public static CspModel PhoneFeatureModel()
{
var model = new CspModel();
var phone = model.AddVariable("phone", Domain.Binary);
var calls = model.AddVariable("calls", Domain.Binary);
var screen = model.AddVariable("screen", Domain.Binary);
var screenBw = model.AddVariable("b/w", Domain.Binary);
var screenColor = model.AddVariable("color", Domain.Binary);
var screenHd = model.AddVariable("hd", Domain.Binary);
var gps = model.AddVariable("gps", Domain.Binary);
var media = model.AddVariable("media", Domain.Binary);
var camera = model.AddVariable("camera", Domain.Binary);
var mp3 = model.AddVariable("mp3", Domain.Binary);
var test = model.AddVariable("internet", Domain.Range(0, 10));
model.AddConstraint(phone == 1);
model.AddConstraint(calls == 1);
model.AddConstraint(screen == 1);
model.AddConstraint(media >= mp3);
model.AddConstraint(media >= camera);
model.AddConstraint(screenColor >= camera);
model.AddConstraint(test <= 5);
model.AddConstraint(screenBw + screenColor + screenHd == screen);
model.AddConstraint(camera == 1);
model.AddConstraint(test >= screenColor);
model.AddConstraint(test <= screenColor);
return model;
}
private static Graph CreateGraphLayout(CspModel model)
{
var graph = new Graph();
graph.Directed = false;
graph.Attr.LayerDirection = LayerDirection.LR;
var createdEdges = new List <string>();
foreach (var variable in model.Variables)
{
var n = graph.AddNode($"{variable.Name}={variable.Value}");
if (variable.Value == -1)
{
n.Attr.FillColor = Microsoft.Msagl.Drawing.Color.Yellow;
}
n.Attr.Shape = Microsoft.Msagl.Drawing.Shape.Box;
foreach (var constraint in model.Constraints.Where(c => c.GetVariables().Any(v => v.Name == variable.Name)))
{
graph.AddNode(constraint.ToString());
//graph.AddEdge(variable.ToString(), constraint.ToString());
foreach (var target in constraint.GetVariables())
{
if (!createdEdges.Contains(constraint.ToString() + "->" + target.Name))
{
graph.AddNode(target.Name + "=" + target.Value);
graph.AddEdge(constraint.ToString(), target.Name + "=" + target.Value).Attr.ArrowheadAtTarget = ArrowStyle.None;
createdEdges.Add(constraint.ToString() + "->" + target.Name);
}
}
}
}
return(graph);
}
public static CspModel AustralianMapColoringModel()
{
var model = new CspModel();
int colors = 3;
var wa = model.AddVariable("wa", Domain.Range(0, colors));
var nt = model.AddVariable("nt", Domain.Range(0, colors));
var sa = model.AddVariable("sa", Domain.Range(0, colors));
var qu = model.AddVariable("ql", Domain.Range(0, colors));
var nsw = model.AddVariable("nsw", Domain.Range(0, colors));
var vi = model.AddVariable("vi", Domain.Range(0, colors));
var ta = model.AddVariable("ta", Domain.Range(0, colors));
model.AddConstraint(wa != nt);
model.AddConstraint(wa != sa);
model.AddConstraint(nt != sa);
model.AddConstraint(nt != qu);
model.AddConstraint(sa != nsw);
model.AddConstraint(sa != vi);
model.AddConstraint(sa != qu);
model.AddConstraint(nsw != vi);
model.AddConstraint(qu != nsw);
return model;
}
public static void PrintModel(CspModel model)
{
foreach (var variable in model.Variables)
{
Console.WriteLine($"{variable.Name} {{{string.Join(", ", variable.Domain.Values)}}}"
+ $" = {variable.Value} (Set: {variable.IsSet})");
}
}
public CspModel Resolve(CspModel model)
{
foreach (var constraint in model.Constraints)
{
var variables = constraint.GetVariables();
if (variables.Count() == 1)
{
if (constraint.Left is VariableNode var && constraint.Right is NumericNode val)
{
var variable = var.Variable;
var value = val.Evaluate();
if (constraint is EqualityConstraint equality)
{
variable.Domain = variable.Domain.Where(d => d == value);
}
else if (constraint is InequalityConstraint inequality)
{
variable.Domain = variable.Domain.Where(d => d != value);
}
else if (constraint is LessThanConstraint lessThan)
{
variable.Domain = variable.Domain.Where(d => d < value);
}
else if (constraint is LessThanOrEqualConstraint lessThanEq)
{
variable.Domain = variable.Domain.Where(d => d <= value);
}
else if (constraint is GreaterThanConstraint greaterThan)
{
variable.Domain = variable.Domain.Where(d => d > value);
}
else if (constraint is GreaterThanOrEqualConstraint greaterThanEq)
{
variable.Domain = variable.Domain.Where(d => d >= value);
}
if (variable.Domain.Count() == 0)
{
throw new EmptyDomainException($"Variable {variable.Name} has an empty domain, solution infeasible.");
}
else if (variable.Domain.Count() == 1)
{
// Assign the variable as early as possible so that the most constraints will come
// into scope. This results in earlier backtracking!
variable.Value = variable.Domain.First();
}
}
}
}
return(model);
}
internal Csp(
IDictionary <string, IEnumerable <T> > domains,
IDictionary <string, IEnumerable <string> > relations,
IEnumerable <Func <string, T, string, T, bool> > constraints
)
{
var variables = domains.Select(d => new Variable <T>(d.Key)).ToList();
_model = new CspModel <T>(
variables,
domains.Select(d => new Domain <T>(d.Key, d.Value)).ToList(),
relations.Select(d => new Relations <T>(d.Key, variables.Where(v => d.Value.Contains(v.Key)))).ToList(),
constraints.Select(d => new Constraint <T>(d)).ToList()
);
}
public static void PrintBoard(CspModel model)
{
var sb = new StringBuilder();
for (int i = 0; i < 9; i++)
{
for (int j = 0; j < 9; j++)
{
char c = model.Variables[9 * i + j].Value.ToString()[0];
sb.Append(c == '0' ? '.' : c);
}
sb.AppendLine();
}
Console.WriteLine(sb.ToString());
}
public static CspModel SudokuSmallModel()
{
var model = new CspModel();
var variables = new List<Variable>();
for (int i = 0; i < 16; i++)
{
var variable = model.AddVariable($"x{i}", Domain.Range(1, 5));
variables.Add(variable);
}
for (int i = 0; i < 16; i++)
{
int row = i / 4;
int col = i % 4;
for (int j = row; j < row + 4; j++)
{
if (i != j)
{
Console.WriteLine($"{i}!={j}");
model.AddConstraint(variables[i] != variables[j]);
}
}
for (int j = col; j < 16; j += 4)
{
if (i != j)
{
model.AddConstraint(variables[i] != variables[j]);
}
}
// TODO: Add diagonal constraints.
}
//model.AddConstraint(variables[0] != variables[1] != variables[4] != variables[5]); => AllDiff(x0, x1, x2, x3)
// also => AllEqual(1,2,3,4)
model.AddConstraint(variables[0] == 1);
model.AddConstraint(variables[1] == 2);
model.AddConstraint(variables[2] == 3);
model.AddConstraint(variables[3] == 4);
return model;
}
public ModelTest()
{
var dummyDomain = new[] { "R", "B", "G" };
var proto = new Dictionary <string, IEnumerable <DummyCspValue> >
{
["SA"] = dummyDomain.Select(c => new DummyCspValue(c)),
["WA"] = dummyDomain.Select(c => new DummyCspValue(c)),
["NT"] = dummyDomain.Select(c => new DummyCspValue(c)),
["Q"] = dummyDomain.Select(c => new DummyCspValue(c)),
["NSW"] = dummyDomain.Select(c => new DummyCspValue(c)),
["V"] = dummyDomain.Select(c => new DummyCspValue(c)),
["T"] = dummyDomain.Select(c => new DummyCspValue(c))
};
var relationsProto = new Dictionary <string, IEnumerable <string> >
{
["SA"] = new[] { "WA", "NT", "Q", "NSW", "V" },
["WA"] = new[] { "SA", "NT" },
["NT"] = new[] { "WA", "Q", "SA" },
["Q"] = new[] { "NSW", "NT", "SA" },
["NSW"] = new[] { "Q", "V", "SA" },
["V"] = new[] { "NSW", "SA" }
};
var variables = proto.Select(d => new Variable <DummyCspValue>(d.Key)).ToList();
_model = new CspModel <DummyCspValue>(
variables,
proto.Select(v => new Domain <DummyCspValue>(v.Key, v.Value)).ToList(),
relationsProto.Select(d => new Relations <DummyCspValue>(d.Key, variables.Where(v => d.Value.Contains(v.Key)))).ToList(),
new[]
{
new Constraint <DummyCspValue>(Eval)
}
);
}
public BacktrackSolver(CspModel model)
{
Model = model;
}
