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/* -*- 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. stergard 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
*/
int
main(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
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