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//
// 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 > 1)
{
n = Convert.ToInt32(args[1]);
}
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);
}
}
}