debruijn.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 Google.OrTools.ConstraintSolver;

public class DeBruijn
{


  /**
   *
   *  ToNum(solver, a, num, base)
   *
   *  channelling between the array a and the number num.
   *
   */
  private static Constraint ToNum(IntVar[] a, IntVar num, int bbase) {
    int len = a.Length;

    IntVar[] tmp = new IntVar[len];
    for(int i = 0; i < len; i++) {
      tmp[i] = (a[i]*(int)Math.Pow(bbase,(len-i-1))).Var();
    }
     return tmp.Sum() == num;
  }



  /**
   *
   * Implements "arbitrary" de Bruijn sequences.
   * See http://www.hakank.org/or-tools/debruijn_binary.py
   *
   */
  private static void Solve(int bbase, int n, int m)
  {
    Solver solver = new Solver("DeBruijn");


    // Ensure that the number of each digit in bin_code is
    // the same. Nice feature, but it can slow things down...
    bool check_same_gcc = false; // true;

    //
    // Decision variables
    //
    IntVar[] x = solver.MakeIntVarArray(m, 0, (int)Math.Pow(bbase, n) - 1, "x");
    IntVar[,] binary = solver.MakeIntVarMatrix(m, n, 0, bbase - 1, "binary");

    // this is the de Bruijn sequence
    IntVar[] bin_code =
      solver.MakeIntVarArray(m, 0, bbase - 1, "bin_code");

    // occurences of each number in bin_code
    IntVar[] gcc = solver.MakeIntVarArray(bbase, 0, m, "gcc");

    // for the branching
    IntVar[] all = new IntVar[2 * m + bbase];
    for(int i = 0; i < m; i++) {
      all[i] = x[i];
      all[m + i] = bin_code[i];
    }
    for(int i = 0; i < bbase; i++) {
      all[2 * m + i] = gcc[i];
    }


    //
    // Constraints
    //

    solver.Add(x.AllDifferent());

    // converts x <-> binary
    for(int i = 0; i < m; i++) {
      IntVar[] t = new IntVar[n];
      for(int j = 0; j < n; j++) {
        t[j] = binary[i,j];
      }
      solver.Add(ToNum(t, x[i], bbase));
    }

    // the de Bruijn condition:
    // the first elements in binary[i] is the same as the last
    // elements in binary[i-1]
    for(int i = 1; i < m; i++) {
      for(int j = 1; j < n; j++) {
        solver.Add(binary[i - 1,j] == binary[i,j - 1]);
      }
    }

    // ... and around the corner
    for(int j = 1; j < n; j++) {
      solver.Add(binary[m - 1,j] == binary[0,j - 1]);
    }

    // converts binary -> bin_code (de Bruijn sequence)
    for(int i = 0; i < m; i++) {
      solver.Add(bin_code[i] == binary[i,0]);

    }


    // extra: ensure that all the numbers in the de Bruijn sequence
    // (bin_code) has the same occurrences (if check_same_gcc is True
    // and mathematically possible)
    solver.Add(bin_code.Distribute(gcc));
    if (check_same_gcc && m % bbase == 0) {
      for(int i = 1; i < bbase; i++) {
        solver.Add(gcc[i] == gcc[i - 1]);
      }
    }

    // symmetry breaking:
    // the minimum value of x should be first
    // solver.Add(x[0] == x.Min());


    //
    // Search
    //
    DecisionBuilder db = solver.MakePhase(all,
                                          Solver.CHOOSE_MIN_SIZE_LOWEST_MAX,
                                          Solver.ASSIGN_MIN_VALUE);

    solver.NewSearch(db);

    while (solver.NextSolution()) {
      Console.Write("x: ");
      for(int i = 0; i < m; i++) {
        Console.Write(x[i].Value() + " ");
      }

      Console.Write("\nde Bruijn sequence:");
      for(int i = 0; i < m; i++) {
        Console.Write(bin_code[i].Value() + " ");
      }

      Console.Write("\ngcc: ");
      for(int i = 0; i < bbase; i++) {
        Console.Write(gcc[i].Value() + " ");
      }
      Console.WriteLine("\n");


      // for debugging etc: show the full binary table
      /*
      Console.Write("binary:");
      for(int i = 0; i < m; i++) {
        for(int j = 0; j < n; j++) {
          Console.Write(binary[i][j].Value() + " ");
        }
        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 bbase = 2;
    int n    = 3;
    int m    = 8;

    if (args.Length > 0) {
      bbase = Convert.ToInt32(args[0]);
    }

    if (args.Length > 1) {
      n = Convert.ToInt32(args[1]);
    }

    if (args.Length > 2) {
      m = Convert.ToInt32(args[2]);
    }

    Solve(bbase, n, m);
  }
}