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