coins_grid.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 Google.OrTools.ConstraintSolver;

public class CoinsGrid
{

  /**
   *
   * Solves the Coins Grid problm.
   * See http://www.hakank.org/google_or_tools/coins_grid.py
   *
   */
  private static void Solve(int n = 31, int c = 14)
  {
    Solver solver = new Solver("CoinsGrid");

    //
    // Decision variables
    //
    IntVar[,] x = solver.MakeIntVarMatrix(n, n, 0, 1 , "x");
    IntVar[] x_flat = x.Flatten();

    //
    // Constraints
    //

    // sum row/columns == c
    for(int i = 0; i < n; i++) {
      IntVar[] row = new IntVar[n];
      IntVar[] col = new IntVar[n];
      for(int j = 0; j < n; j++) {
        row[j] = x[i,j];
        col[j] = x[j,i];
      }
      solver.Add(row.Sum() == c);
      solver.Add(col.Sum() == c);
    }

    // quadratic horizonal distance
    IntVar[] obj_tmp = new IntVar[n * n];
    for(int i = 0; i < n; i++) {
      for(int j = 0; j < n; j++) {
        obj_tmp[i * n + j] = (x[i,j] * (i - j) * (i - j)).Var();
      }
    }
    IntVar obj_var = obj_tmp.Sum().Var();

    //
    // Objective
    //
    OptimizeVar obj = obj_var.Minimize(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("obj: " + obj_var.Value());
      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 = 31;
    int c = 14;

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

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


    Solve(n, c);
  }
}