//
// 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 Partition
{

  /**
   *
   * This is a port of Charles Prud'homme's Java model
   * Partition.java
   * """
   * Partition n numbers into two groups, so that
   * - the sum of the first group equals the sum of the second,
   * - and the sum of the squares of the first group equals the sum of
   *   the squares of the second
   * """
   *
   */
  private static void Solve(int m)
  {

    Solver solver = new Solver("Partition");


    //
    // Decision variables
    //
    IntVar[] x = solver.MakeIntVarArray(m, 1, 2 * m, "x");
    IntVar[] y = solver.MakeIntVarArray(m, 1, 2 * m, "y");


    //
    // Constraints
    //
       // break symmetries
    for (int i = 0; i < m - 1; i++) {
      solver.Add(x[i] < x[i + 1]);
      solver.Add(y[i] < y[i + 1]);
    }
    solver.Add(x[0] < y[0]);

    IntVar[] xy = new IntVar[2 * m];
    for (int i = m - 1; i >= 0; i--) {
      xy[i] = x[i];
      xy[m + i] = y[i];
    }

    solver.Add(xy.AllDifferent());

    int[] coeffs = new int[2 * m];
    for (int i = m - 1; i >= 0; i--) {
      coeffs[i] = 1;
      coeffs[m + i] = -1;
    }
    solver.Add(xy.ScalProd(coeffs) == 0);

    IntVar[] sxy, sx, sy;
    sxy = new IntVar[2 * m];
    sx = new IntVar[m];
    sy = new IntVar[m];
    for (int i = m - 1; i >= 0; i--) {
      sx[i] = x[i].Square().Var();
      sxy[i] = sx[i];
      sy[i] = y[i].Square().Var();
      sxy[m + i] = sy[i];
    }
    solver.Add(sxy.ScalProd(coeffs) == 0);

    solver.Add(x.Sum() == 2 * m * (2 * m + 1) / 4);
    solver.Add(y.Sum() == 2 * m * (2 * m + 1) / 4);
    solver.Add(sx.Sum() == 2 * m * (2 * m + 1) * (4 * m + 1) / 12);
    solver.Add(sy.Sum() == 2 * m * (2 * m + 1) * (4 * m + 1) / 12);

    //
    // Search
    //
    DecisionBuilder db = solver.MakeDefaultPhase(xy);

    SearchMonitor log = solver.MakeSearchLog(10000);
    solver.NewSearch(db, log);

    while (solver.NextSolution()) {
      for(int i = 0; i < m; i++) {
        Console.Write("[" + xy[i].Value() + "] ");
      }
      Console.WriteLine();
      for(int i = 0; i < m; i++) {
        Console.Write("[" + xy[m+i].Value() + "] ");
      }
      Console.WriteLine("\n");
    }

    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 m = 32;
    if (args.Length > 0) {
      m = Convert.ToInt32(args[0]);
    }

    Solve(m);
  }
}