young_tableaux.cs

//
// 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.IO;
using System.Text.RegularExpressions;
using Google.OrTools.ConstraintSolver;


public class YoungTableaux
{


  /**
   *
   * Implements Young tableaux and partitions.
   * See http://www.hakank.org/or-tools/young_tableuax.py
   *
   */
  private static void Solve(int n)
  {
    Solver solver = new Solver("YoungTableaux");

    //
    // data
    //
    Console.WriteLine("n: {0}\n", n);

    //
    // Decision variables
    //
    IntVar[,] x = solver.MakeIntVarMatrix(n, n, 1, n + 1, "x");
    IntVar[] x_flat = x.Flatten();

    // partition structure
    IntVar[] p = solver.MakeIntVarArray(n, 0, n + 1, "p");

    //
    // Constraints
    //
    // 1..n is used exactly once
    for(int i = 1; i <= n; i++) {
      solver.Add(x_flat.Count(i, 1));
    }

    solver.Add(x[0,0] == 1);

    // row wise
    for(int i = 0; i < n; i++) {
      for(int j = 1; j < n; j++) {
        solver.Add(x[i,j] >= x[i,j - 1]);
      }
    }

    // column wise
    for(int j = 0; j < n; j++) {
      for(int i = 1; i < n; i++) {
        solver.Add(x[i,j] >= x[i - 1, j]);
      }
    }

    // calculate the structure (i.e. the partition)
    for(int i = 0; i < n; i++) {
      IntVar[] b = new IntVar[n];
      for(int j = 0; j < n; j++) {
        b[j] = x[i, j] <= n;
      }
      solver.Add(p[i] == b.Sum());
    }

    solver.Add(p.Sum() == n);

    for(int i = 1; i < n; i++) {
      solver.Add(p[i - 1] >= p[i]);
    }



    //
    // Search
    //
    DecisionBuilder db = solver.MakePhase(x_flat,
                                          Solver.CHOOSE_FIRST_UNBOUND,
                                          Solver.ASSIGN_MIN_VALUE);

    solver.NewSearch(db);

    while (solver.NextSolution()) {
      Console.Write("p: ");
      for(int i = 0; i < n; i++) {
        Console.Write(p[i].Value() + " ");
      }
      Console.WriteLine("\nx:");

      for(int i = 0; i < n; i++) {
        for(int j = 0; j < n; j++) {
          long val = x[i,j].Value();
          if (val <= n) {
            Console.Write(val + " ");
          }
        }
        if (p[i].Value() > 0) {
          Console.WriteLine();
        }
      }
      Console.WriteLine();
    }

    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();

  }



  public static void Main(String[] args)
  {
    int n = 5;
    if (args.Length > 0) {
      n = Convert.ToInt32(args[0]);
    }
    Solve(n);
  }
}