public static Theorem <SudokuTable> Create(Z3Context context)
{
var sudokuTheorem = context.NewTheorem <SudokuTable>();
var cells = typeof(SudokuTable).GetProperties();
foreach (var cell in cells)
{
sudokuTheorem = sudokuTheorem.Where(Between1And9(cell));
}
sudokuTheorem = sudokuTheorem.Where(DistinctRows(cells));
sudokuTheorem = sudokuTheorem.Where(DistinctColumns(cells));
sudokuTheorem = sudokuTheorem.Where(t => Z3Methods.Distinct(t.Cell11, t.Cell12, t.Cell13, t.Cell21, t.Cell22, t.Cell23, t.Cell31, t.Cell32, t.Cell33));
sudokuTheorem = sudokuTheorem.Where(t => Z3Methods.Distinct(t.Cell14, t.Cell15, t.Cell16, t.Cell24, t.Cell25, t.Cell26, t.Cell34, t.Cell35, t.Cell36));
sudokuTheorem = sudokuTheorem.Where(t => Z3Methods.Distinct(t.Cell17, t.Cell18, t.Cell19, t.Cell27, t.Cell28, t.Cell29, t.Cell37, t.Cell38, t.Cell39));
sudokuTheorem = sudokuTheorem.Where(t => Z3Methods.Distinct(t.Cell41, t.Cell42, t.Cell43, t.Cell51, t.Cell52, t.Cell53, t.Cell61, t.Cell62, t.Cell63));
sudokuTheorem = sudokuTheorem.Where(t => Z3Methods.Distinct(t.Cell44, t.Cell45, t.Cell46, t.Cell54, t.Cell55, t.Cell56, t.Cell64, t.Cell65, t.Cell66));
sudokuTheorem = sudokuTheorem.Where(t => Z3Methods.Distinct(t.Cell47, t.Cell48, t.Cell49, t.Cell57, t.Cell58, t.Cell59, t.Cell67, t.Cell68, t.Cell69));
sudokuTheorem = sudokuTheorem.Where(t => Z3Methods.Distinct(t.Cell71, t.Cell72, t.Cell73, t.Cell81, t.Cell82, t.Cell83, t.Cell91, t.Cell92, t.Cell93));
sudokuTheorem = sudokuTheorem.Where(t => Z3Methods.Distinct(t.Cell74, t.Cell75, t.Cell76, t.Cell84, t.Cell85, t.Cell86, t.Cell94, t.Cell95, t.Cell96));
sudokuTheorem = sudokuTheorem.Where(t => Z3Methods.Distinct(t.Cell77, t.Cell78, t.Cell79, t.Cell87, t.Cell88, t.Cell89, t.Cell97, t.Cell98, t.Cell99));
return(sudokuTheorem);
}
/// <summary>
/// Creates a Z3-capable theorem to solve a Sudoku
/// </summary>
/// <param name="context">The wrapping Z3 context used to interpret c# Lambda into Z3 constraints</param>
/// <returns>A typed theorem to be further filtered with additional contraints</returns>
public static Theorem <SudokuAsArray> Create(Z3Context context)
{
var sudokuTheorem = context.NewTheorem <SudokuAsArray>();
// Cells have values between 1 and 9
for (int i = 0; i < 9; i++)
{
for (int j = 0; j < 9; j++)
{
//To avoid side effects with lambdas, we copy indices to local variables
var i1 = i;
var j1 = j;
sudokuTheorem = sudokuTheorem.Where(sudoku => sudoku.Cells[i1 * 9 + j1] > 0 && sudoku.Cells[i1 * 9 + j1] < 10);
}
}
// Rows must have distinct digits
for (int r = 0; r < 9; r++)
{
//Again we avoid Lambda closure side effects
var r1 = r;
sudokuTheorem = sudokuTheorem.Where(t => Z3Methods.Distinct(Indices.Select(j => t.Cells[r1 * 9 + j]).ToArray()));
}
// Columns must have distinct digits
for (int c = 0; c < 9; c++)
{
//Preventing closure side effects
var c1 = c;
sudokuTheorem = sudokuTheorem.Where(t => Z3Methods.Distinct(Indices.Select(i => t.Cells[i * 9 + c1]).ToArray()));
}
// Boxes must have distinct digits
for (int b = 0; b < 9; b++)
{
//On évite les effets de bords par closure
var b1 = b;
// We retrieve to top left cell for all boxes, using integer division and remainders.
var iStart = b1 / 3;
var jStart = b1 % 3;
var indexStart = iStart * 3 * 9 + jStart * 3;
sudokuTheorem = sudokuTheorem.Where(t => Z3Methods.Distinct(new int[]
{
t.Cells[indexStart],
t.Cells[indexStart + 1],
t.Cells[indexStart + 2],
t.Cells[indexStart + 9],
t.Cells[indexStart + 10],
t.Cells[indexStart + 11],
t.Cells[indexStart + 18],
t.Cells[indexStart + 19],
t.Cells[indexStart + 20],
}
)
);
}
return(sudokuTheorem);
}
public Sudoku.Core.Sudoku Solve(Sudoku.Core.Sudoku s)
{
using (var ctx = new Z3Context())
{
var theorem = CreateTheorem(ctx, s);
theorem.DefaultCollectionHandling = CollectionHandling.Constants;
return(theorem.Solve());
}
}
///// <summary>
///// The array property is to be used in linq to Z3
///// </summary>
//public int[] Cells
//{
// get => CellsList.ToArray();
// set => CellsList = new List<int>(value);
//}
/// <summary>
/// Creates a Z3 theorem to solve the sudoku, adding the general constraints, and the mask constraints for this particular Sudoku
/// </summary>
/// <param name="context">The linq to Z3 context wrapping Z3</param>
/// <returns>a theorem with all constraints compounded</returns>
public Theorem <SudokuAsArray> CreateTheorem(Z3Context context)
{
var toReturn = Create(context);
for (int i = 0; i < 81; i++)
{
if (Cells[i] != 0)
{
var idx = i;
var cellValue = Cells[i];
toReturn = toReturn.Where(sudoku => sudoku.Cells[idx] == cellValue);
}
}
return(toReturn);
}
private static void Main(string[] args)
{
// Basic Usage
using (var ctx = new Z3Context())
{
ctx.Log = Console.Out; // see internal logging
var theorem = from t in ctx.NewTheorem(new { x = default(bool), y = default(bool) })
where t.x ^ t.y
select t;
var result = theorem.Solve();
Console.WriteLine(result);
}
// Advanced Usage
using (var ctx = new Z3Context())
{
ctx.Log = Console.Out; // see internal logging
var theorem = from t in ctx.NewTheorem <Symbols <int, int> >()
where t.X1 < t.X2 + 1
where t.X1 > 2
where t.X1 != t.X2
select t;
var result = theorem.Solve();
Console.WriteLine(result);
}
// Sudoku Extension Usage (Z3.LinqBinding.Sudoku)
using (var ctx = new Z3Context())
{
var theorem = from t in SudokuTheorem.Create(ctx)
where t.Cell13 == 2 && t.Cell16 == 1 && t.Cell18 == 6
where t.Cell23 == 7 && t.Cell26 == 4
where t.Cell31 == 5 && t.Cell37 == 9
where t.Cell42 == 1 && t.Cell44 == 3
where t.Cell51 == 8 && t.Cell55 == 5 && t.Cell59 == 4
where t.Cell66 == 6 && t.Cell68 == 2
where t.Cell73 == 6 && t.Cell79 == 7
where t.Cell84 == 8 && t.Cell87 == 3
where t.Cell92 == 4 && t.Cell94 == 9 && t.Cell97 == 2
select t;
var result = theorem.Solve();
Console.WriteLine(result);
}
// All samples
using (var ctx = new Z3Context())
{
ctx.Log = Console.Out; // see internal logging
Print(from t in ctx.NewTheorem(new { x = default(bool) })
where t.x && !t.x
select t);
Print(from t in ctx.NewTheorem(new { x = default(bool), y = default(bool) })
where t.x ^ t.y
select t);
Print(from t in ctx.NewTheorem(new { x = default(int), y = default(int) })
where t.x < t.y + 1
where t.x > 2
select t);
Print(from t in ctx.NewTheorem <Symbols <int, int> >()
where t.X1 < t.X2 + 1
where t.X1 > 2
where t.X1 != t.X2
select t);
Print(from t in ctx.NewTheorem <Symbols <int, int, int, int, int> >()
where t.X1 - t.X2 >= 1
where t.X1 - t.X2 <= 3
where t.X1 == (2 * t.X3) + t.X5
where t.X3 == t.X5
where t.X2 == 6 * t.X4
select t);
Print(from t in ctx.NewTheorem <Symbols <int, int> >()
where Z3Methods.Distinct(t.X1, t.X2)
select t);
Print(from t in SudokuTheorem.Create(ctx)
where t.Cell13 == 2 && t.Cell16 == 1 && t.Cell18 == 6
where t.Cell23 == 7 && t.Cell26 == 4
where t.Cell31 == 5 && t.Cell37 == 9
where t.Cell42 == 1 && t.Cell44 == 3
where t.Cell51 == 8 && t.Cell55 == 5 && t.Cell59 == 4
where t.Cell66 == 6 && t.Cell68 == 2
where t.Cell73 == 6 && t.Cell79 == 7
where t.Cell84 == 8 && t.Cell87 == 3
where t.Cell92 == 4 && t.Cell94 == 9 && t.Cell97 == 2
select t);
}
}
private static void Main(string[] args)
{
// Basic Usage
using (var ctx = new Z3Context())
{
ctx.Log = Console.Out; // see internal logging
var theorem = from t in ctx.NewTheorem(new { x = default(bool), y = default(bool) })
where t.x ^ t.y
select t;
var result = theorem.Solve();
Console.WriteLine(result);
}
// Advanced Usage
using (var ctx = new Z3Context())
{
ctx.Log = Console.Out; // see internal logging
var theorem = from t in ctx.NewTheorem <Symbols <int, int> >()
where t.X1 < t.X2 + 1
where t.X1 > 2
where t.X1 != t.X2
select t;
var result = theorem.Solve();
Console.WriteLine(result);
}
// Sudoku Extension Usage (Z3.LinqBinding.Sudoku)
using (var ctx = new Z3Context())
{
var theorem = from t in SudokuTheorem.Create(ctx)
where t.Cell13 == 2 && t.Cell16 == 1 && t.Cell18 == 6
where t.Cell23 == 7 && t.Cell26 == 4
where t.Cell31 == 5 && t.Cell37 == 9
where t.Cell42 == 1 && t.Cell44 == 3
where t.Cell51 == 8 && t.Cell55 == 5 && t.Cell59 == 4
where t.Cell66 == 6 && t.Cell68 == 2
where t.Cell73 == 6 && t.Cell79 == 7
where t.Cell84 == 8 && t.Cell87 == 3
where t.Cell92 == 4 && t.Cell94 == 9 && t.Cell97 == 2
select t;
var result = theorem.Solve();
Console.WriteLine(result);
}
// Sudoku Extension Usage (Z3.LinqBinding.Sudoku)
using (var ctx = new Z3Context())
{
var theorem = SudokuAsArray
.Parse("9.2..54.31...63.255.84.7.6..263.9..1.57.1.29..9.67.53.24.53.6..7.52..3.4.8..4195.") // Very easy
.CreateTheorem(ctx);
var result = theorem.Solve();
Console.WriteLine(result);
theorem = SudokuAsArray
.Parse("..48...1767.9.....5.8.3...43..74.1...69...78...1.69..51...8.3.6.....6.9124...15..") // Easy
.CreateTheorem(ctx);
result = theorem.Solve();
Console.WriteLine(result);
theorem = SudokuAsArray
.Parse("..6.......8..542...4..9..7...79..3......8.4..6.....1..2.3.67981...5...4.478319562") // Medium
.CreateTheorem(ctx);
result = theorem.Solve();
Console.WriteLine(result);
theorem = SudokuAsArray
.Parse("....9.4.8.....2.7..1.7....32.4..156...........952..7.19....5.1..3.4.....1.2.7....") // Hard
.CreateTheorem(ctx);
result = theorem.Solve();
Console.WriteLine(result);
}
// Solving Canibals & Missionaires
using (var ctx = new Z3Context())
{
var can = new MissionariesAndCannibals()
{
NbMissionaries = 3, SizeBoat = 2, Length = 50
};
var startTime = stopwatch.Elapsed;
var minimal = MissionariesAndCannibals.SearchMinimal(can);
var endTime = stopwatch.Elapsed;
Console.WriteLine("Minimal Solution to missionaries and cannibals through Binary search");
Console.WriteLine(minimal == null ? "none" : minimal.ToString());
Console.WriteLine($"Time to solve: {endTime - startTime}");
var theorem = can.Create(ctx);
startTime = stopwatch.Elapsed;
minimal = theorem.Optimize(Optimization.Minimize, objMnC => objMnC.Length);
endTime = stopwatch.Elapsed;
Console.WriteLine("Minimal Solution to missionaries and cannibals through Z3 optimization");
Console.WriteLine(minimal == null ? "none" : minimal.ToString());
Console.WriteLine($"Time to solve: {endTime - startTime}");
}
// Testing simplification
using (var ctx = new Z3Context())
{
//ctx.Log = Console.Out;
var can = new MissionariesAndCannibals()
{
NbMissionaries = 3, SizeBoat = 2, Length = 30
};
Console.WriteLine($"Non simplified version");
Console.WriteLine();
var theorem = can.Create(ctx);
theorem.SimplifyLambdas = false;
var startTime = stopwatch.Elapsed;
var minimal = theorem.Optimize(Optimization.Minimize, objMnC => objMnC.Length);
var endTime = stopwatch.Elapsed;
Console.WriteLine("Minimal Solution to missionaries and cannibals non simplified through Z3 optimization");
Console.WriteLine($"Time to solve: {endTime - startTime}");
Console.WriteLine($"simplified version");
Console.WriteLine();
theorem.SimplifyLambdas = true;
startTime = stopwatch.Elapsed;
minimal = theorem.Optimize(Optimization.Minimize, objMnC => objMnC.Length);
endTime = stopwatch.Elapsed;
Console.WriteLine("Minimal Solution to missionaries and cannibals simplified through Z3 optimization");
Console.WriteLine($"Time to solve: {endTime - startTime}");
}
//AllSamplesInSameContext();
Console.Read();
}
private static void AllSamplesInSameContext()
{
// All samples
using (var ctx = new Z3Context())
{
ctx.Log = Console.Out; // see internal logging
Print(from t in ctx.NewTheorem(new
{
x = default(bool)
})
where t.x && !t.x
select t);
Print(from t in ctx.NewTheorem(new
{
x = default(bool),
y = default(bool)
})
where t.x ^ t.y
select t);
Print(from t in ctx.NewTheorem(new
{
x = default(int),
y = default(int)
})
where t.x < t.y + 1
where t.x > 2
select t);
Print(from t in ctx.NewTheorem <Symbols <int, int> >()
where t.X1 < t.X2 + 1
where t.X1 > 2
where t.X1 != t.X2
select t);
Print(from t in ctx.NewTheorem <Symbols <int, int, int, int, int> >()
where t.X1 - t.X2 >= 1
where t.X1 - t.X2 <= 3
where t.X1 == (2 * t.X3) + t.X5
where t.X3 == t.X5
where t.X2 == 6 * t.X4
select t);
Print(from t in ctx.NewTheorem <Symbols <int, int> >()
where Z3Methods.Distinct(t.X1, t.X2)
select t);
Print(from t in SudokuTheorem.Create(ctx)
where t.Cell13 == 2 && t.Cell16 == 1 && t.Cell18 == 6
where t.Cell23 == 7 && t.Cell26 == 4
where t.Cell31 == 5 && t.Cell37 == 9
where t.Cell42 == 1 && t.Cell44 == 3
where t.Cell51 == 8 && t.Cell55 == 5 && t.Cell59 == 4
where t.Cell66 == 6 && t.Cell68 == 2
where t.Cell73 == 6 && t.Cell79 == 7
where t.Cell84 == 8 && t.Cell87 == 3
where t.Cell92 == 4 && t.Cell94 == 9 && t.Cell97 == 2
select t);
// Sudoku Extension Usage Z3.LinqBinding.Sudoku demonstrating array capabilities
Print <SudokuAsArray>(SudokuAsArray
.Parse("9.2..54.31...63.255.84.7.6..263.9..1.57.1.29..9.67.53.24.53.6..7.52..3.4.8..4195.") // Very easy
.CreateTheorem(ctx));
Print <SudokuAsArray>(SudokuAsArray
.Parse("..48...1767.9.....5.8.3...43..74.1...69...78...1.69..51...8.3.6.....6.9124...15..") // Easy
.CreateTheorem(ctx));
Print <SudokuAsArray>(SudokuAsArray
.Parse("..6.......8..542...4..9..7...79..3......8.4..6.....1..2.3.67981...5...4.478319562") // Medium
.CreateTheorem(ctx));
Print <SudokuAsArray>(SudokuAsArray
.Parse("....9.4.8.....2.7..1.7....32.4..156...........952..7.19....5.1..3.4.....1.2.7....") // Hard
.CreateTheorem(ctx));
// Solving Canibals & Missionaires
var can = new MissionariesAndCannibals()
{
NbMissionaries = 3, SizeBoat = 2, Length = 50
};
Print <MissionariesAndCannibals>(can.Create(ctx));
}
}