dudeney.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 DudeneyNumbers
{


  private static Constraint ToNum(IntVar[] a, IntVar num, int bbase) {
    int len = a.Length;

    IntVar[] tmp = new IntVar[len];
    for(int i = 0; i < len; i++) {
      tmp[i] = (a[i]*(int)Math.Pow(bbase,(len-i-1))).Var();
    }
     return tmp.Sum() == num;
  }


  /**
   *
   * Dudeney numbers
   * From Pierre Schaus blog post
   * Dudeney number
   * http://cp-is-fun.blogspot.com/2010/09/test-python.html
   * """
   * I discovered yesterday Dudeney Numbers
   * A Dudeney Numbers is a positive integer that is a perfect cube such that the sum
   * of its decimal digits is equal to the cube root of the number. There are only six
   * Dudeney Numbers and those are very easy to find with CP.
   * I made my first experience with google cp solver so find these numbers (model below)
   * and must say that I found it very convenient to build CP models in python!
   * When you take a close look at the line:
   *     solver.Add(sum([10**(n-i-1)*x[i] for i in range(n)]) == nb)
   * It is difficult to argue that it is very far from dedicated
   * optimization languages!
   * """
   *
   * Also see: http://en.wikipedia.org/wiki/Dudeney_number
   *
   */
  private static void Solve()
  {

    Solver solver = new Solver("DudeneyNumbers");

    //
    // data
    //
    int n = 6;

    //
    // Decision variables
    //
    IntVar[] x = solver.MakeIntVarArray(n, 0, 9, "x");
    IntVar nb = solver.MakeIntVar(3, (int)Math.Pow(10,n), "nb");
    IntVar s = solver.MakeIntVar(1,9*n+1,"s");

    //
    // Constraints
    //
    solver.Add(nb == s*s*s);
    solver.Add(x.Sum() == s);

    // solver.Add(ToNum(x, nb, 10));

    // alternative
    solver.Add((from i in Enumerable.Range(0, n)
                select (x[i]*(int)Math.Pow(10,n-i-1)).Var()).
               ToArray().Sum() == nb);


    //
    // Search
    //
    DecisionBuilder db = solver.MakePhase(x,
                                          Solver.INT_VAR_DEFAULT,
                                          Solver.INT_VALUE_DEFAULT);


    solver.NewSearch(db);

    while (solver.NextSolution()) {
      Console.WriteLine(nb.Value());
    }

    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();

  }
}