145 lines
3.7 KiB
C#
145 lines
3.7 KiB
C#
//
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// Copyright 2012 Hakan Kjellerstrand
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//
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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using System;
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using System.Collections;
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using System.Collections.Generic;
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using System.Linq;
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using Google.OrTools.ConstraintSolver;
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public class PerfectSquareSequence
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{
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/**
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*
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* Perfect square sequence.
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*
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* From 'Fun with num3ers'
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* "Sequence"
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* http://benvitale-funwithnum3ers.blogspot.com/2010/11/sequence.html
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* """
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* If we take the numbers from 1 to 15
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* (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15)
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* and rearrange them in such an order that any two consecutive
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* numbers in the sequence add up to a perfect square, we get,
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*
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* 8 1 15 10 6 3 13 12 4 5 11 14 2 7 9
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* 9 16 25 16 9 16 25 16 9 16 25 16 9 16
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*
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*
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* I ask the readers the following:
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*
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* Can you take the numbers from 1 to 25 to produce such an arrangement?
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* How about the numbers from 1 to 100?
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* """
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*
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* Via http://wildaboutmath.com/2010/11/26/wild-about-math-bloggers-111910
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*
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*
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* Also see http://www.hakank.org/or-tools/perfect_square_sequence.py
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*
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*/
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private static int Solve(int n = 15, int print_solutions=1, int show_num_sols=0)
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{
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Solver solver = new Solver("PerfectSquareSequence");
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IEnumerable<int> RANGE = Enumerable.Range(0, n);
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// create the table of possible squares
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int[] squares = new int[n-1];
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for(int i = 1; i < n; i++) {
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squares[i-1] = i*i;
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}
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//
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// Decision variables
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//
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IntVar[] x = solver.MakeIntVarArray(n, 1, n, "x");
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//
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// Constraints
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//
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solver.Add(x.AllDifferent());
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for(int i = 1; i < n; i++) {
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solver.Add((x[i-1]+x[i]).Member(squares));
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}
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// symmetry breaking
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solver.Add(x[0] < x[n-1]);
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//
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// Search
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//
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DecisionBuilder db = solver.MakePhase(x,
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Solver.CHOOSE_FIRST_UNBOUND,
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Solver.INT_VALUE_DEFAULT);
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solver.NewSearch(db);
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int num_solutions = 0;
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while (solver.NextSolution()) {
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num_solutions++;
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if (print_solutions > 0) {
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Console.Write("x: ");
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foreach(int i in RANGE) {
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Console.Write(x[i].Value() + " ");
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}
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Console.WriteLine();
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}
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if (show_num_sols > 0 && num_solutions >= show_num_sols) {
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break;
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}
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}
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if (print_solutions > 0) {
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Console.WriteLine("\nSolutions: {0}", solver.Solutions());
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Console.WriteLine("WallTime: {0}ms", solver.WallTime());
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Console.WriteLine("Failures: {0}", solver.Failures());
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Console.WriteLine("Branches: {0} ", solver.Branches());
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}
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solver.EndSearch();
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return num_solutions;
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}
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public static void Main(String[] args)
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{
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int n = 15;
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if (args.Length > 0) {
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n = Convert.ToInt32(args[0]);
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}
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if (n == 0) {
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for(int i = 2; i < 100; i++) {
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int num_solutions = Solve(i, 0, 0);
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Console.WriteLine("{0}: {1} solution(s)", i, num_solutions);
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}
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} else {
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int num_solutions = Solve(n);
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Console.WriteLine("{0}: {1} solution(s)", n, num_solutions);
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}
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}
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}
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