54 lines
1.0 KiB
Plaintext
54 lines
1.0 KiB
Plaintext
[section:extended_euclidean Extended Euclidean Algorithm]
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[section Introduction]
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The extended Euclidean algorithm solves the integer relation /mx + ny/ = gcd(/m/, /n/) for /x/ and /y/.
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[endsect]
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[section Synopsis]
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#include <boost/integer/extended_euclidean.hpp>
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namespace boost { namespace integer {
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template<class Z>
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struct euclidean_result_t {
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Z gcd;
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Z x;
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Z y;
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};
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template<class Z>
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euclidean_result_t<Z> extended_euclidean(Z m, Z n);
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}}
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[endsect]
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[section Usage]
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int m = 12;
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int n = 15;
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auto res = extended_euclidean(m, n);
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int gcd = res.gcd;
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int x = res.x;
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int y = res.y;
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// mx + ny = gcd(m,n) should now hold
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[endsect]
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[section References]
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Wagstaff, Samuel S., ['The Joy of Factoring], Vol. 68. American Mathematical Soc., 2013.
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[endsect]
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[endsect]
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[/
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Copyright 2018 Nick Thompson.
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Distributed under the Boost Software License, Version 1.0.
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(See accompanying file LICENSE_1_0.txt or copy at
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https://www.boost.org/LICENSE_1_0.txt).
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]
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