131 lines
3.2 KiB
C#
131 lines
3.2 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.IO;
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using System.Text.RegularExpressions;
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using Google.OrTools.ConstraintSolver;
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public class Partition
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{
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/**
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*
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* This is a port of Charles Prud'homme's Java model
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* Partition.java
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* """
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* Partition n numbers into two groups, so that
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* - the sum of the first group equals the sum of the second,
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* - and the sum of the squares of the first group equals the sum of
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* the squares of the second
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* """
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*
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*/
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private static void Solve(int m)
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{
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Solver solver = new Solver("Partition");
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//
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// Decision variables
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//
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IntVar[] x = solver.MakeIntVarArray(m, 1, 2 * m, "x");
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IntVar[] y = solver.MakeIntVarArray(m, 1, 2 * m, "y");
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//
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// Constraints
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//
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// break symmetries
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for (int i = 0; i < m - 1; i++) {
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solver.Add(x[i] < x[i + 1]);
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solver.Add(y[i] < y[i + 1]);
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}
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solver.Add(x[0] < y[0]);
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IntVar[] xy = new IntVar[2 * m];
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for (int i = m - 1; i >= 0; i--) {
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xy[i] = x[i];
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xy[m + i] = y[i];
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}
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solver.Add(xy.AllDifferent());
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int[] coeffs = new int[2 * m];
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for (int i = m - 1; i >= 0; i--) {
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coeffs[i] = 1;
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coeffs[m + i] = -1;
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}
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solver.Add(xy.ScalProd(coeffs) == 0);
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IntVar[] sxy, sx, sy;
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sxy = new IntVar[2 * m];
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sx = new IntVar[m];
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sy = new IntVar[m];
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for (int i = m - 1; i >= 0; i--) {
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sx[i] = x[i].Square().Var();
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sxy[i] = sx[i];
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sy[i] = y[i].Square().Var();
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sxy[m + i] = sy[i];
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}
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solver.Add(sxy.ScalProd(coeffs) == 0);
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solver.Add(x.Sum() == 2 * m * (2 * m + 1) / 4);
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solver.Add(y.Sum() == 2 * m * (2 * m + 1) / 4);
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solver.Add(sx.Sum() == 2 * m * (2 * m + 1) * (4 * m + 1) / 12);
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solver.Add(sy.Sum() == 2 * m * (2 * m + 1) * (4 * m + 1) / 12);
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//
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// Search
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//
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DecisionBuilder db = solver.MakeDefaultPhase(xy);
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SearchMonitor log = solver.MakeSearchLog(10000);
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solver.NewSearch(db, log);
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while (solver.NextSolution()) {
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for(int i = 0; i < m; i++) {
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Console.Write("[" + xy[i].Value() + "] ");
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}
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Console.WriteLine();
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for(int i = 0; i < m; i++) {
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Console.Write("[" + xy[m+i].Value() + "] ");
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}
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Console.WriteLine("\n");
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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 m = 32;
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if (args.Length > 0) {
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m = Convert.ToInt32(args[0]);
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}
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Solve(m);
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}
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}
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