//
// 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 Seseman
{

  /**
   *
   * Solves the Seseman convent problem.
   * See http://www.hakank.org/google_or_tools/seseman.py
   *
   */
  private static void Solve(int n = 3)
  {
    Solver solver = new Solver("Seseman");

    //
    // data
    //
    int border_sum = n * n;

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


    //
    // Constraints
    //  

    // zero in all middle cells
    for(int i = 1; i < n-1; i++) {
      for(int j = 1; j < n-1; j++) {
        solver.Add(x[i,j] == 0);
      }
    }

    // all borders must be >= 1
    for(int i = 0; i < n; i++) {
      for(int j = 0; j < n; j++) {
        if (i == 0 || j == 0 || i == n - 1 || j == n - 1) {
          solver.Add(x[i,j] >= 1);
        }
      }
    }

    // sum the four borders
    IntVar[] border1 = new IntVar[n];
    IntVar[] border2 = new IntVar[n];
    IntVar[] border3 = new IntVar[n];
    IntVar[] border4 = new IntVar[n];
    for(int i = 0; i < n; i++) {
      border1[i] = x[i,0];
      border2[i] = x[i,n-1];
      border3[i] = x[0,i];
      border4[i] = x[n-1,i];
    }
    solver.Add(border1.Sum() == border_sum);
    solver.Add(border2.Sum() == border_sum);
    solver.Add(border3.Sum() == border_sum);
    solver.Add(border4.Sum() == border_sum);


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

    solver.NewSearch(db);
    while (solver.NextSolution()) {
      Console.WriteLine("total_sum: {0} ", total_sum.Value());
      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();

  }

  public static void Main(String[] args)
  {
    int n = 3;

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

    Solve(n);
  }
}