//
// 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.Text.RegularExpressions;
using Google.OrTools.ConstraintSolver;


public class QuasigroupCompletion
{

  static int X = 0;

  /*
   * default problem
   *
   * Example from Ruben Martins and Inès Lynce
   * Breaking Local Symmetries in Quasigroup Completion Problems, page 3
   * The solution is unique:
   *
   *   1 3 2 5 4
   *   2 5 4 1 3
   *   4 1 3 2 5
   *   5 4 1 3 2
   *   3 2 5 4 1
   */ 
  static int default_n = 5;
  static int[,] default_problem = {{1, X, X, X, 4},
                                   {X, 5, X, X, X},
                                   {4, X, X, 2, X},
                                   {X, 4, X, X, X},
                                   {X, X, 5, X, 1}};


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


  /**
   *
   * Solves the Quasigroup Completion problem.
   * See http://www.hakank.org/or-tools/quasigroup_completion.py
   *
   */
  private static void Solve()
  {
    Solver solver = new Solver("QuasigroupCompletion");

    //
    // data
    //
    Console.WriteLine("Problem:");
    for(int i = 0; i < n; i++) {
      for(int j = 0; j < n; j++) {
        Console.Write(problem[i,j] + " ");
      }
      Console.WriteLine();
    }
    Console.WriteLine();


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

    //
    // Constraints
    //  
   for(int i = 0; i < n; i++) {
      for(int j = 0; j < n; j++) {
        if (problem[i,j] > X) {
          solver.Add(x[i,j] == problem[i,j]);
        }
      }
    }

    //
    // rows and columns must be different
    //

    // rows
    for(int i = 0; i < n; i++) {
      IntVar[] row = new IntVar[n];
      for(int j = 0; j < n; j++) {
        row[j] = x[i,j];
      }
      solver.Add(row.AllDifferent());
    }

    // columns
    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.AllDifferent());
    }


    //
    // Search
    //
    DecisionBuilder db = solver.MakePhase(x_flat,
                                          Solver.INT_VAR_SIMPLE,
                                          Solver.ASSIGN_MIN_VALUE);

    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("{0} ", 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();

  }


  /**
   *
   * Reads a Quasigroup completion file.
   * File format:
   *  # a comment which is ignored
   *  % a comment which also is ignored
   *  number of rows (n)
   *  <
   *    row number of space separated entries
   *  >
   * 
   * "." or "0" means unknown, integer 1..n means known value
   * 
   * Example
   *   5
   *    1 . . . 4
   *   . 5 . . .
   *   4 . . 2 .
   *   . 4 . . .
   *   . . 5 . 1
   *
   */
  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
        problem = new int[n,n];
      } else {
        // the problem matrix
        String[] row = Regex.Split(str, " ");
        for(int i = 0; i < n; i++) {
          String s = row[i];
          if (s.Equals(".")) {
            problem[lineCount - 1, i] = 0;
          } else {
            problem[lineCount - 1, i] = 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 {
      problem = default_problem;
      n = default_n;
    }

    Solve();
  }
}