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48 lines
1.1 KiB
Plaintext
48 lines
1.1 KiB
Plaintext
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[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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std::tuple<Z, Z, 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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The tuple returned by the extended Euclidean algorithm contains, the greatest common divisor, /x/, and /y/, in that order:
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int m = 12;
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int n = 15;
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auto tup = extended_euclidean(m, n);
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int gcd = std::get<0>(tup);
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int x = std::get<1>(tup);
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int y = std::get<2>(tup);
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// mx + ny = gcd(m,n)
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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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http://www.boost.org/LICENSE_1_0.txt).
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]
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