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73 lines
1.3 KiB
Python
73 lines
1.3 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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"""
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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: PatOnTheBack
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# @Last modified time: 2019-07-05
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import sys
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def extended_euclidean_algorithm(m, n):
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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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"""
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a = 0
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a_prime = 1
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b = 1
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b_prime = 0
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q = 0
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r = 0
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if m > n:
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c = m
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d = n
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else:
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c = n
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d = m
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while True:
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q = int(c / d)
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r = c % d
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if r == 0:
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break
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c = d
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d = r
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t = a_prime
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a_prime = a
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a = t - q * a
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t = b_prime
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b_prime = b
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b = t - q * b
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pair = None
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if m > n:
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pair = (a, b)
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else:
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pair = (b, a)
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return pair
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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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m = int(sys.argv[1])
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n = int(sys.argv[2])
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print(extended_euclidean_algorithm(m, n))
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if __name__ == "__main__":
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main()
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