curious_set_of_integers.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 CuriousSetOfIntegers
{


  public static void Decreasing(Solver solver, IntVar[] x) {
    for(int i = 0; i < x.Length - 1; i++) {
      solver.Add(x[i] <= x[i+1]);
    }
  }


  /**
   *
   * Crypto problem in Google CP Solver.
   *
   * Martin Gardner (February 1967):
   * """
   * The integers 1,3,8, and 120 form a set with a remarkable property: the
   * product of any two integers is one less than a perfect square. Find
   * a fifth number that can be added to the set without destroying
   * this property.
   * """
   *
   * Also see, http://www.hakank.org/or-tools/curious_set_of_integers.py
   *
   */
  private static void Solve()
  {

    Solver solver = new Solver("CuriousSetOfIntegers");

    //
    // data
    //
    int n = 5;
    int max_val = 10000;

    //
    // Decision variables
    //
    IntVar[] x = solver.MakeIntVarArray(n, 0, max_val, "x");

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

    for(int i = 0; i < n - 1; i++) {
      for(int j = i + 1; j < n; j++) {
        IntVar p = solver.MakeIntVar(0, max_val);
        solver.Add((p.Square() - 1) - (x[i] * x[j]) == 0);
      }
    }

    // Symmetry breaking
    Decreasing(solver, x);

    // This is the original problem
    // Which is the fifth number?
    int[] v = {1,3,8,120};
    IntVar[] b = (from i in Enumerable.Range(0, n)
                  select x[i].IsMember(v)).ToArray();
    solver.Add(b.Sum() == 4);


    //
    // Search
    //
    DecisionBuilder db = solver.MakePhase(x,
                                          Solver.CHOOSE_MIN_SIZE_LOWEST_MIN,
                                          Solver.ASSIGN_MIN_VALUE);


    solver.NewSearch(db);

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

    Solve();

  }
}