contiguity_regular.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.Linq;
using System.Diagnostics;
using Google.OrTools.ConstraintSolver;

public class ContiguityRegular
{


  /*
   * Global constraint regular
   *
   * This is a translation of MiniZinc's regular constraint (defined in
   * lib/zinc/globals.mzn), via the Comet code refered above.
   * All comments are from the MiniZinc code.
   * """
   * The sequence of values in array 'x' (which must all be in the range 1..S)
   * is accepted by the DFA of 'Q' states with input 1..S and transition
   * function 'd' (which maps (1..Q, 1..S) -> 0..Q)) and initial state 'q0'
   * (which must be in 1..Q) and accepting states 'F' (which all must be in
   * 1..Q).  We reserve state 0 to be an always failing state.
   * """
   *
   * x : IntVar array
   * Q : number of states
   * S : input_max
   * d : transition matrix
   * q0: initial state
   * F : accepting states
   *
   */
  static void MyRegular(Solver solver,
                        IntVar[] x,
                        int Q,
                        int S,
                        int[,] d,
                        int q0,
                        int[] F) {



    Debug.Assert(Q > 0, "regular: 'Q' must be greater than zero");
    Debug.Assert(S > 0, "regular: 'S' must be greater than zero");

    // d2 is the same as d, except we add one extra transition for
    // each possible input;  each extra transition is from state zero
    // to state zero.  This allows us to continue even if we hit a
    // non-accepted input.
    int[][] d2 = new int[Q+1][];
    for(int i = 0; i <= Q; i++) {
      int[] row = new int[S];
      for(int j = 0; j < S; j++) {
        if (i == 0) {
          row[j] = 0;
        } else {
          row[j] = d[i-1,j];
        }
      }
      d2[i] = row;
    }

    int[] d2_flatten = (from i in Enumerable.Range(0, Q+1)
                        from j in Enumerable.Range(0, S)
                        select d2[i][j]).ToArray();

    // If x has index set m..n, then a[m-1] holds the initial state
    // (q0), and a[i+1] holds the state we're in after processing
    // x[i].  If a[n] is in F, then we succeed (ie. accept the
    // string).
    int m = 0;
    int n = x.Length;

    IntVar[] a = solver.MakeIntVarArray(n+1-m, 0,Q+1, "a");
    // Check that the final state is in F
    solver.Add(a[a.Length-1].Member(F));
    // First state is q0
    solver.Add(a[m] == q0);

    for(int i = 0; i < n; i++) {
      solver.Add(x[i] >= 1);
      solver.Add(x[i] <= S);
      // Determine a[i+1]: a[i+1] == d2[a[i], x[i]]
      solver.Add(a[i+1] == d2_flatten.Element(((a[i]*S)+(x[i]-1))));

    }

  }


  static void MyContiguity(Solver solver, IntVar[] x) {

    // the DFA (for regular)
    int n_states = 3;
    int input_max = 2;
    int initial_state = 1; // note: state 0 is used for the failing state
                           // in MyRegular

    // all states are accepting states
    int[] accepting_states = {1,2,3};

    // The regular expression 0*1*0*
    int[,] transition_fn =
      {
        {1,2}, // state 1 (start): input 0 -> state 1, input 1 -> state 2 i.e. 0*
        {3,2}, // state 2: 1*
        {3,0}, // state 3: 0*
      };

    MyRegular(solver, x, n_states, input_max, transition_fn,
              initial_state, accepting_states);



  }


  /**
   *
   * Global constraint contiguity using regular
   *
   * This is a decomposition of the global constraint global contiguity.
   *
   * From Global Constraint Catalogue
   * http://www.emn.fr/x-info/sdemasse/gccat/Cglobal_contiguity.html
   * """
   * Enforce all variables of the VARIABLES collection to be assigned to 0 or 1.
   * In addition, all variables assigned to value 1 appear contiguously.
   *
   * Example:
   * (<0, 1, 1, 0>)
   *
   * The global_contiguity constraint holds since the sequence 0 1 1 0 contains
   * no more than one group of contiguous 1.
   * """
   *
   * Also see http://www.hakank.org/or-tools/contiguity_regular.py
   *
   */
  private static void Solve()
  {
    Solver solver = new Solver("ContiguityRegular");

    //
    // Data
    //
    int n = 7; // length of the array


    //
    // Decision variables
    //

    // Note: We use 1..2 (instead of 0..1) and subtract 1 in the solution
    IntVar[] reg_input = solver.MakeIntVarArray(n, 1, 2, "reg_input");


    //
    // Constraints
    //
    MyContiguity(solver, reg_input);


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

    solver.NewSearch(db);

    while (solver.NextSolution()) {
      for(int i = 0; i < n; i++) {
        // Note: here we subtract 1 to get 0..1
        Console.Write((reg_input[i].Value()-1) + " ");
      }
      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)
  {
    Solve();
  }
}