StepFunctionSampleSat.cs

// Copyright 2010-2021 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.

using System;
using Google.OrTools.Sat;
using Google.OrTools.Util;

public class VarArraySolutionPrinter : CpSolverSolutionCallback
{
    public VarArraySolutionPrinter(IntVar[] variables)
    {
        variables_ = variables;
    }

    public override void OnSolutionCallback()
    {
        {
            foreach (IntVar v in variables_)
            {
                Console.Write(String.Format("{0}={1} ", v.ShortString(), Value(v)));
            }
            Console.WriteLine();
        }
    }

    private IntVar[] variables_;
}

public class StepFunctionSampleSat
{
    static void Main()
    {
        // Create the CP-SAT model.
        CpModel model = new CpModel();

        // Declare our primary variable.
        IntVar x = model.NewIntVar(0, 20, "x");

        // Create the expression variable and implement the step function
        // Note it is not defined for var == 2.
        //
        //        -               3
        // -- --      ---------   2
        //                        1
        //      -- ---            0
        // 0 ================ 20
        //
        IntVar expr = model.NewIntVar(0, 3, "expr");

        // expr == 0 on [5, 6] U [8, 10]
        ILiteral b0 = model.NewBoolVar("b0");
        model.AddLinearExpressionInDomain(x, Domain.FromValues(new long[] { 5, 6, 8, 9, 10 })).OnlyEnforceIf(b0);
        model.Add(expr == 0).OnlyEnforceIf(b0);

        // expr == 2 on [0, 1] U [3, 4] U [11, 20]
        ILiteral b2 = model.NewBoolVar("b2");
        model
            .AddLinearExpressionInDomain(
                x,
                Domain.FromIntervals(new long[][] { new long[] { 0, 1 }, new long[] { 3, 4 }, new long[] { 11, 20 } }))
            .OnlyEnforceIf(b2);
        model.Add(expr == 2).OnlyEnforceIf(b2);

        // expr == 3 when x == 7
        ILiteral b3 = model.NewBoolVar("b3");
        model.Add(x == 7).OnlyEnforceIf(b3);
        model.Add(expr == 3).OnlyEnforceIf(b3);

        // At least one bi is true. (we could use a sum == 1).
        model.AddBoolOr(new ILiteral[] { b0, b2, b3 });

        // Search for x values in increasing order.
        model.AddDecisionStrategy(new IntVar[] { x }, DecisionStrategyProto.Types.VariableSelectionStrategy.ChooseFirst,
                                  DecisionStrategyProto.Types.DomainReductionStrategy.SelectMinValue);

        // Create the solver.
        CpSolver solver = new CpSolver();

        // Force solver to follow the decision strategy exactly.
        solver.StringParameters = "search_branching:FIXED_SEARCH";

        VarArraySolutionPrinter cb = new VarArraySolutionPrinter(new IntVar[] { x, expr });
        solver.SearchAllSolutions(model, cb);
    }
}