futoshiki.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 Futoshiki
{

  /**
   *
   * Futoshiki problem.
   *
   * From http://en.wikipedia.org/wiki/Futoshiki
   * """
   * The puzzle is played on a square grid, such as 5 x 5. The objective
   * is to place the numbers 1 to 5 (or whatever the dimensions are)
   * such that each row, and column contains each of the digits 1 to 5.
   * Some digits may be given at the start. In addition, inequality
   * constraints are also initially specifed between some of the squares,
   * such that one must be higher or lower than its neighbour. These
   * constraints must be honoured as the grid is filled out.
   * """
   *
   * Also see http://www.hakank.org/or-tools/futoshiki.py
   *
   */
  private static void Solve(int[,] values, int[,] lt)
  {

    Solver solver = new Solver("Futoshiki");

    int size = values.GetLength(0);
    IEnumerable<int> RANGE = Enumerable.Range(0, size);
    IEnumerable<int> NUMQD = Enumerable.Range(0, lt.GetLength(0));

    //
    // Decision variables
    //
    IntVar[,] field =  solver.MakeIntVarMatrix(size, size, 1, size, "field");
    IntVar[] field_flat = field.Flatten();

    //
    // Constraints
    //


    // set initial values
    foreach(int row in RANGE) {
      foreach(int col in RANGE) {
        if (values[row,col] > 0) {
          solver.Add(field[row,col] == values[row,col]);
        }
      }
    }


    // all rows have to be different
    foreach(int row in RANGE) {
      solver.Add((from col in RANGE
                  select field[row,col]).ToArray().AllDifferent());
    }


    // all columns have to be different
    foreach(int col in RANGE) {
      solver.Add((from row in RANGE
                  select field[row,col]).ToArray().AllDifferent());
    }


    // all < constraints are satisfied
    // Also: make 0-based
    foreach(int i in NUMQD) {
      solver.Add(field[ lt[i,0]-1, lt[i,1]-1 ] <
                 field[ lt[i,2]-1, lt[i,3]-1 ] );
    }




    //
    // Search
    //
    DecisionBuilder db = solver.MakePhase(field_flat,
                                          Solver.CHOOSE_FIRST_UNBOUND,
                                          Solver.ASSIGN_MIN_VALUE);

    solver.NewSearch(db);

    while (solver.NextSolution()) {
      foreach(int i in RANGE) {
        foreach(int j in RANGE) {
          Console.Write("{0} ", field[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)
  {

    //
    // Example from Tailor model futoshiki.param/futoshiki.param
    // Solution:
    // 5 1 3 2 4
    // 1 4 2 5 3
    // 2 3 1 4 5
    // 3 5 4 1 2
    // 4 2 5 3 1
    //
    // Futoshiki instance, by Andras Salamon
    // specify the numbers in the grid
    //
    int[,] values1 = {
                      {0, 0, 3, 2, 0},
                      {0, 0, 0, 0, 0},
                      {0, 0, 0, 0, 0},
                      {0, 0, 0, 0, 0},
                      {0, 0, 0, 0, 0}};


    // [i1,j1, i2,j2] requires that values[i1,j1] < values[i2,j2]
    // Note: 1-based
    int [,] lt1 = {
                   {1,2,  1,1},
                   {1,4,  1,5},
                   {2,3,  1,3},
                   {3,3,  2,3},
                   {3,4,  2,4},
                   {2,5,  3,5},
                   {3,2,  4,2},
                   {4,4,  4,3},
                   {5,2,  5,1},
                   {5,4,  5,3},
                   {5,5,  4,5}};


    //
    // Example from http://en.wikipedia.org/wiki/Futoshiki
    // Solution:
    // 5 4 3 2 1
    // 4 3 1 5 2
    // 2 1 4 3 5
    // 3 5 2 1 4
    // 1 2 5 4 3
    //
    int[,] values2 = {
               {0, 0, 0, 0, 0},
               {4, 0, 0, 0, 2},
               {0, 0, 4, 0, 0},
               {0, 0, 0, 0, 4},
               {0, 0, 0, 0, 0}};

    // Note: 1-based
    int[,] lt2 = {
           {1,2,  1,1},
           {1,4,  1,3},
           {1,5,  1,4},
           {4,4,  4,5},
           {5,1,  5,2},
           {5,2,  5,3}
           };

    Console.WriteLine("Problem 1");
    Solve(values1, lt1);

    Console.WriteLine("\nProblem 2");
    Solve(values2, lt2);

  }
}