org.chocosolver.samples.integer.SchurLemma Maven / Gradle / Ivy

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/**
 * Copyright (c) 2015, Ecole des Mines de Nantes
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. 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.
 * 3. All advertising materials mentioning features or use of this software
 *    must display the following acknowledgement:
 *    This product includes software developed by the .
 * 4. Neither the name of the  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  ''AS IS'' AND ANY
 * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
 * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
 * DISCLAIMED. IN NO EVENT SHALL  BE LIABLE FOR ANY
 * DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
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package org.chocosolver.samples.integer;

import org.chocosolver.samples.AbstractProblem;
import org.chocosolver.solver.Solver;
import org.chocosolver.solver.constraints.IntConstraintFactory;
import org.chocosolver.solver.search.strategy.IntStrategyFactory;
import org.chocosolver.solver.variables.BoolVar;
import org.chocosolver.solver.variables.VariableFactory;
import org.chocosolver.util.ESat;
import org.chocosolver.util.tools.ArrayUtils;
import org.kohsuke.args4j.Option;

/**
 * CSPLib: prob015:

 * "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.
 * 

 * One natural generalization is to consider partitioning into k boxes (for k>3)."
 * 
 * 

 *
 * @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() {
        System.out.println(String.format("Schur's lemma (%d,%d)", 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");
        }
        System.out.println(st.toString());
    }

    public static void main(String[] args) {
        new SchurLemma().execute(args);
    }
}