146 lines
3.6 KiB
C#
146 lines
3.6 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 Google.OrTools.ConstraintSolver;
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public class MagicSquare
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{
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/**
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*
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* Solves the Magic Square problem.
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* See http://www.hakank.org/or-tools/magic_square.py
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*
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*/
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private static void Solve(int n = 4, int num = 0, int print = 1)
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{
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Solver solver = new Solver("MagicSquare");
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Console.WriteLine("n: {0}", n);
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//
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// Decision variables
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//
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IntVar[,] x = solver.MakeIntVarMatrix(n, n, 1, n * n, "x");
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// for the branching
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IntVar[] x_flat = x.Flatten();
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//
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// Constraints
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//
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long s = (n * (n * n + 1)) / 2;
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Console.WriteLine("s: " + s);
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IntVar[] diag1 = new IntVar[n];
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IntVar[] diag2 = new IntVar[n];
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for (int i = 0; i < n; i++)
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{
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IntVar[] row = new IntVar[n];
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for (int j = 0; j < n; j++)
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{
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row[j] = x[i, j];
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}
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// sum row to s
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solver.Add(row.Sum() == s);
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diag1[i] = x[i, i];
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diag2[i] = x[i, n - i - 1];
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}
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// sum diagonals to s
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solver.Add(diag1.Sum() == s);
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solver.Add(diag2.Sum() == s);
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// sum columns to s
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for (int j = 0; j < n; j++)
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{
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IntVar[] col = new IntVar[n];
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for (int i = 0; i < n; i++)
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{
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col[i] = x[i, j];
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}
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solver.Add(col.Sum() == s);
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}
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// all are different
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solver.Add(x_flat.AllDifferent());
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// symmetry breaking: upper left is 1
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// solver.Add(x[0,0] == 1);
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//
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// Search
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//
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DecisionBuilder db = solver.MakePhase(x_flat, Solver.CHOOSE_FIRST_UNBOUND, Solver.ASSIGN_CENTER_VALUE);
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solver.NewSearch(db);
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int c = 0;
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while (solver.NextSolution())
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{
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if (print != 0)
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{
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for (int i = 0; i < n; i++)
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{
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for (int j = 0; j < n; j++)
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{
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Console.Write(x[i, j].Value() + " ");
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}
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Console.WriteLine();
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}
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Console.WriteLine();
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}
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c++;
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if (num > 0 && c >= num)
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{
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break;
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}
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}
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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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solver.EndSearch();
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}
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public static void Main(String[] args)
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{
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int n = 4;
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int num = 0;
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int print = 1;
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if (args.Length > 1)
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{
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n = Convert.ToInt32(args[1]);
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}
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if (args.Length > 2)
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{
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num = Convert.ToInt32(args[2]);
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}
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if (args.Length > 3)
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{
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print = Convert.ToInt32(args[3]);
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}
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Solve(n, num, print);
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}
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}
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