054: N-Queens

//
// 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.Linq;
using Google.OrTools.ConstraintSolver;

public class NQueens
{
  /**
   *
   * Solves the N-Queens problem.
   *
   * Syntax: nqueens.exe n num print
   * where 
   *    n    : size of board
   *    num  : number of solutions to calculate
   *    print: print the results (if > 0)
   *
   */
  private static void Solve(int n=8, int num=0, int print=1)
  {
    Solver solver = new Solver("N-Queens");

    //
    // Decision variables
    //
    IntVar[] q = solver.MakeIntVarArray(n, 0, n-1, "q");


    //
    // Constraints
    //  
    solver.Add(q.AllDifferent());

    IntVar[] q1 = new IntVar[n];
    IntVar[] q2 = new IntVar[n];
    for(int i = 0; i < n; i++) {
      q1[i] = (q[i] + i).Var();
      q2[i] = (q[i] - i).Var();
    }
    solver.Add(q1.AllDifferent());
    solver.Add(q2.AllDifferent());

    // Alternative version: it works as well but are not that clear
    /*
    solver.Add((from i in Enumerable.Range(0, n)
                select (q[i] + i).Var()).ToArray().AllDifferent());

    solver.Add((from i in Enumerable.Range(0, n)
                select (q[i] - i).Var()).ToArray().AllDifferent());
    */

    //
    // Search
    //
    DecisionBuilder db = solver.MakePhase(q,
                                          Solver.CHOOSE_MIN_SIZE_LOWEST_MAX,
                                          Solver.ASSIGN_CENTER_VALUE);

    solver.NewSearch(db);
    int c = 0;
    while (solver.NextSolution()) {
      if (print > 0) {
        for(int i = 0; i < n; i++) {
          Console.Write("{0} ", q[i].Value());
        }
      
        Console.WriteLine();
      }
      c++;
      if (num > 0 && c >= num) {
        break;
      }
    }

    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 = 8;
    int num = 0;
    int print = 1;

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

    if (args.Length > 1) {
      num = Convert.ToInt32(args[1]);
    }
    if (args.Length > 2) {
      print = Convert.ToInt32(args[2]);
    }

    Console.WriteLine("n: {0} num: {1} print: {2}", n, num, print);

    Solve(n, num, print);
  }
}