126 lines
3.5 KiB
Java
126 lines
3.5 KiB
Java
// Copyright 2011 Hakan Kjellerstrand hakank@gmail.com
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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package com.google.ortools.contrib;
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import com.google.ortools.Loader;
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import com.google.ortools.constraintsolver.DecisionBuilder;
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import com.google.ortools.constraintsolver.IntVar;
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import com.google.ortools.constraintsolver.Solver;
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import java.io.*;
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import java.text.*;
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import java.util.*;
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public class MagicSquare {
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/** Solves the Magic Square problem. See http://www.hakank.org/google_or_tools/magic_square.py */
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private static void solve(int n, int num) {
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Solver solver = new Solver("MagicSquare");
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System.out.println("n: " + n);
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//
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// variables
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//
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IntVar[][] x = new IntVar[n][n];
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// for the branching
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IntVar[] x_flat = new IntVar[n * n];
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//
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// constraints
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//
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final long s = (n * (n * n + 1)) / 2;
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System.out.println("s: " + s);
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// IntVar s = solver.makeIntVar(0, n*n*n, "s");
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IntVar[] diag1 = new IntVar[n];
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IntVar[] diag2 = new IntVar[n];
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for (int i = 0; i < n; i++) {
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IntVar[] row = new IntVar[n];
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for (int j = 0; j < n; j++) {
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x[i][j] = solver.makeIntVar(1, n * n, "x[" + i + "," + j + "]");
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x_flat[i * n + j] = x[i][j];
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row[j] = x[i][j];
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}
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// sum row to s
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solver.addConstraint(solver.makeSumEquality(row, s));
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diag1[i] = x[i][i];
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diag2[i] = x[i][n - i - 1];
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}
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// sum diagonals to s
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solver.addConstraint(solver.makeSumEquality(diag1, s));
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solver.addConstraint(solver.makeSumEquality(diag2, s));
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// sum columns to s
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for (int j = 0; j < n; j++) {
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IntVar[] col = new IntVar[n];
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for (int i = 0; i < n; i++) {
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col[i] = x[i][j];
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}
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solver.addConstraint(solver.makeSumEquality(col, s));
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}
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// all are different
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solver.addConstraint(solver.makeAllDifferent(x_flat));
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// symmetry breaking: upper left is 1
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// solver.addConstraint(solver.makeEquality(x[0][0], 1));
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//
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// Solve
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//
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DecisionBuilder db =
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solver.makePhase(x_flat, solver.CHOOSE_FIRST_UNBOUND, solver.ASSIGN_CENTER_VALUE);
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solver.newSearch(db);
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int c = 0;
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while (solver.nextSolution()) {
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for (int i = 0; i < n; i++) {
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for (int j = 0; j < n; j++) {
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System.out.print(x[i][j].value() + " ");
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}
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System.out.println();
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}
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System.out.println();
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c++;
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if (num > 0 && c >= num) {
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break;
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}
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}
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solver.endSearch();
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// Statistics
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System.out.println();
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System.out.println("Solutions: " + solver.solutions());
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System.out.println("Failures: " + solver.failures());
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System.out.println("Branches: " + solver.branches());
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System.out.println("Wall time: " + solver.wallTime() + "ms");
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}
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public static void main(String[] args) throws Exception {
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Loader.loadNativeLibraries();
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int n = 4;
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int num = 0;
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if (args.length > 0) {
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n = Integer.parseInt(args[0]);
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}
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if (args.length > 1) {
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num = Integer.parseInt(args[1]);
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}
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MagicSquare.solve(n, num);
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}
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}
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