CpModel.cs

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// Copyright 2010-2018 Google LLC
// 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.

namespace Google.OrTools.Sat
{
  using System;
  using System.Collections.Generic;
  using Google.OrTools.Util;

  public class CpModel
  {
    public CpModel()
    {
      model_ = new CpModelProto();
      constant_map_ = new Dictionary<long, int>();
    }

    // Getters.

    public CpModelProto Model
    {
      get { return model_; }
    }

    int Negated(int index)
    {
      return -index - 1;
    }

    // Integer variables and constraints.

    public IntVar NewIntVar(long lb, long ub, string name)
    {
      return new IntVar(model_, new Domain(lb, ub), name);
    }

    public IntVar NewIntVarFromDomain(Domain domain, string name)
    {
      return new IntVar(model_, domain, name);
    }
    // Constants (named or not).

    // TODO: Cache constant.
    public IntVar NewConstant(long value)
    {
      return new IntVar(model_, new Domain(value), String.Format("{0}", value));
    }

    public IntVar NewConstant(long value, string name)
    {
      return new IntVar(model_, new Domain(value), name);
    }

    public IntVar NewBoolVar(string name)
    {
      return new IntVar(model_, new Domain(0, 1), name);
    }

    public Constraint AddLinearConstraint(LinearExpr linear_expr, long lb,
                                          long ub)
    {
      return AddLinearExpressionInDomain(linear_expr, new Domain(lb, ub));
    }

    public Constraint AddLinearExpressionInDomain(LinearExpr linear_expr, Domain domain)
    {
      Dictionary<IntVar, long> dict = new Dictionary<IntVar, long>();
      long constant = LinearExpr.GetVarValueMap(linear_expr, 1L, dict);
      Constraint ct = new Constraint(model_);
      LinearConstraintProto linear = new LinearConstraintProto();
      foreach (KeyValuePair<IntVar, long> term in dict)
      {
        linear.Vars.Add(term.Key.Index);
        linear.Coeffs.Add(term.Value);
      }
      foreach (long value in domain.FlattenedIntervals())
      {
        if (value == Int64.MinValue || value == Int64.MaxValue)
        {
          linear.Domain.Add(value);
        }
        else
        {
          linear.Domain.Add(value - constant);
        }
      }
      ct.Proto.Linear = linear;
      return ct;
    }

    public Constraint Add(BoundedLinearExpression lin)
    {
      switch (lin.CtType)
      {
        case BoundedLinearExpression.Type.BoundExpression:
          {
            return AddLinearExpressionInDomain(lin.Left, new Domain(lin.Lb, lin.Ub));
          }
        case BoundedLinearExpression.Type.VarEqVar:
          {
            return AddLinearExpressionInDomain(lin.Left - lin.Right, new Domain(0));
          }
        case BoundedLinearExpression.Type.VarDiffVar:
          {
            return AddLinearExpressionInDomain(
                lin.Left - lin.Right,
                Domain.FromFlatIntervals(new long[] { Int64.MinValue, -1, 1,
                                                      Int64.MaxValue }));
          }
        case BoundedLinearExpression.Type.VarEqCst:
          {
            return AddLinearExpressionInDomain(lin.Left,
                                               new Domain(lin.Lb, lin.Lb));
          }
        case BoundedLinearExpression.Type.VarDiffCst:
          {
            return AddLinearExpressionInDomain(
               lin.Left,
               Domain.FromFlatIntervals(
                   new long[] { Int64.MinValue, lin.Lb - 1, lin.Lb + 1, Int64.MaxValue }));
          }
      }
      return null;
    }

    public Constraint AddAllDifferent(IEnumerable<IntVar> vars)
    {
      Constraint ct = new Constraint(model_);
      AllDifferentConstraintProto alldiff = new AllDifferentConstraintProto();
      foreach (IntVar var in vars)
      {
        alldiff.Vars.Add(var.Index);
      }
      ct.Proto.AllDiff = alldiff;
      return ct;
    }

    public Constraint AddElement(IntVar index, IEnumerable<IntVar> vars,
                                 IntVar target)
    {
      Constraint ct = new Constraint(model_);
      ElementConstraintProto element = new ElementConstraintProto();
      element.Index = index.Index;
      foreach (IntVar var in vars)
      {
        element.Vars.Add(var.Index);
      }
      element.Target = target.Index;
      ct.Proto.Element = element;
      return ct;
    }

    public Constraint AddElement(IntVar index, IEnumerable<long> values,
                                 IntVar target)
    {
      Constraint ct = new Constraint(model_);
      ElementConstraintProto element = new ElementConstraintProto();
      element.Index = index.Index;
      foreach (long value in values)
      {
        element.Vars.Add(ConvertConstant(value));
      }
      element.Target = target.Index;
      ct.Proto.Element = element;
      return ct;
    }

    public Constraint AddElement(IntVar index, IEnumerable<int> values,
                                 IntVar target)
    {
      Constraint ct = new Constraint(model_);
      ElementConstraintProto element = new ElementConstraintProto();
      element.Index = index.Index;
      foreach (int value in values)
      {
        element.Vars.Add(ConvertConstant(value));
      }
      element.Target = target.Index;
      ct.Proto.Element = element;
      return ct;
    }

    public Constraint AddCircuit(IEnumerable<Tuple<int, int, ILiteral>> arcs)
    {
      Constraint ct = new Constraint(model_);
      CircuitConstraintProto circuit = new CircuitConstraintProto();
      foreach (var arc in arcs)
      {
        circuit.Tails.Add(arc.Item1);
        circuit.Heads.Add(arc.Item2);
        circuit.Literals.Add(arc.Item3.GetIndex());
      }
      ct.Proto.Circuit = circuit;
      return ct;
    }

    public Constraint AddAllowedAssignments(IEnumerable<IntVar> vars,
                                            long[,] tuples)
    {
      Constraint ct = new Constraint(model_);
      TableConstraintProto table = new TableConstraintProto();
      foreach (IntVar var in vars)
      {
        table.Vars.Add(var.Index);
      }
      for (int i = 0; i < tuples.GetLength(0); ++i)
      {
        for (int j = 0; j < tuples.GetLength(1); ++j)
        {
          table.Values.Add(tuples[i, j]);
        }
      }
      ct.Proto.Table = table;
      return ct;
    }

    public Constraint AddForbiddenAssignments(IEnumerable<IntVar> vars,
                                              long[,] tuples)
    {
      Constraint ct = AddAllowedAssignments(vars, tuples);
      ct.Proto.Table.Negated = true;
      return ct;
    }

    public Constraint AddAutomaton(IEnumerable<IntVar> vars,
                                  long starting_state,
                                  long[,] transitions,
                                  IEnumerable<long> final_states)
    {
      Constraint ct = new Constraint(model_);
      AutomatonConstraintProto aut = new AutomatonConstraintProto();
      foreach (IntVar var in vars)
      {
        aut.Vars.Add(var.Index);
      }
      aut.StartingState = starting_state;
      foreach (long f in final_states)
      {
        aut.FinalStates.Add(f);
      }
      for (int i = 0; i < transitions.GetLength(0); ++i)
      {
        aut.TransitionTail.Add(transitions[i, 0]);
        aut.TransitionLabel.Add(transitions[i, 1]);
        aut.TransitionHead.Add(transitions[i, 2]);
      }

      ct.Proto.Automaton = aut;
      return ct;
    }

    public Constraint AddAutomaton(
        IEnumerable<IntVar> vars,
        long starting_state,
        IEnumerable<Tuple<long, long, long>> transitions,
        IEnumerable<long> final_states)
    {
      Constraint ct = new Constraint(model_);
      AutomatonConstraintProto aut = new AutomatonConstraintProto();
      foreach (IntVar var in vars)
      {
        aut.Vars.Add(var.Index);
      }
      aut.StartingState = starting_state;
      foreach (long f in final_states)
      {
        aut.FinalStates.Add(f);
      }
      foreach (Tuple<long, long, long> transition in transitions)
      {

        aut.TransitionHead.Add(transition.Item1);
        aut.TransitionLabel.Add(transition.Item2);
        aut.TransitionTail.Add(transition.Item3);
      }

      ct.Proto.Automaton = aut;
      return ct;
    }

    public Constraint AddInverse(IEnumerable<IntVar> direct,
                                 IEnumerable<IntVar> reverse)
    {
      Constraint ct = new Constraint(model_);
      InverseConstraintProto inverse = new InverseConstraintProto();
      foreach (IntVar var in direct)
      {
        inverse.FDirect.Add(var.Index);
      }
      foreach (IntVar var in reverse)
      {
        inverse.FInverse.Add(var.Index);
      }
      ct.Proto.Inverse = inverse;
      return ct;
    }

    public Constraint AddReservoirConstraint<I>(IEnumerable<IntVar> times,
                                                IEnumerable<I> demands,
                                                long min_level, long max_level)
    {
      Constraint ct = new Constraint(model_);
      ReservoirConstraintProto res = new ReservoirConstraintProto();
      foreach (IntVar var in times)
      {
        res.Times.Add(var.Index);
      }
      foreach (I d in demands)
      {
        res.Demands.Add(Convert.ToInt64(d));
      }

      ct.Proto.Reservoir = res;
      return ct;
    }

    public Constraint AddReservoirConstraintWithActive<I>(
      IEnumerable<IntVar> times,
      IEnumerable<I> demands,
      IEnumerable<IntVar> actives,
      long min_level, long max_level)
    {
      Constraint ct = new Constraint(model_);
      ReservoirConstraintProto res = new ReservoirConstraintProto();
      foreach (IntVar var in times)
      {
        res.Times.Add(var.Index);
      }
      foreach (I d in demands)
      {
        res.Demands.Add(Convert.ToInt64(d));
      }
      foreach (IntVar var in actives)
      {
        res.Actives.Add(var.Index);
      }

      ct.Proto.Reservoir = res;
      return ct;
    }

    public void AddMapDomain(
        IntVar var, IEnumerable<IntVar> bool_vars, long offset = 0)
    {
      int i = 0;
      foreach (IntVar bool_var in bool_vars)
      {
        int b_index = bool_var.Index;
        int var_index = var.Index;

        ConstraintProto ct1 = new ConstraintProto();
        LinearConstraintProto lin1 = new LinearConstraintProto();
        lin1.Vars.Add(var_index);
        lin1.Coeffs.Add(1L);
        lin1.Domain.Add(offset + i);
        lin1.Domain.Add(offset + i);
        ct1.Linear = lin1;
        ct1.EnforcementLiteral.Add(b_index);
        model_.Constraints.Add(ct1);

        ConstraintProto ct2 = new ConstraintProto();
        LinearConstraintProto lin2 = new LinearConstraintProto();
        lin2.Vars.Add(var_index);
        lin2.Coeffs.Add(1L);
        lin2.Domain.Add(Int64.MinValue);
        lin2.Domain.Add(offset + i - 1);
        lin2.Domain.Add(offset + i + 1);
        lin2.Domain.Add(Int64.MaxValue);
        ct2.Linear = lin2;
        ct2.EnforcementLiteral.Add(-b_index - 1);
        model_.Constraints.Add(ct2);

        i++;
      }
    }

    public Constraint AddImplication(ILiteral a, ILiteral b)
    {
      Constraint ct = new Constraint(model_);
      BoolArgumentProto or = new BoolArgumentProto();
      or.Literals.Add(a.Not().GetIndex());
      or.Literals.Add(b.GetIndex());
      ct.Proto.BoolOr = or;
      return ct;
    }

    public Constraint AddBoolOr(IEnumerable<ILiteral> literals)
    {
      Constraint ct = new Constraint(model_);
      BoolArgumentProto bool_argument = new BoolArgumentProto();
      foreach (ILiteral lit in literals)
      {
        bool_argument.Literals.Add(lit.GetIndex());
      }
      ct.Proto.BoolOr = bool_argument;
      return ct;
    }

    public Constraint AddBoolAnd(IEnumerable<ILiteral> literals)
    {
      Constraint ct = new Constraint(model_);
      BoolArgumentProto bool_argument = new BoolArgumentProto();
      foreach (ILiteral lit in literals)
      {
        bool_argument.Literals.Add(lit.GetIndex());
      }
      ct.Proto.BoolAnd = bool_argument;
      return ct;
    }

    public Constraint AddBoolXor(IEnumerable<ILiteral> literals)
    {
      Constraint ct = new Constraint(model_);
      BoolArgumentProto bool_argument = new BoolArgumentProto();
      foreach (ILiteral lit in literals)
      {
        bool_argument.Literals.Add(lit.GetIndex());
      }
      ct.Proto.BoolXor = bool_argument;
      return ct;
    }

    public Constraint AddMinEquality(IntVar target, IEnumerable<IntVar> vars)
    {
      Constraint ct = new Constraint(model_);
      IntegerArgumentProto args = new IntegerArgumentProto();
      foreach (IntVar var in vars)
      {
        args.Vars.Add(var.Index);
      }
      args.Target = target.Index;
      ct.Proto.IntMin = args;
      return ct;
    }

    public Constraint AddMaxEquality(IntVar target, IEnumerable<IntVar> vars)
    {
      Constraint ct = new Constraint(model_);
      IntegerArgumentProto args = new IntegerArgumentProto();
      foreach (IntVar var in vars)
      {
        args.Vars.Add(var.Index);
      }
      args.Target = target.Index;
      ct.Proto.IntMax = args;
      return ct;
    }

    public Constraint AddDivisionEquality<T, N, D>(T target, N num, D denom)
    {
      Constraint ct = new Constraint(model_);
      IntegerArgumentProto args = new IntegerArgumentProto();
      args.Vars.Add(GetOrCreateIndex(num));
      args.Vars.Add(GetOrCreateIndex(denom));
      args.Target = GetOrCreateIndex(target);
      ct.Proto.IntDiv = args;
      return ct;
    }

    public Constraint AddAbsEquality(IntVar target, IntVar var)
    {
      Constraint ct = new Constraint(model_);
      IntegerArgumentProto args = new IntegerArgumentProto();
      args.Vars.Add(var.Index);
      args.Vars.Add(-var.Index - 1);
      args.Target = target.Index;
      ct.Proto.IntMax = args;
      return ct;
    }

    public Constraint AddModuloEquality<T, V, M>(T target, V v, M m)
    {
      Constraint ct = new Constraint(model_);
      IntegerArgumentProto args = new IntegerArgumentProto();
      args.Vars.Add(GetOrCreateIndex(v));
      args.Vars.Add(GetOrCreateIndex(m));
      args.Target = GetOrCreateIndex(target);
      ct.Proto.IntMod = args;
      return ct;
    }

    public Constraint AddProdEquality(IntVar target, IEnumerable<IntVar> vars)
    {
      Constraint ct = new Constraint(model_);
      IntegerArgumentProto args = new IntegerArgumentProto();
      args.Target = target.Index;
      foreach (IntVar var in vars)
      {
        args.Vars.Add(var.Index);
      }
      ct.Proto.IntProd = args;
      return ct;
    }

    // Scheduling support

    public IntervalVar NewIntervalVar<S, D, E>(
        S start, D duration, E end, string name)
    {
      return new IntervalVar(model_,
                             GetOrCreateIndex(start),
                             GetOrCreateIndex(duration),
                             GetOrCreateIndex(end),
                             name);
    }


    public IntervalVar NewOptionalIntervalVar<S, D, E>(
        S start, D duration, E end, ILiteral is_present, string name)
    {
      int i = is_present.GetIndex();
      return new IntervalVar(model_,
                             GetOrCreateIndex(start),
                             GetOrCreateIndex(duration),
                             GetOrCreateIndex(end),
                             i,
                             name);
    }

    public Constraint AddNoOverlap(IEnumerable<IntervalVar> intervals)
    {
      Constraint ct = new Constraint(model_);
      NoOverlapConstraintProto args = new NoOverlapConstraintProto();
      foreach (IntervalVar var in intervals)
      {
        args.Intervals.Add(var.GetIndex());
      }
      ct.Proto.NoOverlap = args;
      return ct;
    }

    public Constraint AddNoOverlap2D(IEnumerable<IntervalVar> x_intervals,
                                     IEnumerable<IntervalVar> y_intervals)
    {
      Constraint ct = new Constraint(model_);
      NoOverlap2DConstraintProto args = new NoOverlap2DConstraintProto();
      foreach (IntervalVar var in x_intervals)
      {
        args.XIntervals.Add(var.GetIndex());
      }
      foreach (IntervalVar var in y_intervals)
      {
        args.YIntervals.Add(var.GetIndex());
      }
      ct.Proto.NoOverlap2D = args;
      return ct;
    }

    public Constraint AddCumulative<D, C>(IEnumerable<IntervalVar> intervals,
                                          IEnumerable<D> demands,
                                          C capacity)
    {
      Constraint ct = new Constraint(model_);
      CumulativeConstraintProto cumul = new CumulativeConstraintProto();
      foreach (IntervalVar var in intervals)
      {
        cumul.Intervals.Add(var.GetIndex());
      }
      foreach (D demand in demands)
      {
        cumul.Demands.Add(GetOrCreateIndex(demand));
      }
      cumul.Capacity = GetOrCreateIndex(capacity);
      ct.Proto.Cumulative = cumul;
      return ct;
    }


    // Objective.
    public void Minimize(LinearExpr obj)
    {
      SetObjective(obj, true);
    }

    public void Maximize(LinearExpr obj)
    {
      SetObjective(obj, false);
    }

    public void Minimize()
    {
      SetObjective(null, true);
    }

    public void Maximize()
    {
      SetObjective(null, false);
    }

    public void AddVarToObjective(IntVar var)
    {
      if ((Object)var == null) return;
      model_.Objective.Vars.Add(var.Index);
      model_.Objective.Coeffs.Add(model_.Objective.ScalingFactor > 0 ? 1 : -1);
    }

    public void AddTermToObjective(IntVar var, long coeff)
    {
      if (coeff == 0 || (Object)var == null) return;
      model_.Objective.Vars.Add(var.Index);
      model_.Objective.Coeffs.Add(model_.Objective.ScalingFactor > 0 ? coeff : -coeff);
    }

    bool HasObjective()
    {
      return model_.Objective == null;
    }

    // Search Decision.

    public void AddDecisionStrategy(IEnumerable<IntVar> vars,
                                    DecisionStrategyProto.Types.VariableSelectionStrategy var_str,
                                    DecisionStrategyProto.Types.DomainReductionStrategy dom_str)
    {
      DecisionStrategyProto ds = new DecisionStrategyProto();
      foreach (IntVar var in vars)
      {
        ds.Variables.Add(var.Index);
      }
      ds.VariableSelectionStrategy = var_str;
      ds.DomainReductionStrategy = dom_str;
      model_.SearchStrategy.Add(ds);
    }

    // Internal methods.

    void SetObjective(LinearExpr obj, bool minimize)
    {
      CpObjectiveProto objective = new CpObjectiveProto();
      if (obj == null)
      {
        objective.Offset = 0L;
        objective.ScalingFactor = minimize ? 1L : -1;
      }
      else if (obj is IntVar)
      {
        objective.Offset = 0L;
        objective.Vars.Add(obj.Index);
        if (minimize)
        {
          objective.Coeffs.Add(1L);
          objective.ScalingFactor = 1L;
        }
        else
        {
          objective.Coeffs.Add(-1L);
          objective.ScalingFactor = -1L;
        }
      }
      else
      {
        Dictionary<IntVar, long> dict = new Dictionary<IntVar, long>();
        long constant = LinearExpr.GetVarValueMap(obj, 1L, dict);
        if (minimize)
        {
          objective.ScalingFactor = 1L;
          objective.Offset = constant;
        }
        else
        {
          objective.ScalingFactor = -1L;
          objective.Offset = -constant;
        }
        foreach (KeyValuePair<IntVar, long> it in dict)
        {
          objective.Vars.Add(it.Key.Index);          
          objective.Coeffs.Add(minimize ? it.Value : -it.Value);
        }
      }
      model_.Objective = objective;
    }

    public String ModelStats()
    {
      return SatHelper.ModelStats(model_);
    }

    public String Validate()
    {
      return SatHelper.ValidateModel(model_);
    }

    private int ConvertConstant(long value)
    {
      if (constant_map_.ContainsKey(value))
      {
        return constant_map_[value];
      }
      else
      {
        int index = model_.Variables.Count;
        IntegerVariableProto var = new IntegerVariableProto();
        var.Domain.Add(value);
        var.Domain.Add(value);
        constant_map_.Add(value, index);
        model_.Variables.Add(var);
        return index;
      }
    }

    private int GetOrCreateIndex<X>(X x)
    {
      if (typeof(X) == typeof(IntVar))
      {
        IntVar vx = (IntVar)(Object)x;
        return vx.Index;
      }
      if (typeof(X) == typeof(long) || typeof(X) == typeof(int))
      {
        return ConvertConstant(Convert.ToInt64(x));
      }
      throw new ArgumentException("Cannot extract index from argument");
    }

    private CpModelProto model_;
    private Dictionary<long, int> constant_map_;
  }

}  // namespace Google.OrTools.Sat