fill_a_pix.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.IO;
using System.Linq;
using System.Text.RegularExpressions;
using Google.OrTools.ConstraintSolver;


public class FillAPix
{

  static int X = -1;

  //
  // Default problem.
  // Puzzle 1 from
  // http://www.conceptispuzzles.com/index.aspx?uri=puzzle/fill-a-pix/rules

  //
  static int default_n = 10;
  static int[,] default_puzzle = {{X,X,X,X,X,X,X,X,0,X},
                                  {X,8,8,X,2,X,0,X,X,X},
                                  {5,X,8,X,X,X,X,X,X,X},
                                  {X,X,X,X,X,2,X,X,X,2},
                                  {1,X,X,X,4,5,6,X,X,X},
                                  {X,0,X,X,X,7,9,X,X,6},
                                  {X,X,X,6,X,X,9,X,X,6},
                                  {X,X,6,6,8,7,8,7,X,5},
                                  {X,4,X,6,6,6,X,6,X,4},
                                  {X,X,X,X,X,X,3,X,X,X}};

  // for the actual problem
  static int n;
  static int[,] puzzle;


  /**
   *
   * Fill-a-Pix problem
   *
   * From http://www.conceptispuzzles.com/index.aspx?uri=puzzle/fill-a-pix/basiclogic
   * """
   * Each puzzle consists of a grid containing clues in various places. The
   * object is to reveal a hidden picture by painting the squares around each
   * clue so that the number of painted squares, including the square with
   * the clue, matches the value of the clue.
   * """
   *
   * http://www.conceptispuzzles.com/index.aspx?uri=puzzle/fill-a-pix/rules
   * """
   * Fill-a-Pix is a Minesweeper-like puzzle based on a grid with a pixilated
   * picture hidden inside. Using logic alone, the solver determines which
   * squares are painted and which should remain empty until the hidden picture
   * is completely exposed.
   * """
   *
   * Fill-a-pix History:
   * http://www.conceptispuzzles.com/index.aspx?uri=puzzle/fill-a-pix/history
   *
   * Also see http://www.hakank.org/google_or_tools/fill_a_pix.py
   *
   *
   */
  private static void Solve()
  {
    Solver solver = new Solver("FillAPix");

    //
    // data
    //
    int[] S = {-1, 0, 1};

    Console.WriteLine("Problem:");
    for(int i = 0; i < n; i++) {
      for(int j = 0; j < n; j++) {
        if (puzzle[i,j] > X) {
          Console.Write(puzzle[i,j] + " ");
        } else {
          Console.Write("X ");
        }
      }
      Console.WriteLine();
    }
    Console.WriteLine();


    //
    // Decision variables
    //
    IntVar[,] pict = solver.MakeIntVarMatrix(n, n, 0, 1, "pict");
    IntVar[] pict_flat = pict.Flatten(); // for branching

    //
    // Constraints
    //  
    for(int i = 0; i < n; i++) {
      for(int j = 0; j < n; j++) {
        if (puzzle[i,j] > X) {

          // this cell is the sum of all surrounding cells
          var tmp = from a in S from b in S where 
            i + a >= 0 &&
            j + b >= 0 &&
            i + a < n &&
            j + b < n
            select(pict[i+a,j+b]);

          solver.Add(tmp.ToArray().Sum() == puzzle[i,j]);

        }
      }
    }


    //
    // Search
    //
    DecisionBuilder db = solver.MakePhase(pict_flat,
                                          Solver.INT_VAR_DEFAULT,
                                          Solver.INT_VALUE_DEFAULT);

    solver.NewSearch(db);

    int sol = 0;
    while (solver.NextSolution()) {
      sol++;
      Console.WriteLine("Solution #{0} ", sol + " ");
      for(int i = 0; i < n; i++) {
        for(int j = 0; j < n; j++){ 
          Console.Write(pict[i,j].Value() == 1 ? "#" : " ");
        }
        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();

  }


  /**
   *
   * Reads a Fill-a-Pix file.
   * File format:
   *  # a comment which is ignored
   *  % a comment which also is ignored
   *  number of rows and columns (n x n)
   *  <
   *    row number of neighbours lines...
   *  >
   * 
   * 0..8 means number of neighbours, "." mean unknown (may be a mine)
   * 
   * Example (from fill_a_pix1.txt):
   *
   * 10
   * ........0.
   * .88.2.0...
   * 5.8.......
   * .....2...2
   * 1...456...
   * .0...79..6
   * ...6..9..6
   * ..668787.5
   * .4.666.6.4
   * ......3...
   *
   */
  private static void readFile(String file) {

    Console.WriteLine("readFile(" + file + ")");
    int lineCount = 0;
        
    TextReader inr = new StreamReader(file);
    String str;
    while ((str = inr.ReadLine()) != null && str.Length > 0) {
      
      str = str.Trim();
      
      // ignore comments
      if(str.StartsWith("#") || str.StartsWith("%")) {
        continue;
      }
      
      Console.WriteLine(str);
      if (lineCount == 0) {
        n = Convert.ToInt32(str); // number of rows
        puzzle = new int[n,n];
      } else {
        // the problem matrix
        String[] row = Regex.Split(str, "");
        for(int j = 1; j <= n; j++) {
          String s = row[j];
          if (s.Equals(".")) {
            puzzle[lineCount-1, j-1] = -1;
          } else {
            puzzle[lineCount-1, j-1] = Convert.ToInt32(s);
          }
        }
      }
      
      lineCount++;
      
    } // end while
    
    inr.Close();
    
  } // end readFile




  public static void Main(String[] args)
  {
    String file = "";
    if (args.Length > 0) {
      file = args[0];
      readFile(file);
    } else {
      puzzle = default_puzzle;
      n = default_n;
    }

    Solve();
  }
}