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/**
* \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 :
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