122 lines
4.2 KiB
Java
122 lines
4.2 KiB
Java
/**
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* Copyright (c) 1999-2011, Ecole des Mines de Nantes
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* All rights reserved.
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions are met:
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*
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* * Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* * Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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* * Neither the name of the Ecole des Mines de Nantes nor the
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* names of its contributors may be used to endorse or promote products
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* derived from this software without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND ANY
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* EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
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* WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
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* DISCLAIMED. IN NO EVENT SHALL THE REGENTS AND CONTRIBUTORS BE LIABLE FOR ANY
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* DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
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* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
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* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*/
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import com.google.ortools.constraintsolver.*;
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/**
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* Partition n numbers into two groups, so that
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* - the sum of the first group equals the sum of the second,
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* - and the sum of the squares of the first group equals the sum of
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* the squares of the second
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* <br/>
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*
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* @author Charles Prud'homme
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* @since 18/03/11
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*/
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public class Partition {
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static {
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System.loadLibrary("jniortools");
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}
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/**
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* Partition Problem.
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*/
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private static void solve(int m) {
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Solver solver = new Solver("Partition " + m);
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IntVar[] x, y;
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x = solver.makeIntVarArray(m, 1, 2 * m, "x");
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y = solver.makeIntVarArray(m, 1, 2 * m, "y");
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// break symmetries
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for (int i = 0; i < m - 1; i++) {
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solver.addConstraint(solver.makeLess(x[i], x[i + 1]));
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solver.addConstraint(solver.makeLess(y[i], y[i + 1]));
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}
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solver.addConstraint(solver.makeLess(x[0], y[0]));
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IntVar[] xy = new IntVar[2 * m];
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for (int i = m - 1; i >= 0; i--) {
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xy[i] = x[i];
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xy[m + i] = y[i];
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}
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solver.addConstraint(solver.makeAllDifferent(xy));
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int[] coeffs = new int[2 * m];
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for (int i = m - 1; i >= 0; i--) {
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coeffs[i] = 1;
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coeffs[m + i] = -1;
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}
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solver.addConstraint(solver.makeScalProdEquality(xy, coeffs, 0));
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IntVar[] sxy, sx, sy;
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sxy = new IntVar[2 * m];
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sx = new IntVar[m];
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sy = new IntVar[m];
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for (int i = m - 1; i >= 0; i--) {
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sx[i] = solver.makeSquare(x[i]).var();
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sxy[i] = sx[i];
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sy[i] = solver.makeSquare(y[i]).var();
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sxy[m + i] = sy[i];
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}
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solver.addConstraint(solver.makeScalProdEquality(sxy, coeffs, 0));
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solver.addConstraint(
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solver.makeSumEquality(x, 2 * m * (2 * m + 1) / 4));
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solver.addConstraint(
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solver.makeSumEquality(y, 2 * m * (2 * m + 1) / 4));
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solver.addConstraint(
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solver.makeSumEquality(sx, 2 * m * (2 * m + 1) * (4 * m + 1) / 12));
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solver.addConstraint(
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solver.makeSumEquality(sy, 2 * m * (2 * m + 1) * (4 * m + 1) / 12));
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DecisionBuilder db = solver.makeDefaultPhase(xy);
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SolutionCollector collector = solver.makeFirstSolutionCollector();
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collector.add(xy);
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SearchMonitor log = solver.makeSearchLog(10000);
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solver.newSearch(db, log, collector);
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solver.nextSolution();
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System.out.println("Solution solution");
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for (int i = 0; i < m; ++i) {
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System.out.print("[" + collector.value(0, xy[i]) + "] ");
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}
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System.out.printf("\n");
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for (int i = 0; i < m; ++i) {
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System.out.print("[" + collector.value(0, xy[m+i]) + "] ");
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}
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System.out.println();
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}
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public static void main(String[] args) throws Exception {
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Partition.solve(32);
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}
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}
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