Python/maths/extended_euclidean_algorithm.py
CenTdemeern1 04698538d8
Misc fixes across multiple algorithms ()
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Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Dhruv Manilawala <dhruvmanila@gmail.com>
2022-10-16 10:55:38 +05:30

87 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")
return 1
a = int(sys.argv[1])
b = int(sys.argv[2])
print(extended_euclidean_algorithm(a, b))
return 0
if __name__ == "__main__":
raise SystemExit(main())