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Diffstat (limited to 'include/2geom/choose.h')
-rw-r--r-- | include/2geom/choose.h | 147 |
1 files changed, 147 insertions, 0 deletions
diff --git a/include/2geom/choose.h b/include/2geom/choose.h new file mode 100644 index 0000000..106d04f --- /dev/null +++ b/include/2geom/choose.h @@ -0,0 +1,147 @@ +/** + * \file + * \brief Calculation of binomial cefficients + *//* + * Copyright 2006 Nathan Hurst <njh@mail.csse.monash.edu.au> + * + * This library is free software; you can redistribute it and/or + * modify it either under the terms of the GNU Lesser General Public + * License version 2.1 as published by the Free Software Foundation + * (the "LGPL") or, at your option, under the terms of the Mozilla + * Public License Version 1.1 (the "MPL"). If you do not alter this + * notice, a recipient may use your version of this file under either + * the MPL or the LGPL. + * + * You should have received a copy of the LGPL along with this library + * in the file COPYING-LGPL-2.1; if not, write to the Free Software + * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA + * You should have received a copy of the MPL along with this library + * in the file COPYING-MPL-1.1 + * + * The contents of this file are subject to the Mozilla Public License + * Version 1.1 (the "License"); you may not use this file except in + * compliance with the License. You may obtain a copy of the License at + * http://www.mozilla.org/MPL/ + * + * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY + * OF ANY KIND, either express or implied. See the LGPL or the MPL for + * the specific language governing rights and limitations. + * + */ + +#ifndef LIB2GEOM_SEEN_CHOOSE_H +#define LIB2GEOM_SEEN_CHOOSE_H + +#include <vector> + +namespace Geom { + +/** + * @brief Given a multiple of binomial(n, k), modify it to the same multiple of binomial(n + 1, k). + */ +template <typename T> +constexpr void binomial_increment_n(T &b, int n, int k) +{ + b = b * (n + 1) / (n + 1 - k); +} + +/** + * @brief Given a multiple of binomial(n, k), modify it to the same multiple of binomial(n - 1, k). + */ +template <typename T> +constexpr void binomial_decrement_n(T &b, int n, int k) +{ + b = b * (n - k) / n; +} + +/** + * @brief Given a multiple of binomial(n, k), modify it to the same multiple of binomial(n, k + 1). + */ +template <typename T> +constexpr void binomial_increment_k(T &b, int n, int k) +{ + b = b * (n - k) / (k + 1); +} + +/** + * @brief Given a multiple of binomial(n, k), modify it to the same multiple of binomial(n, k - 1). + */ +template <typename T> +constexpr void binomial_decrement_k(T &b, int n, int k) +{ + b = b * k / (n + 1 - k); +} + +/** + * @brief Calculate the (n, k)th binomial coefficient. + */ +template <typename T> +constexpr T choose(unsigned n, unsigned k) +{ + if (k > n) { + return 0; + } + T b = 1; + int max = std::min(k, n - k); + for (int i = 0; i < max; i++) { + binomial_increment_k(b, n, i); + } + return b; +} + +/** + * @brief Class for calculating and accessing a row of Pascal's triangle. + */ +template <typename ValueType> +class BinomialCoefficient +{ +public: + using value_type = ValueType; + using container_type = std::vector<value_type>; + + BinomialCoefficient(unsigned int _n) + : n(_n) + { + coefficients.reserve(n / 2 + 1); + coefficients.emplace_back(1); + value_type b = 1; + for (int i = 0; i < n / 2; i++) { + binomial_increment_k(b, n, i); + coefficients.emplace_back(b); + } + } + + unsigned int size() const + { + return degree() + 1; + } + + unsigned int degree() const + { + return n; + } + + value_type operator[](unsigned int k) const + { + return coefficients[std::min(k, n - k)]; + } + +private: + int const n; + container_type coefficients; +}; + +} // namespace Geom + +#endif // LIB2GEOM_SEEN_CHOOSE_H + +/* + Local Variables: + mode:c++ + c-file-style:"stroustrup" + c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +)) + indent-tabs-mode:nil + fill-column:99 + End: +*/ +// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:fileencoding=utf-8:textwidth=99 : |