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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 {
// XXX: Can we keep only the left terms easily?
// this would more than halve the array
// row index becomes n2 = n/2, row2 = n2*(n2+1)/2, row = row2*2+(n&1)?n2:0
// we could also leave off the ones
template <typename T>
T choose(unsigned n, unsigned k) {
static std::vector<T> pascals_triangle;
static unsigned rows_done = 0;
// indexing is (0,0,), (1,0), (1,1), (2, 0)...
// to get (i, j) i*(i+1)/2 + j
if(/*k < 0 ||*/ k > n) return 0;
if(rows_done <= n) {// we haven't got there yet
if(rows_done == 0) {
pascals_triangle.push_back(1);
rows_done = 1;
}
while(rows_done <= n) {
unsigned p = pascals_triangle.size() - rows_done;
pascals_triangle.push_back(1);
for(unsigned i = 0; i < rows_done-1; i++) {
pascals_triangle.push_back(pascals_triangle[p]
+ pascals_triangle[p+1]);
p++;
}
pascals_triangle.push_back(1);
rows_done ++;
}
}
unsigned row = (n*(n+1))/2;
return pascals_triangle[row+k];
}
// Is it faster to store them or compute them on demand?
/*template <typename T>
T choose(unsigned n, unsigned k) {
T r = 1;
for(unsigned i = 1; i <= k; i++)
r = (r*(n-k+i))/i;
return r;
}*/
template <typename ValueType>
class BinomialCoefficient
{
public:
typedef ValueType value_type;
typedef std::vector<value_type> container_type;
BinomialCoefficient(unsigned int _n)
: n(_n), m(n >> 1)
{
coefficients.reserve(m+1);
coefficients.push_back(1);
int h = m + 1;
value_type bct = 1;
for (int i = 1; i < h; ++i)
{
bct *= (n-i+1);
bct /= i;
coefficients.push_back(bct);
}
}
unsigned int size() const
{
return degree() +1;
}
unsigned int degree() const
{
return n;
}
value_type operator[] (unsigned int k) const
{
if (k > m) k = n - k;
return coefficients[k];
}
private:
const int n;
const unsigned int m;
container_type coefficients;
};
} // end 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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