/* * choose.h * * 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 _CHOOSE_H #define _CHOOSE_H // 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]; } #endif

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