com
|
|
# @Last modified by: pikulet
|
|
# @Last modified time: 2020-10-02
|
|
from __future__ import annotations
|
|
|
|
import sys
|
|
|
|
|
|
def extended_euclidean_algorithm(a: int, b: int) -> tuple[int, int]:
|
|
"""
|
|
Extended Euclidean Algorithm.
|
|
|
|
Finds 2 numbers a and b such that it satisfies
|
|
the equation am + bn = gcd(m, n) (a.k.a Bezout's Identity)
|
|
|
|
>>> extended_euclidean_algorithm(1, 24)
|
|
(1, 0)
|
|
|
|
>>> extended_euclidean_algorithm(8, 14)
|
|
(2, -1)
|
|
|
|
>>> extended_euclidean_algorithm(240, 46)
|
|
(-9, 47)
|
|
|
|
>>> extended_euclidean_algorithm(1, -4)
|
|
(1, 0)
|
|
|
|
>>> extended_euclidean_algorithm(-2, -4)
|
|
(-1, 0)
|
|
|
|
>>> extended_euclidean_algorithm(0, -4)
|
|
(0, -1)
|
|
|
|
>>> extended_euclidean_algorithm(2, 0)
|
|
(1, 0)
|
|
|
|
"""
|
|
# base cases
|
|
if abs(a) == 1:
|
|
return a, 0
|
|
elif abs(b) == 1:
|
|
return 0, b
|
|
|
|
old_remainder, remainder = a, b
|
|
old_coeff_a, coeff_a = 1, 0
|
|
old_coeff_b, coeff_b = 0, 1
|
|
|
|
while remainder != 0:
|
|
quotient = old_remainder // remainder
|
|
old_remainder, remainder = remainder, old_remainder - quotient * remainder
|
|
old_coeff_a, coeff_a = coeff_a, old_coeff_a - quotient * coeff_a
|
|
old_coeff_b, coeff_b = coeff_b, old_coeff_b - quotient * coeff_b
|
|
|
|
# sign correction for negative numbers
|
|
if a < 0:
|
|
old_coeff_a = -old_coeff_a
|
|
if b < 0:
|
|
old_coeff_b = -old_coeff_b
|
|
|
|
return old_coeff_a, old_coeff_b
|
|
|
|
|
|
def main():
|
|
"""Call Extended Euclidean Algorithm."""
|
|
if len(sys.argv) < 3:
|
|
print("2 integer arguments required")
|
|
exit(1)
|
|
a = int(sys.argv[1])
|
|
b = int(sys.argv[2])
|
|
print(extended_euclidean_algorithm(a, b))
|
|
|
|
|
|
if __name__ == "__main__":
|
|
main()
|