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How to: Apply a Constraint Programming Directive

Solver Foundation 3.0

You can use constraint programming to find every possible coloring of a map with four colors. The map has four countries and none of the neighboring countries can be the same color.

The following steps show how to use Solver Foundation to create and solve the map coloring problem by using the Solver Foundation Services layer.

To apply a constraint programming directive to map coloring

  1. Create a Console Application named MapColoring.

  2. Add a reference to Microsoft Solver Foundation on the .NET tab.

  3. Add the following Imports or using statements to the top of the Program code file.

    
    using Microsoft.SolverFoundation.Services;
    using Microsoft.SolverFoundation.Common;
    
    
    
  4. In the Main method, add the following code to get the context environment for a solver and create a new model.

    
    SolverContext context = SolverContext.GetContext();
    Model model = context.CreateModel();
    
    
    
  5. Create a domain variable that represents the four colors available for the map and four decision variables that represent four countries.

    
    Domain colors = Domain.Enum("red", "green", "blue", "yellow");
    Decision be = new Decision(colors, "belgium");
    Decision de = new Decision(colors, "germany");
    Decision fr = new Decision(colors, "france");
    Decision nl = new Decision(colors, "netherlands");
    model.AddDecisions(be, de, fr, nl);
    
    
    
  6. Add five constraints that prevent neighboring countries from having the same color.

    
    model.AddConstraints("borders", 
      be != de, be != fr, be != nl, de != fr, de != nl);
    
    
    
  7. Add a constraint programming directive and solve the model. Then, write the solutions to the console window.

    
    Solution solution = context.Solve(new ConstraintProgrammingDirective());
    while (solution.Quality != SolverQuality.Infeasible) {
      Console.WriteLine("Belgium: {0}\tGermany: {1}\tFrance: {2}\tNetherlands: {3}",
        be, de, fr, nl);
      solution.GetNext();
    }
    
    
    
  8. Press F5 to build and run the code.

    The command window shows the following results.

    Belgium: green Germany: red France: blue Netherlands: blue

    Belgium: green Germany: red France: yellow Netherlands: blue

    Belgium: green Germany: red France: blue Netherlands: yellow

    Belgium: green Germany: red France: yellow Netherlands: yellow

    Belgium: blue Germany: red France: green Netherlands: green

    Belgium: blue Germany: red France: green Netherlands: yellow

    Belgium: blue Germany: red France: yellow Netherlands: green

    Belgium: blue Germany: red France: yellow Netherlands: yellow

    Belgium: yellow Germany: red France: green Netherlands: green

    Belgium: yellow Germany: red France: blue Netherlands: green

    Belgium: yellow Germany: red France: green Netherlands: blue

    Belgium: yellow Germany: red France: blue Netherlands: blue

    Belgium: red Germany: green France: blue Netherlands: blue

    Belgium: red Germany: green France: blue Netherlands: yellow

    Belgium: red Germany: green France: yellow Netherlands: blue

    Belgium: red Germany: green France: yellow Netherlands: yellow

    Belgium: blue Germany: green France: red Netherlands: red

    Belgium: blue Germany: green France: yellow Netherlands: red

    Belgium: blue Germany: green France: red Netherlands: yellow

    Belgium: blue Germany: green France: yellow Netherlands: yellow

    Belgium: yellow Germany: green France: red Netherlands: red

    Belgium: yellow Germany: green France: red Netherlands: blue

    Belgium: yellow Germany: green France: blue Netherlands: red

    Belgium: yellow Germany: green France: blue Netherlands: blue

    Belgium: red Germany: blue France: green Netherlands: green

    Belgium: red Germany: blue France: yellow Netherlands: green

    Belgium: red Germany: blue France: green Netherlands: yellow

    Belgium: red Germany: blue France: yellow Netherlands: yellow

    Belgium: green Germany: blue France: red Netherlands: red

    Belgium: green Germany: blue France: red Netherlands: yellow

    Belgium: green Germany: blue France: yellow Netherlands: red

    Belgium: green Germany: blue France: yellow Netherlands: yellow

    Belgium: yellow Germany: blue France: red Netherlands: red

    Belgium: yellow Germany: blue France: green Netherlands: red

    Belgium: yellow Germany: blue France: red Netherlands: green

    Belgium: yellow Germany: blue France: green Netherlands: green

    Belgium: red Germany: yellow France: green Netherlands: green

    Belgium: red Germany: yellow France: green Netherlands: blue

    Belgium: red Germany: yellow France: blue Netherlands: green

    Belgium: red Germany: yellow France: blue Netherlands: blue

    Belgium: green Germany: yellow France: red Netherlands: red

    Belgium: green Germany: yellow France: blue Netherlands: red

    Belgium: green Germany: yellow France: red Netherlands: blue

    Belgium: green Germany: yellow France: blue Netherlands: blue

    Belgium: blue Germany: yellow France: red Netherlands: red

    Belgium: blue Germany: yellow France: red Netherlands: green

    Belgium: blue Germany: yellow France: green Netherlands: red

    Belgium: blue Germany: yellow France: green Netherlands: green

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