magic_square_and_cards.cs

//
// 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 System.Collections;
using System.Collections.Generic;
using System.Linq;
using Google.OrTools.ConstraintSolver;


public class MagicSquareAndCards
{

  /**
   *
   * Magic squares and cards problem.
   *
   * Martin Gardner (July 1971)
   * """
   * Allowing duplicates values, what is the largest constant sum for an order-3
   * magic square that can be formed with nine cards from the deck.
   * """
   *
   *
   * Also see http://www.hakank.org/or-tools/magic_square_and_cards.py
   *
   */
  private static void Solve(int n=3)
  {

    Solver solver = new Solver("MagicSquareAndCards");

    IEnumerable<int> RANGE = Enumerable.Range(0, n);


    //
    // Decision variables
    //
    IntVar[,] x =  solver.MakeIntVarMatrix(n, n, 1, 13, "x");
    IntVar[] x_flat = x.Flatten();

    IntVar s = solver.MakeIntVar(1, 13*4, "s");
    IntVar[] counts = solver.MakeIntVarArray(14, 0, 4, "counts");

    //
    // Constraints
    //

    solver.Add(x_flat.Distribute(counts));

    // the standard magic square constraints (sans all_different)
    foreach(int i in RANGE) {
      // rows
      solver.Add( (from j in RANGE select x[i,j]).ToArray().Sum() == s);

      // columns
      solver.Add( (from j in RANGE select x[j,i]).ToArray().Sum() == s);
    }

    // diagonals
    solver.Add( (from i in RANGE select x[i,i]).ToArray().Sum() == s);
    solver.Add( (from i in RANGE select x[i,n-i-1]).ToArray().Sum() == s);


    // redundant constraint
    solver.Add(counts.Sum() == n*n);


    //
    // Objective
    //
    OptimizeVar obj = s.Maximize(1);

    //
    // Search
    //
    DecisionBuilder db = solver.MakePhase(x_flat,
                                          Solver.CHOOSE_FIRST_UNBOUND,
                                          Solver.ASSIGN_MAX_VALUE);

    solver.NewSearch(db, obj);

    while (solver.NextSolution()) {
      Console.WriteLine("s: {0}", s.Value());
      Console.Write("counts:");
      for(int i = 0; i < 14; i++) {
        Console.Write(counts[i].Value() + " ");
      }
      Console.WriteLine();
      for(int i = 0; i < n; i++) {
        for(int j = 0; j < n; j++) {
            Console.Write(x[i,j].Value() + " ");
        }
        Console.WriteLine();
      }
      Console.WriteLine();
    }

    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 = 3;

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

    Solve(n);
  }
}