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April 2, 2016 16:52
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def egcd(a, b): | |
""" | |
References: https://en.wikibooks.org/wiki/Algorithm_Implementation/Mathematics/Extended_Euclidean_algorithm | |
""" | |
x, y, u, v = 0, 1, 1, 0 | |
while a != 0: | |
q, r = b // a, b % a | |
m, n = x - u * q, y - v * q | |
b, a, x, y, u, v = a, r, u, v, m, n | |
gcd = b | |
return gcd, x, y | |
def gcd(*numbers): | |
""" | |
Reference: https://gist.github.com/endolith/114336 | |
""" | |
from fractions import gcd | |
return reduce(gcd, numbers) | |
def lcm(numbers): | |
""" | |
Reference: https://gist.github.com/endolith/114336 | |
""" | |
def lcm(a, b): | |
return (a * b) // gcd(a, b) | |
return reduce(lcm, numbers, 1) | |
def generalized_crt(ak, nk): | |
""" | |
ak : Parameter, [a1, a2, ..., ak] | |
nk : Parameter, [n1, n2, ..., nk] | |
should be len(ak) == len(nk) | |
""" | |
assert len(ak) == len(nk) | |
N = reduce(lambda x, y: x * y, nk, 1) | |
l = lcm(nk) | |
s = 0 | |
for n, a in zip(nk, ak): | |
m = N / n | |
g, x, y = egcd(m, n) | |
s += (m / g) * x * a | |
s %= l | |
return s | |
if __name__ == "__main__": | |
x = 545 | |
a1, n1 = 101, 111 | |
a2, n2 = 6, 77 | |
a3, n3 = 35, 85 | |
print generalized_crt([a1, a2, a3], [n1, n2, n3]), x |
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http://elliptic-shiho.hatenablog.com/entry/2016/04/03/020117