| Line | Branch | Exec | Source |
|---|---|---|---|
| 1 | /** | ||
| 2 | * \file | ||
| 3 | * \brief Calculation of binomial cefficients | ||
| 4 | *//* | ||
| 5 | * Copyright 2006 Nathan Hurst <njh@mail.csse.monash.edu.au> | ||
| 6 | * | ||
| 7 | * This library is free software; you can redistribute it and/or | ||
| 8 | * modify it either under the terms of the GNU Lesser General Public | ||
| 9 | * License version 2.1 as published by the Free Software Foundation | ||
| 10 | * (the "LGPL") or, at your option, under the terms of the Mozilla | ||
| 11 | * Public License Version 1.1 (the "MPL"). If you do not alter this | ||
| 12 | * notice, a recipient may use your version of this file under either | ||
| 13 | * the MPL or the LGPL. | ||
| 14 | * | ||
| 15 | * You should have received a copy of the LGPL along with this library | ||
| 16 | * in the file COPYING-LGPL-2.1; if not, write to the Free Software | ||
| 17 | * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA | ||
| 18 | * You should have received a copy of the MPL along with this library | ||
| 19 | * in the file COPYING-MPL-1.1 | ||
| 20 | * | ||
| 21 | * The contents of this file are subject to the Mozilla Public License | ||
| 22 | * Version 1.1 (the "License"); you may not use this file except in | ||
| 23 | * compliance with the License. You may obtain a copy of the License at | ||
| 24 | * http://www.mozilla.org/MPL/ | ||
| 25 | * | ||
| 26 | * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY | ||
| 27 | * OF ANY KIND, either express or implied. See the LGPL or the MPL for | ||
| 28 | * the specific language governing rights and limitations. | ||
| 29 | * | ||
| 30 | */ | ||
| 31 | |||
| 32 | #ifndef LIB2GEOM_SEEN_CHOOSE_H | ||
| 33 | #define LIB2GEOM_SEEN_CHOOSE_H | ||
| 34 | |||
| 35 | #include <vector> | ||
| 36 | |||
| 37 | namespace Geom { | ||
| 38 | |||
| 39 | /** | ||
| 40 | * @brief Given a multiple of binomial(n, k), modify it to the same multiple of binomial(n + 1, k). | ||
| 41 | */ | ||
| 42 | template <typename T> | ||
| 43 | constexpr void binomial_increment_n(T &b, int n, int k) | ||
| 44 | { | ||
| 45 | b = b * (n + 1) / (n + 1 - k); | ||
| 46 | } | ||
| 47 | |||
| 48 | /** | ||
| 49 | * @brief Given a multiple of binomial(n, k), modify it to the same multiple of binomial(n - 1, k). | ||
| 50 | */ | ||
| 51 | template <typename T> | ||
| 52 | 1960 | constexpr void binomial_decrement_n(T &b, int n, int k) | |
| 53 | { | ||
| 54 | 1960 | b = b * (n - k) / n; | |
| 55 | 1960 | } | |
| 56 | |||
| 57 | /** | ||
| 58 | * @brief Given a multiple of binomial(n, k), modify it to the same multiple of binomial(n, k + 1). | ||
| 59 | */ | ||
| 60 | template <typename T> | ||
| 61 | 475134 | constexpr void binomial_increment_k(T &b, int n, int k) | |
| 62 | { | ||
| 63 | 475134 | b = b * (n - k) / (k + 1); | |
| 64 | 475134 | } | |
| 65 | |||
| 66 | /** | ||
| 67 | * @brief Given a multiple of binomial(n, k), modify it to the same multiple of binomial(n, k - 1). | ||
| 68 | */ | ||
| 69 | template <typename T> | ||
| 70 | ✗ | constexpr void binomial_decrement_k(T &b, int n, int k) | |
| 71 | { | ||
| 72 | ✗ | b = b * k / (n + 1 - k); | |
| 73 | ✗ | } | |
| 74 | |||
| 75 | /** | ||
| 76 | * @brief Calculate the (n, k)th binomial coefficient. | ||
| 77 | */ | ||
| 78 | template <typename T> | ||
| 79 | constexpr T choose(unsigned n, unsigned k) | ||
| 80 | { | ||
| 81 | if (k > n) { | ||
| 82 | return 0; | ||
| 83 | } | ||
| 84 | T b = 1; | ||
| 85 | int max = std::min(k, n - k); | ||
| 86 | for (int i = 0; i < max; i++) { | ||
| 87 | binomial_increment_k(b, n, i); | ||
| 88 | } | ||
| 89 | return b; | ||
| 90 | } | ||
| 91 | |||
| 92 | /** | ||
| 93 | * @brief Class for calculating and accessing a row of Pascal's triangle. | ||
| 94 | */ | ||
| 95 | template <typename ValueType> | ||
| 96 | class BinomialCoefficient | ||
| 97 | { | ||
| 98 | public: | ||
| 99 | using value_type = ValueType; | ||
| 100 | using container_type = std::vector<value_type>; | ||
| 101 | |||
| 102 | BinomialCoefficient(unsigned int _n) | ||
| 103 | : n(_n) | ||
| 104 | { | ||
| 105 | coefficients.reserve(n / 2 + 1); | ||
| 106 | coefficients.emplace_back(1); | ||
| 107 | value_type b = 1; | ||
| 108 | for (int i = 0; i < n / 2; i++) { | ||
| 109 | binomial_increment_k(b, n, i); | ||
| 110 | coefficients.emplace_back(b); | ||
| 111 | } | ||
| 112 | } | ||
| 113 | |||
| 114 | unsigned int size() const | ||
| 115 | { | ||
| 116 | return degree() + 1; | ||
| 117 | } | ||
| 118 | |||
| 119 | unsigned int degree() const | ||
| 120 | { | ||
| 121 | return n; | ||
| 122 | } | ||
| 123 | |||
| 124 | value_type operator[](unsigned int k) const | ||
| 125 | { | ||
| 126 | return coefficients[std::min(k, n - k)]; | ||
| 127 | } | ||
| 128 | |||
| 129 | private: | ||
| 130 | int const n; | ||
| 131 | container_type coefficients; | ||
| 132 | }; | ||
| 133 | |||
| 134 | } // namespace Geom | ||
| 135 | |||
| 136 | #endif // LIB2GEOM_SEEN_CHOOSE_H | ||
| 137 | |||
| 138 | /* | ||
| 139 | Local Variables: | ||
| 140 | mode:c++ | ||
| 141 | c-file-style:"stroustrup" | ||
| 142 | c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +)) | ||
| 143 | indent-tabs-mode:nil | ||
| 144 | fill-column:99 | ||
| 145 | End: | ||
| 146 | */ | ||
| 147 | // vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:fileencoding=utf-8:textwidth=99 : | ||
| 148 |