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dominating-queens.cpp

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00001 /* -*- mode: C++; c-basic-offset: 2; indent-tabs-mode: nil -*- */
00002 /*
00003  *  Main authors:
00004  *     Christian Schulte <schulte@gecode.org>
00005  *
00006  *  Copyright:
00007  *     Christian Schulte, 2011
00008  *
00009  *  This file is part of Gecode, the generic constraint
00010  *  development environment:
00011  *     http://www.gecode.org
00012  *
00013  *  Permission is hereby granted, free of charge, to any person obtaining
00014  *  a copy of this software and associated documentation files (the
00015  *  "Software"), to deal in the Software without restriction, including
00016  *  without limitation the rights to use, copy, modify, merge, publish,
00017  *  distribute, sublicense, and/or sell copies of the Software, and to
00018  *  permit persons to whom the Software is furnished to do so, subject to
00019  *  the following conditions:
00020  *
00021  *  The above copyright notice and this permission notice shall be
00022  *  included in all copies or substantial portions of the Software.
00023  *
00024  *  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
00025  *  EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
00026  *  MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
00027  *  NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
00028  *  LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
00029  *  OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
00030  *  WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
00031  *
00032  */
00033 
00034 #include <gecode/driver.hh>
00035 #include <gecode/int.hh>
00036 #include <gecode/minimodel.hh>
00037 
00038 using namespace Gecode;
00039 
00053 class DominatingQueens : public IntMinimizeScript {
00054 protected:
00056   const int n;
00058   IntVarArray b;
00060   IntVar q;
00062   int xy(int x, int y) const {
00063     return y*n + x;
00064   }
00066   int x(int xy) const {
00067     return xy % n;
00068   }
00070   int y(int xy) const {
00071     return xy / n;
00072   }
00074   IntSet attacked(int xy) {
00075     IntArgs a;
00076     for (int i=0; i<n; i++)
00077       for (int j=0; j<n; j++)
00078         if ((i == x(xy)) || // Same row
00079             (j == y(xy)) || // Same column
00080             (abs(i-x(xy)) == abs(j-y(xy)))) // Same diagonal
00081           a << DominatingQueens::xy(i,j);
00082     return IntSet(a);
00083   }
00084 public:
00086   DominatingQueens(const SizeOptions& opt)
00087     : IntMinimizeScript(opt),
00088       n(opt.size()), b(*this,n*n,0,n*n-1), q(*this,1,n) {
00089 
00090     // Constrain field to the fields that can attack a field
00091     for (int i=0; i<n*n; i++)
00092       dom(*this, b[i], attacked(i));
00093 
00094     // At most q queens can be placed
00095     nvalues(*this, b, IRT_LQ, q);
00096 
00097     /*
00098      * According to: P. R. J. Ístergard and W. D. Weakley, Values
00099      * of Domination Numbers of the Queen's Graph, Electronic Journal
00100      * of Combinatorics, 8:1-19, 2001, for n <= 120, the minimal number
00101      * of queens is either ceil(n/2) or ceil(n/2 + 1).
00102      */
00103     if (n <= 120)
00104       dom(*this, q, (n+1)/2, (n+1)/2 + 1);
00105 
00106     branch(*this, b, INT_VAR_SIZE_MIN(), INT_VAL_MIN());
00107     // Try the easier solution first
00108     branch(*this, q, INT_VAL_MAX());
00109   }
00110 
00112   virtual IntVar cost(void) const {
00113     return q;
00114   }
00115 
00117   DominatingQueens(DominatingQueens& s)
00118     : IntMinimizeScript(s), n(s.n) {
00119     b.update(*this, s.b);
00120     q.update(*this, s.q);
00121   }
00122 
00124   virtual Space*
00125   copy(void) {
00126     return new DominatingQueens(*this);
00127   }
00128 
00130   virtual void
00131   print(std::ostream& os) const {
00132     os << "\tNumber of Queens: " << q << std::endl;
00133     os << "\tBoard: " << b << std::endl;
00134     if (b.assigned()) {
00135       // Print a nice board
00136       bool* placed = new bool[n*n];
00137       for (int i=0; i<n*n; i++)
00138         placed[i] = false;
00139       for (int i=0; i<n*n; i++)
00140         placed[b[i].val()] = true;
00141       for (int j=0; j<n; j++) {
00142         std::cout << "\t\t";
00143         for (int i=0; i<n; i++)
00144           std::cout << (placed[xy(i,j)] ? 'Q' : '.') << ' ';
00145         std::cout << std::endl;
00146       }
00147       delete [] placed;
00148     }
00149     os << std::endl;
00150   }
00151 };
00152 
00156 int
00157 main(int argc, char* argv[]) {
00158   SizeOptions opt("DominatingQueens");
00159   opt.size(7);
00160   opt.solutions(0);
00161   opt.parse(argc,argv);
00162   IntMinimizeScript::run<DominatingQueens,BAB,SizeOptions>(opt);
00163   return 0;
00164 }
00165 
00166 // STATISTICS: example-any
00167