perfect_square_sequence.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.Collections.Generic;
using System.Linq;
using Google.OrTools.ConstraintSolver;


public class PerfectSquareSequence
{

  /**
   *
   * Perfect square sequence.
   *
   * From 'Fun with num3ers'
   * "Sequence"
   * http://benvitale-funwithnum3ers.blogspot.com/2010/11/sequence.html
   * """
   * If we take the numbers from 1 to 15 
   *    (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15) 
   * and rearrange them in such an order that any two consecutive 
   * numbers in the sequence add up to a perfect square, we get,
   *  
   *  8     1     15     10     6     3     13     12      4      5     11     14        2      7      9
   *      9    16    25     16     9     16     25     16     9     16     25     16       9     16
   *
   *  
   * I ask the readers the following:
   *  
   * Can you take the numbers from 1 to 25 to produce such an arrangement?
   * How about the numbers from 1 to 100?
   * """
   *
   * Via http://wildaboutmath.com/2010/11/26/wild-about-math-bloggers-111910
   *
   *
   * Also see http://www.hakank.org/or-tools/perfect_square_sequence.py 
   *
   */
  private static int Solve(int n = 15, int print_solutions=1, int show_num_sols=0)
  {

    Solver solver = new Solver("PerfectSquareSequence");

    IEnumerable<int> RANGE = Enumerable.Range(0, n);

    // create the table of possible squares
    int[] squares = new int[n-1];
    for(int i = 1; i < n; i++) {
      squares[i-1] = i*i;
    }

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


    //
    // Constraints
    //

    solver.Add(x.AllDifferent());

    for(int i = 1; i < n; i++) {
      solver.Add((x[i-1]+x[i]).Member(squares));
    }

    // symmetry breaking
    solver.Add(x[0] < x[n-1]);


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

    solver.NewSearch(db);

    int num_solutions = 0;
    while (solver.NextSolution()) {
      num_solutions++;
      if (print_solutions > 0) {
        Console.Write("x:  ");
        foreach(int i in RANGE) {
          Console.Write(x[i].Value() + " ");
        }
        Console.WriteLine();
      }

      if (show_num_sols > 0 && num_solutions >= show_num_sols) {
        break;
      }
    }

    if (print_solutions > 0) {
      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();

    return num_solutions;

  }

  public static void Main(String[] args)
  {
    int n = 15;
    if (args.Length > 0) {
      n = Convert.ToInt32(args[0]);
    }

    if (n == 0) {
      for(int i = 2; i < 100; i++) {
        int num_solutions = Solve(i, 0, 0);
        Console.WriteLine("{0}: {1} solution(s)", i, num_solutions);
      }
      
    } else {
      int num_solutions = Solve(n);
      Console.WriteLine("{0}: {1} solution(s)", n, num_solutions);
    }
  }
}