/**
* Copyright (c) 1999-2014, Ecole des Mines de Nantes
* All rights reserved.
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* modification, are permitted provided that the following conditions are met:
*
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* * Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* * Neither the name of the Ecole des Mines de Nantes nor the
* names of its contributors may be used to endorse or promote products
* derived from this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND ANY
* EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
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*/
package samples.integer;
import org.kohsuke.args4j.Option;
import org.slf4j.LoggerFactory;
import samples.AbstractProblem;
import solver.Solver;
import solver.constraints.IntConstraintFactory;
import solver.search.strategy.IntStrategyFactory;
import solver.variables.BoolVar;
import solver.variables.VariableFactory;
import util.ESat;
import util.tools.ArrayUtils;
/**
* CSPLib: prob015:<br/>
* "The problem is to put n balls labelled {1,...n} into 3 boxes so that
* for any triple of balls (x,y,z) with x+y=z, not all are in the same box.
* This has a solution iff n < 14.
* <br/>
* One natural generalization is to consider partitioning into k boxes (for k>3)."
* <p/>
* <br/>
*
* @author Charles Prud'homme
* @since 19/08/11
*/
public class SchurLemma extends AbstractProblem {
@Option(name = "-n", usage = "Number of balls.", required = false)
int n = 43;
@Option(name = "-k", usage = "Number of boxes.", required = false)
int k = 4;
BoolVar[][] M;
@Override
public void createSolver() {
solver = new Solver();
}
@Override
public void buildModel() {
M = VariableFactory.boolMatrix("b", n, k, solver); // M_ij is true iff ball i is in box j
for (int i = 0; i < n; i++) {
solver.post(IntConstraintFactory.sum(M[i], VariableFactory.fixed(1, solver)));
}
for (int i = 0; i < k; i++) {
for (int x = 1; x <= n; x++) {
for (int y = 1; y <= n; y++) {
for (int z = 1; z <= n; z++) {
if (x + y == z)
solver.post(IntConstraintFactory.sum(new BoolVar[]{M[x - 1][i], M[y - 1][i], M[z - 1][i]}, VariableFactory.bounded("sum", 0, 2, solver)));
}
}
}
}
}
@Override
public void configureSearch() {
solver.set(IntStrategyFactory.lexico_LB(ArrayUtils.flatten(M)));
}
@Override
public void solve() {
solver.findSolution();
}
@Override
public void prettyOut() {
LoggerFactory.getLogger("bench").info("Schur's lemma ({},{})", new Object[]{n, k});
StringBuilder st = new StringBuilder();
if (solver.isFeasible() == ESat.TRUE) {
for (int i = 0; i < k; i++) {
st.append("\tBox #").append(i + 1).append(": ");
for (int j = 0; j < n; j++) {
if (M[j][i].getValue() > 0) {
st.append(j + 1).append(" ");
}
}
st.append("\n");
}
} else {
st.append("\tINFEASIBLE");
}
LoggerFactory.getLogger("bench").info(st.toString());
}
public static void main(String[] args) {
new SchurLemma().execute(args);
}
}