019: Magic Squares and Sequences

//
// Copyright 2012 Hakan Kjellerstrand
//
// 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.

using System;
using Google.OrTools.ConstraintSolver;

public class MagicSquare
{

  /**
   *
   * Solves the Magic Square problem.
   * See http://www.hakank.org/or-tools/magic_square.py
   *
   */
  private static void Solve(int n = 4, int num = 0, int print = 1)
  {
    Solver solver = new Solver("MagicSquare");

    Console.WriteLine("n: {0}", n);

    //
    // Decision variables
    //
    IntVar[,] x = solver.MakeIntVarMatrix(n, n, 1, n*n, "x");
    // for the branching
    IntVar[] x_flat = x.Flatten();

    
    //
    // Constraints
    //
    long s = (n * (n * n + 1)) / 2;
    Console.WriteLine("s: " + 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++) {
        row[j] = x[i,j];
      }
      // sum row to s
      solver.Add(row.Sum() == s);

      diag1[i] = x[i,i];
      diag2[i] = x[i,n - i - 1];
    }

    // sum diagonals to s
    solver.Add(diag1.Sum() == s);
    solver.Add(diag2.Sum() == 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.Add(col.Sum() == s);
    }

    // all are different
    solver.Add(x_flat.AllDifferent());

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


    //
    // Search
    //

    DecisionBuilder db = solver.MakePhase(x_flat,
                                          Solver.CHOOSE_FIRST_UNBOUND,
                                          Solver.ASSIGN_CENTER_VALUE);


    solver.NewSearch(db);

    int c = 0;
    while (solver.NextSolution()) {
      if (print != 0) {
        for(int i = 0; i < n; i++) {
          for(int j = 0; j < n; j++) {
            Console.Write(x[i,j].Value() + " ");
          }
          Console.WriteLine();
        }
        Console.WriteLine();
      }

      c++;
      if (num > 0 && c >= num) {
        break;
      }
    }

    Console.WriteLine("\nSolutions: {0}", solver.Solutions());
    Console.WriteLine("WallTime: {0}ms", solver.WallTime());
    Console.WriteLine("Failures: {0}", solver.Failures());
    Console.WriteLine("Branches: {0} ", solver.Branches());

    solver.EndSearch();

  }

  public static void Main(String[] args)
  {
    int n = 4;
    int num = 0;
    int print = 1;

    if (args.Length > 0) {
      n = Convert.ToInt32(args[0]);
    }

    if (args.Length > 1) {
      num = Convert.ToInt32(args[1]);
    }

    if (args.Length > 2) {
      print = Convert.ToInt32(args[2]);
    }

    Solve(n, num, print);
  }
}