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/* -*- mode: C++; c-basic-offset: 2; indent-tabs-mode: nil -*- */
/*
* Main authors:
* Christian Schulte <[email protected]>
*
* Copyright:
* Christian Schulte, 2001
*
* 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: Magic squares
*
* Compute magic squares of arbitrary size
*
* See problem 19 at http://www.csplib.org/.
*
* \ingroup Example
*
*/
class MagicSquare : public Script {
private:
/// Size of magic square
const int n;
/// Fields of square
IntVarArray x;
public:
/// Branching to use for model
enum {
BRANCH_SIZE, ///< Branch by size
BRANCH_AFC_SIZE ///< Branch by size over AFC
};
/// Post constraints
MagicSquare(const SizeOptions& opt)
: Script(opt), n(opt.size()), x(*this,n*n,1,n*n) {
// Number of fields on square
const int nn = n*n;
// Sum of all a row, column, or diagonal
const int s = nn*(nn+1) / (2*n);
// Matrix-wrapper for the square
Matrix<IntVarArray> m(x, n, n);
for (int i = n; i--; ) {
linear(*this, m.row(i), IRT_EQ, s, opt.ipl());
linear(*this, m.col(i), IRT_EQ, s, opt.ipl());
}
// Both diagonals must have sum s
{
IntVarArgs d1y(n);
IntVarArgs d2y(n);
for (int i = n; i--; ) {
d1y[i] = m(i,i);
d2y[i] = m(n-i-1,i);
}
linear(*this, d1y, IRT_EQ, s, opt.ipl());
linear(*this, d2y, IRT_EQ, s, opt.ipl());
}
// All fields must be distinct
distinct(*this, x, opt.ipl());
// Break some (few) symmetries
rel(*this, m(0,0), IRT_GR, m(0,n-1));
rel(*this, m(0,0), IRT_GR, m(n-1,0));
switch (opt.branching()) {
case BRANCH_SIZE:
branch(*this, x, INT_VAR_SIZE_MIN(), INT_VAL_SPLIT_MIN());
break;
case BRANCH_AFC_SIZE:
branch(*this, x, INT_VAR_AFC_SIZE_MAX(opt.decay()), INT_VAL_SPLIT_MIN());
break;
}
}
/// Constructor for cloning \a s
MagicSquare(MagicSquare& s) : Script(s), n(s.n) {
x.update(*this, s.x);
}
/// Copy during cloning
virtual Space*
copy(void) {
return new MagicSquare(*this);
}
/// Print solution
virtual void
print(std::ostream& os) const {
// Matrix-wrapper for the square
Matrix<IntVarArray> m(x, n, n);
for (int i = 0; i<n; i++) {
os << "\t";
for (int j = 0; j<n; j++) {
os.width(2);
os << m(i,j) << " ";
}
os << std::endl;
}
}
};
/** \brief Main-function
* \relates MagicSquare
*/
int
main(int argc, char* argv[]) {
SizeOptions opt("MagicSquare");
opt.iterations(1);
opt.size(7);
opt.branching(MagicSquare::BRANCH_SIZE);
opt.branching(MagicSquare::BRANCH_SIZE, "size");
opt.branching(MagicSquare::BRANCH_AFC_SIZE, "afc-size");
opt.parse(argc,argv);
Script::run<MagicSquare,DFS,SizeOptions>(opt);
return 0;
}
// STATISTICS: example-any