mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-12-18 01:00:15 +00:00
73 lines
1.3 KiB
Python
73 lines
1.3 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)
|
|
"""
|
|
|
|
# @Author: S. Sharma <silentcat>
|
|
# @Date: 2019-02-25T12:08:53-06:00
|
|
# @Email: silentcat@protonmail.com
|
|
# @Last modified by: PatOnTheBack
|
|
# @Last modified time: 2019-07-05
|
|
|
|
import sys
|
|
|
|
|
|
def extended_euclidean_algorithm(m, n):
|
|
"""
|
|
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)
|
|
"""
|
|
a = 0
|
|
a_prime = 1
|
|
b = 1
|
|
b_prime = 0
|
|
q = 0
|
|
r = 0
|
|
if m > n:
|
|
c = m
|
|
d = n
|
|
else:
|
|
c = n
|
|
d = m
|
|
|
|
while True:
|
|
q = int(c / d)
|
|
r = c % d
|
|
if r == 0:
|
|
break
|
|
c = d
|
|
d = r
|
|
|
|
t = a_prime
|
|
a_prime = a
|
|
a = t - q * a
|
|
|
|
t = b_prime
|
|
b_prime = b
|
|
b = t - q * b
|
|
|
|
pair = None
|
|
if m > n:
|
|
pair = (a, b)
|
|
else:
|
|
pair = (b, a)
|
|
return pair
|
|
|
|
|
|
def main():
|
|
"""Call Extended Euclidean Algorithm."""
|
|
if len(sys.argv) < 3:
|
|
print("2 integer arguments required")
|
|
exit(1)
|
|
m = int(sys.argv[1])
|
|
n = int(sys.argv[2])
|
|
print(extended_euclidean_algorithm(m, n))
|
|
|
|
|
|
if __name__ == "__main__":
|
|
main()
|