Decider

An Open Source .Net Constraint Programming Solver

Installation

Install using nuget for .Net Core 2.1

 dotnet add package Decider

Variables

Create constrained integer variables

var s = new VariableInteger("s", 0, 9);
var e = new VariableInteger("e", 0, 9);
var n = new VariableInteger("n", 0, 9);
var d = new VariableInteger("d", 0, 9);
var m = new VariableInteger("m", 1, 9);
var o = new VariableInteger("o", 0, 9);
var r = new VariableInteger("r", 0, 9);
var y = new VariableInteger("y", 0, 9);
var c0 = new VariableInteger("c0", 0, 1);
var c1 = new VariableInteger("c1", 0, 1);
var c2 = new VariableInteger("c2", 0, 1);
var c3 = new VariableInteger("c3", 0, 1);

Constraints

Define the constraints of your problem

var constraints = new List<IConstraint>
{
    new AllDifferentInteger(new [] { s, e, n, d, m, o, r, y }),
    new ConstraintInteger(d + e == (10 * c0) + y),
    new ConstraintInteger(n + r + c0 == (10 * c1) + e),
    new ConstraintInteger(e + o + c1 == (10 * c2) + n),
    new ConstraintInteger(s + m + c2 == (10 * c3) + o),
    new ConstraintInteger(c3 == m)
};

Search

Find a solution using Decider's search routines

var variables = new [] { c0, c1, c2, c3, s, e, n, d, m, o, r, y };
IState<int> state = new StateInteger(variables, constraints);

state.StartSearch(out StateOperationResult searchResult);

Console.WriteLine("    {0} {1} {2} {3} ", s, e, n, d);
Console.WriteLine("  + {0} {1} {2} {3} ", m, o, r, e);
Console.WriteLine("  ---------");
Console.WriteLine("  {0} {1} {2} {3} {4} ", m, o, n, e, y);

Console.WriteLine("Runtime:\t{0}\nBacktracks:\t{1}\n", state.Runtime, state.Backtracks);

Which results in

    9 5 6 7
  + 1 0 8 5
  ---------
  1 0 6 5 2

Runtime:        00:00:00.0290211
Backtracks:     85

Find All Solutions

Display all solutions to the n-queens problem

state.StartSearch(out StateOperationResult searchResult,
    out IList<IDictionary<string, IVariable<int>>> solutions);

foreach (var solution in solutions)
{
    for (var i = 0; i < variables.Length; ++i)
    {
        for (var j = 0; j < variables.Length; ++j)
            Console.Write(solution[i.ToString()].InstantiatedValue == j ? "Q" : ".");

        Console.WriteLine();
    }
    Console.WriteLine();
}

Which results in

Q.......
....Q...
.......Q
.....Q..
..Q.....
......Q.
.Q......
...Q....

Q.......
.....Q..
.......Q
..Q.....
......Q.
...Q....
.Q......
....Q...

and a further ninety solutions.

Optimise

Create an integer variable to optimise

new ConstraintInteger(optimise == a + b + c + d + e + f + g + h)

Specify an upper time bound on how long you search, say, five minutes

var timeout = 60 * 5;
var solution = default(IDictionary<string, IVariable<int>>);
state.StartSearch(out StateOperationResult searchResult, optimise, out solution, timeout);

Constrained Arrays

Index integer arrays with constained integer variables

var a = new VariableInteger("a", 0, 9);
var array = new ConstrainedArray(new int[] { 0, 23, 52, 62, 75, 73, 47, 20, 87, 27 });
    
var constraint = new ConstraintInteger(array[a] < 40)

More Examples?

Fork the repo to see more examples, some toy and some real world, of Decider in action.

Licence

Released under the MIT licence, Decider is freely available for commercial use.

Author

I have a PhD in Constraint Programming and love turning NP-complete problems into CSPs. Visit my blog at http://lifebeyondfife.com/.

mafifi/Decider