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123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168/* -*- mode: C++; c-basic-offset: 2; indent-tabs-mode: nil -*- *//* * Main authors: * Christian Schulte <schulte@gecode.org> * * Copyright: * Christian Schulte, 2011 * * This file is part of Gecode, the generic constraint * development environment: * http://www.gecode.org * * Permission is hereby granted, free of charge, to any person obtaining * a copy of this software and associated documentation files (the * "Software"), to deal in the Software without restriction, including * without limitation the rights to use, copy, modify, merge, publish, * distribute, sublicense, and/or sell copies of the Software, and to * permit persons to whom the Software is furnished to do so, subject to * the following conditions: * * The above copyright notice and this permission notice shall be * included in all copies or substantial portions of the Software. * * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE * LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION * OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION * WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. * */
#include <gecode/driver.hh>#include <gecode/int.hh>#include <gecode/minimodel.hh>
using namespace Gecode;
/** * \brief %Example: Dominating Queens * * Place a number of queens on a n times n chessboard such that * each squares is either attacked or occupied by a queen. * * The model is taken from: C. Bessiere, E. Hebrard, B. Hnich, * Z. Kiziltan, and T. Walsh, Filtering Algorithms for the NValue * Constraint, Constraints, 11(4), 271-293, 2006. * * \ingroup Example * */class DominatingQueens : public IntMinimizeScript {protected: /// Size of the board const int n; /// Fields on the board IntVarArray b; /// Number of queens IntVar q; /// Compute coordinate pair from \a x and \a y int xy(int x, int y) const { return y*n + x; } /// Compute x coordinate from pair \a xy int x(int xy) const { return xy % n; } /// Compute y coordinate from pair \a xy int y(int xy) const { return xy / n; } /// Compute set of fields that can be attacked by \a xy IntSet attacked(int xy) { IntArgs a; for (int i=0; i<n; i++) for (int j=0; j<n; j++) if ((i == x(xy)) || // Same row (j == y(xy)) || // Same column (abs(i-x(xy)) == abs(j-y(xy)))) // Same diagonal a << DominatingQueens::xy(i,j); return IntSet(a); }public: /// The actual problem DominatingQueens(const SizeOptions& opt) : IntMinimizeScript(opt), n(opt.size()), b(*this,n*n,0,n*n-1), q(*this,1,n) {
// Constrain field to the fields that can attack a field for (int i=0; i<n*n; i++) dom(*this, b[i], attacked(i));
// At most q queens can be placed nvalues(*this, b, IRT_LQ, q);
/* * According to: P. R. J. Östergard and W. D. Weakley, Values * of Domination Numbers of the Queen's Graph, Electronic Journal * of Combinatorics, 8:1-19, 2001, for n <= 120, the minimal number * of queens is either ceil(n/2) or ceil(n/2 + 1). */ if (n <= 120) dom(*this, q, (n+1)/2, (n+1)/2 + 1);
branch(*this, b, INT_VAR_SIZE_MIN(), INT_VAL_MIN()); // Try the easier solution first branch(*this, q, INT_VAL_MAX()); }
/// Return cost virtual IntVar cost(void) const { return q; }
/// Constructor for cloning \a s DominatingQueens(DominatingQueens& s) : IntMinimizeScript(s), n(s.n) { b.update(*this, s.b); q.update(*this, s.q); }
/// Perform copying during cloning virtual Space* copy(void) { return new DominatingQueens(*this); }
/// Print solution virtual void print(std::ostream& os) const { os << "\tNumber of Queens: " << q << std::endl; os << "\tBoard: " << b << std::endl; if (b.assigned()) { // Print a nice board bool* placed = new bool[n*n]; for (int i=0; i<n*n; i++) placed[i] = false; for (int i=0; i<n*n; i++) placed[b[i].val()] = true; for (int j=0; j<n; j++) { std::cout << "\t\t"; for (int i=0; i<n; i++) std::cout << (placed[xy(i,j)] ? 'Q' : '.') << ' '; std::cout << std::endl; } delete [] placed; } os << std::endl; }};
/** \brief Main-function * \relates DominatingQueens */intmain(int argc, char* argv[]) { SizeOptions opt("DominatingQueens"); opt.size(7); opt.solutions(0); opt.parse(argc,argv); IntMinimizeScript::run<DominatingQueens,BAB,SizeOptions>(opt); return 0;}
// STATISTICS: example-any