147 lines
3.7 KiB
C#
147 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.IO;
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using System.Text.RegularExpressions;
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using Google.OrTools.ConstraintSolver;
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public class YoungTableaux
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{
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/**
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*
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* Implements Young tableaux and partitions.
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* See http://www.hakank.org/or-tools/young_tableuax.py
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*
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*/
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private static void Solve(int n)
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{
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Solver solver = new Solver("YoungTableaux");
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//
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// data
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//
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Console.WriteLine("n: {0}\n", 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 + 1, "x");
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IntVar[] x_flat = x.Flatten();
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// partition structure
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IntVar[] p = solver.MakeIntVarArray(n, 0, n + 1, "p");
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//
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// Constraints
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//
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// 1..n is used exactly once
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for (int i = 1; i <= n; i++)
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{
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solver.Add(x_flat.Count(i, 1));
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}
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solver.Add(x[0, 0] == 1);
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// row wise
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for (int i = 0; i < n; i++)
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{
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for (int j = 1; j < n; j++)
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{
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solver.Add(x[i, j] >= x[i, j - 1]);
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}
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}
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// column wise
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for (int j = 0; j < n; j++)
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{
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for (int i = 1; i < n; i++)
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{
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solver.Add(x[i, j] >= x[i - 1, j]);
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}
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}
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// calculate the structure (i.e. the partition)
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for (int i = 0; i < n; i++)
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{
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IntVar[] b = new IntVar[n];
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for (int j = 0; j < n; j++)
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{
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b[j] = x[i, j] <= n;
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}
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solver.Add(p[i] == b.Sum());
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}
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solver.Add(p.Sum() == n);
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for (int i = 1; i < n; i++)
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{
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solver.Add(p[i - 1] >= p[i]);
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}
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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_MIN_VALUE);
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solver.NewSearch(db);
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while (solver.NextSolution())
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{
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Console.Write("p: ");
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for (int i = 0; i < n; i++)
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{
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Console.Write(p[i].Value() + " ");
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}
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Console.WriteLine("\nx:");
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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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long val = x[i, j].Value();
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if (val <= n)
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{
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Console.Write(val + " ");
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}
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}
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if (p[i].Value() > 0)
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{
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Console.WriteLine();
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}
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}
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Console.WriteLine();
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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 = 5;
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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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Solve(n);
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}
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}
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