MagicSquare.java

// Copyright 2011 Hakan Kjellerstrand hakank@gmail.com
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
package com.google.ortools.contrib;

import com.google.ortools.Loader;
import com.google.ortools.constraintsolver.DecisionBuilder;
import com.google.ortools.constraintsolver.IntVar;
import com.google.ortools.constraintsolver.Solver;
import java.io.*;
import java.text.*;
import java.util.*;

public class MagicSquare {
  /** Solves the Magic Square problem. See http://www.hakank.org/google_or_tools/magic_square.py */
  private static void solve(int n, int num) {
    Solver solver = new Solver("MagicSquare");

    System.out.println("n: " + n);

    //
    // variables
    //
    IntVar[][] x = new IntVar[n][n];

    // for the branching
    IntVar[] x_flat = new IntVar[n * n];

    //
    // constraints
    //
    final long s = (n * (n * n + 1)) / 2;
    System.out.println("s: " + s);
    // IntVar s = solver.makeIntVar(0, n*n*n, "s");

    IntVar[] diag1 = new IntVar[n];
    IntVar[] diag2 = new IntVar[n];
    for (int i = 0; i < n; i++) {
      IntVar[] row = new IntVar[n];
      for (int j = 0; j < n; j++) {
        x[i][j] = solver.makeIntVar(1, n * n, "x[" + i + "," + j + "]");
        x_flat[i * n + j] = x[i][j];
        row[j] = x[i][j];
      }
      // sum row to s
      solver.addConstraint(solver.makeSumEquality(row, s));

      diag1[i] = x[i][i];
      diag2[i] = x[i][n - i - 1];
    }
    // sum diagonals to s
    solver.addConstraint(solver.makeSumEquality(diag1, s));
    solver.addConstraint(solver.makeSumEquality(diag2, s));

    // sum columns to s
    for (int j = 0; j < n; j++) {
      IntVar[] col = new IntVar[n];
      for (int i = 0; i < n; i++) {
        col[i] = x[i][j];
      }
      solver.addConstraint(solver.makeSumEquality(col, s));
    }

    // all are different
    solver.addConstraint(solver.makeAllDifferent(x_flat));

    // symmetry breaking: upper left is 1
    // solver.addConstraint(solver.makeEquality(x[0][0], 1));

    //
    // Solve
    //
    DecisionBuilder db =
        solver.makePhase(x_flat, solver.CHOOSE_FIRST_UNBOUND, solver.ASSIGN_CENTER_VALUE);
    solver.newSearch(db);
    int c = 0;
    while (solver.nextSolution()) {
      for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
          System.out.print(x[i][j].value() + " ");
        }
        System.out.println();
      }
      System.out.println();
      c++;
      if (num > 0 && c >= num) {
        break;
      }
    }
    solver.endSearch();

    // Statistics
    System.out.println();
    System.out.println("Solutions: " + solver.solutions());
    System.out.println("Failures: " + solver.failures());
    System.out.println("Branches: " + solver.branches());
    System.out.println("Wall time: " + solver.wallTime() + "ms");
  }

  public static void main(String[] args) throws Exception {
    Loader.loadNativeLibraries();
    int n = 4;
    int num = 0;

    if (args.length > 0) {
      n = Integer.parseInt(args[0]);
    }

    if (args.length > 1) {
      num = Integer.parseInt(args[1]);
    }

    MagicSquare.solve(n, num);
  }
}