public void SecondaryColumnsCanBeCoveredOnlyOnceLikePrimaryColumns()
{
// Arrange
var matrix = new List <List <int> >
{
new List <int> {
1, 0, 0, 0, 1
}, // 0
new List <int> {
0, 1, 1, 0, 0
}, // 1
new List <int> {
1, 0, 0, 1, 0
}, // 2
new List <int> {
0, 0, 1, 1, 0
}, // 3
new List <int> {
0, 1, 0, 0, 1
}, // 4
new List <int> {
0, 0, 1, 0, 1
} // 5
};
var dlx = new Dlx();
// Act
var solutions = dlx.Solve(matrix, d => d, r => r, 4).ToList();
// Assert
Assert.That(solutions, Has.Count.EqualTo(1));
Assert.That(solutions.Select(s => s.RowIndexes), Contains.Item(new[] { 1, 2 }));
}
public void SearchStepEventsHaveIncreasingIteration()
{
var matrix = new[, ]
{
{ 0, 0, 1, 0, 1, 1, 0 },
{ 1, 0, 0, 1, 0, 0, 1 },
{ 0, 1, 1, 0, 0, 1, 0 },
{ 1, 0, 0, 1, 0, 0, 0 },
{ 0, 1, 0, 0, 0, 0, 1 },
{ 0, 0, 0, 1, 1, 0, 1 }
};
var dlx = new Dlx();
var searchStepEventArgs = new List <SearchStepEventArgs>();
dlx.SearchStep += (_, e) => searchStepEventArgs.Add(e);
// ReSharper disable once ReturnValueOfPureMethodIsNotUsed
dlx.Solve(matrix).First();
Assert.That(searchStepEventArgs.Count, Is.GreaterThanOrEqualTo(5));
foreach (var index in Enumerable.Range(0, 5))
{
Assert.That(searchStepEventArgs[index].Iteration, Is.EqualTo(index));
}
}
private void SolvePuzzleInBackground()
{
var tetraSticks = Model.TetraSticks.All.Where(ts => ts.Tag != _tetraStickToOmit.Tag).ToImmutableList();
var rows = RowBuilder.BuildRows(tetraSticks);
var matrix = DlxMatrixBuilder.BuildDlxMatrix(tetraSticks, rows);
var dlx = new Dlx(_cancellationToken);
dlx.SearchStep += (_, searchStepEventArgs) =>
{
var placedTetraSticks = searchStepEventArgs.RowIndexes.Select(idx => rows[idx]).ToImmutableList();
_synchronizationContext.Post(_onSearchStep, placedTetraSticks);
};
//var solutions = dlx.Solve(matrix, d => d, r => r, 75);
//foreach (var solution in solutions)
//{
// var placedTetraSticks = solution.RowIndexes.Select(idx => rows[idx]).ToImmutableList();
// _synchronizationContext.Post(_onSolutionFound, placedTetraSticks);
//}
var solution = dlx.Solve(matrix, d => d, r => r, 75).First();
{
var placedTetraSticks = solution.RowIndexes.Select(idx => rows[idx]).ToImmutableList();
_synchronizationContext.Post(_onSolutionFound, placedTetraSticks);
}
_synchronizationContext.Post(_onDoneSolving);
}
public void SecondaryColumnsCanBeCoveredOnlyOnceLikePrimaryColumns()
{
// Arrange
var matrix = new List <List <int> >
{
new List <int> {
1, 0, 0, 0, 1
}, // 0
new List <int> {
0, 1, 1, 0, 0
}, // 1
new List <int> {
1, 0, 0, 1, 0
}, // 2
new List <int> {
0, 0, 1, 1, 0
}, // 3
new List <int> {
0, 1, 0, 0, 1
}, // 4
new List <int> {
0, 0, 1, 0, 1
} // 5
};
var dlx = new Dlx();
// Act
var solutions = dlx.Solve(matrix, d => d, r => r, 4).ToList();
// Assert
AssertSolutions(solutions, new[] {
new[] { 1, 2 }
});
}
public void SolutionFoundEventFiresOnceForEachSolutionTaken(int numSolutionsToTake)
{
var matrix = new[, ]
{
{ 1, 0, 0, 0 },
{ 0, 1, 1, 0 },
{ 1, 0, 0, 1 },
{ 0, 0, 1, 1 },
{ 0, 1, 0, 0 },
{ 0, 0, 1, 0 }
};
var dlx = new Dlx();
var solutionFoundEventArgs = new List <SolutionFoundEventArgs>();
dlx.SolutionFound += (_, e) => solutionFoundEventArgs.Add(e);
// ReSharper disable once ReturnValueOfPureMethodIsNotUsed
dlx.Solve(matrix).Take(numSolutionsToTake).ToList();
Assert.That(solutionFoundEventArgs.Count, Is.EqualTo(numSolutionsToTake));
foreach (var index in Enumerable.Range(0, numSolutionsToTake))
{
Assert.That(solutionFoundEventArgs[index].SolutionIndex, Is.EqualTo(index));
}
}
public Sudoku ResoudreSudoku(Sudoku s)
{
var internalRows = BuildInternalRowsForGrid(s);
var dlxRows = BuildDlxRows(internalRows);
var solutions = new Dlx()
.Solve(dlxRows, d => d, r => r)
.Where(solution => VerifySolution(internalRows, solution))
.ToImmutableList();
Console.WriteLine();
if (solutions.Any())
{
Console.WriteLine($"First solution (of {solutions.Count}):");
Console.WriteLine();
DrawSolution(internalRows, solutions.First());
Console.WriteLine();
}
else
{
Console.WriteLine("No solutions found!");
}
Console.Read();
return(s);
}
public void CanGetTheFirstSolutionUsingFirst()
{
// Arrange
var matrix = new[, ]
{
{ 1, 0, 0, 0 },
{ 0, 1, 1, 0 },
{ 1, 0, 0, 1 },
{ 0, 0, 1, 1 },
{ 0, 1, 0, 0 },
{ 0, 0, 1, 0 }
};
var dlx = new Dlx();
var numSolutionFoundEventsRaised = 0;
dlx.SolutionFound += (_, __) => numSolutionFoundEventsRaised++;
// Act
var firstSolution = dlx.Solve(matrix).First();
// Assert
Assert.That(firstSolution.RowIndexes, Is.EquivalentTo(new[] { 0, 3, 4 })
.Or
.EquivalentTo(new[] { 1, 2 })
.Or
.EquivalentTo(new[] { 2, 4, 5 }));
Assert.That(numSolutionFoundEventsRaised, Is.EqualTo(1));
}
public Sudoku.Core.Sudoku Solve(Sudoku.Core.Sudoku s)
{
var strGrid = new List <string>(9);
for (int i = 0; i < 9; i++)
{
var i1 = i;
strGrid.Add(string.Join("", Indices.Select(j => s.Cells[i1 * 9 + j]).Select(i2 => i2 == 0 ? " " : i2.ToString(CultureInfo.InvariantCulture))));
}
var grid = new Grid(ImmutableList.Create(strGrid.ToArray()));
/*int[,] mySudoku = new int[9, 9];
* for (int i = 0; i < 9; i++) {
* for (int j = 0; j < 9; j++) {
* mySudoku[i, j] = mySudoku[i, s.Cells[j]];
* }
* }
*/
//var internalRows = BuildInternalRowsForSudoku(mySudoku);
var internalRows = BuildInternalRowsForSudoku(grid);
var dlxRows = BuildDlxRows(internalRows);
var solutions = new Dlx()
.Solve(dlxRows, d => d, r => r)
.Where(solution => VerifySolution(internalRows, solution))
.ToImmutableList();
//return SolutionToGrid(internalRows, solutions.First());
return(SolutionToSudoku(internalRows, solutions.First(), s));
}
public void CanGetTheFirstSolutionUsingFirst()
{
// Arrange
var matrix = new[, ]
{
{ 1, 0, 0, 0 },
{ 0, 1, 1, 0 },
{ 1, 0, 0, 1 },
{ 0, 0, 1, 1 },
{ 0, 1, 0, 0 },
{ 0, 0, 1, 0 }
};
var dlx = new Dlx();
var numSolutionFoundEventsRaised = 0;
dlx.SolutionFound += (_, __) => numSolutionFoundEventsRaised++;
// Act
var firstSolution = dlx.Solve(matrix).First();
AssertSolution(firstSolution, new[] {
new[] { 0, 3, 4 },
new[] { 1, 2 },
new[] { 2, 4, 5 },
});
Assert.Equal(numSolutionFoundEventsRaised, 1);
}
public IEnumerable <PiecePlacement> Solve()
{
BuildMatrixAndDictionary();
var dlx = new Dlx();
var solution = dlx.Solve(_data, d => d, r => r.MatrixRow).First();
return(solution.RowIndexes.Select(rowIndex => _data[rowIndex].PiecePlacement));
}
public SudokuLib.Sudoku Solve(SudokuLib.Sudoku sudoku)
{
var matrix = createMatrix(sudoku);
var dlx = new Dlx();
var firstTwoSolutions = dlx.Solve(matrix).First();
SudokuLib.Sudoku toReturn = createSudoku(firstTwoSolutions);
return(toReturn);
}
public Solver(IEnumerable <Piece> pieces, int boardSize)
{
_cancellationTokenSource = new CancellationTokenSource();
_dlx = new Dlx(_cancellationTokenSource.Token);
_pieces = pieces.ToArray();
_board = new Board(boardSize);
_board.ForceColourOfSquareZeroZeroToBeWhite();
SearchSteps = new ConcurrentQueue <SearchStep>();
}
public void EmptyMatrixReturnsNoSolutions()
{
// Arrange
var matrix = new bool[0, 0];
var dlx = new Dlx();
// Act
var solutions = dlx.Solve(matrix);
// Assert
Assert.That(solutions.Count(), Is.EqualTo(0));
}
public void EmptyMatrixReturnsNoSolutions()
{
// Arrange
var matrix = new bool[0, 0];
var dlx = new Dlx();
// Act
var solutions = dlx.Solve(matrix);
// Assert
Assert.Empty(solutions);
}
//Création d'une méthode qui prend en entrée un string (le sudoku non résolu) et qui renvoie un string (le sudoku résolu).
//De base le code duquel on s'est inspiré ne renvoyait rien, la sortie était sous forme d'un Console.WriteLine()
private static string Sudokusolution(string sudoku)
{
//Récupération du sudoku à résoudre depuis le string en entrée et transfert dans une ImmutableList.
var grid = new Grid(ImmutableList.Create(
sudoku.Substring(0, 9),
sudoku.Substring(9, 9),
sudoku.Substring(18, 9),
sudoku.Substring(27, 9),
sudoku.Substring(36, 9),
sudoku.Substring(45, 9),
sudoku.Substring(54, 9),
sudoku.Substring(63, 9),
sudoku.Substring(72, 9)));
var internalRows = BuildInternalRowsForGrid(grid);
var dlxRows = BuildDlxRows(internalRows);
var solutions = new Dlx()
.Solve(BuildDlxRows(internalRows), d => d, r => r)
.Where(solution => VerifySolution(internalRows, solution))
.ToImmutableList();
if (solutions.Any())
{
//Enlever commentaire pour afficher les solutions dans la console
//Console.WriteLine($"First solution (of {solutions.Count}):");
//Console.WriteLine();
//SolutionToGrid(internalRows, solutions.First()).Draw();
//Console.WriteLine();
//Ajout de ce bout de code pour avoir une sortie de type string contenant le sudoku résolu.
string s = "";
for (int i = 0; i <= 8; i++)
{
for (int j = 0; j <= 8; j++)
{
s += SolutionToGrid(internalRows, solutions.First()).ValueAt(i, j).ToString();
}
}
return(s);
}
else
{
//Console.WriteLine("No solutions found!");
return("No solutions found!");
}
}
public void MatrixWithSingleRowOfAllZerosReturnsNoSolutions()
{
// Arrange
var matrix = new[, ]
{
{ 0, 0, 0 }
};
var dlx = new Dlx();
// Act
var solutions = dlx.Solve(matrix).ToList();
// Assert
Assert.That(solutions, Has.Count.EqualTo(0));
}
public void MatrixWithSingleRowOfAllZerosReturnsNoSolutions()
{
// Arrange
var matrix = new[, ]
{
{ 0, 0, 0 }
};
var dlx = new Dlx();
// Act
var solutions = dlx.Solve(matrix).ToList();
// Assert
Assert.Empty(solutions);
}
private static void Main()
{
var puzzle = new Puzzle();
var internalRows = InternalRowBuilder.BuildInternalRows(puzzle);
var dlxMatrix = DlxMatrixBuilder.BuildDlxMatrix(puzzle, internalRows);
var dlx = new Dlx();
var solution = dlx.Solve(dlxMatrix, rows => rows, row => row.Bits).FirstOrDefault();
if (solution != null)
{
DumpSolutionSimple(solution, dlxMatrix);
Console.WriteLine();
DumpSolutionCube(puzzle, solution, dlxMatrix);
}
}
public void ExactCoverProblemsWithNoSolutionsTest()
{
Func <int, string> makeLabel = numSolutions => string.Format(
"Expected no solutions but got {0}",
numSolutions);
var arbMatrix = Arb.From(GenMatrixOfIntWithNoSolutions());
var property = Prop.ForAll(arbMatrix, matrix =>
{
var solutions = new Dlx().Solve(matrix).ToList();
return((!solutions.Any()).Label(makeLabel(solutions.Count())));
});
Check.One(Config, property);
}
private bool TryRemoveNumber(int index)
{
int number = _puzzle[index];
_puzzle[index] = 0;
SudokuExactCover();
MakeExactCoverGridFromSudoku();
IEnumerable <Solution> solutions = new Dlx().Solve(_problemMatrix);
if (solutions.Count() == 1)
{
return(true);
}
_puzzle[index] = number;
return(false);
}
public void CancelledEventFiresUsingCancellationToken()
{
var matrix = new bool[0, 0];
var cancellationTokenSource = new CancellationTokenSource();
var dlx = new Dlx(cancellationTokenSource.Token);
var cancelledEventHasBeenRaised = false;
dlx.Cancelled += (_, __) => cancelledEventHasBeenRaised = true;
dlx.Started += (_, __) => cancellationTokenSource.Cancel();
var thread = new Thread(() => dlx.Solve(matrix).FirstOrDefault());
thread.Start();
thread.Join();
Assert.True(cancelledEventHasBeenRaised);
}
private static void Demo2()
{
var matrix = new[, ]
{
{ 1, 0, 0, 0 },
{ 0, 1, 1, 0 },
{ 1, 0, 0, 1 },
{ 0, 0, 1, 1 },
{ 0, 1, 0, 0 },
{ 0, 0, 1, 0 }
};
var dlx = new Dlx();
var solutions = dlx.Solve(matrix);
PrintSolutions(matrix, solutions);
}
public void MatrixWithSingleRowOfAllOnesReturnsOneSolution()
{
// Arrange
var matrix = new[, ]
{
{ 1, 1, 1 }
};
var dlx = new Dlx();
// Act
var solutions = dlx.Solve(matrix).ToList();
// Assert
AssertSolutions(solutions, new[] {
new[] { 0 }
});
}
public void MatrixWithSingleRowOfAllOnesReturnsOneSolution()
{
// Arrange
var matrix = new[, ]
{
{ 1, 1, 1 }
};
var dlx = new Dlx();
// Act
var solutions = dlx.Solve(matrix).ToList();
// Assert
Assert.That(solutions, Has.Count.EqualTo(1));
Assert.That(solutions[0].RowIndexes.Count(), Is.EqualTo(1));
Assert.That(solutions.Select(s => s.RowIndexes), Contains.Item(new[] { 0 }));
}
public void SolveWithArbitraryDataStuctureAndCustomPredicate()
{
// Arrange
var data = new List <Tuple <char[], string> >
{
Tuple.Create(new[] { 'X', 'O', 'O' }, "Some data associated with row 0"),
Tuple.Create(new[] { 'O', 'X', 'O' }, "Some data associated with row 1"),
Tuple.Create(new[] { 'O', 'O', 'X' }, "Some data associated with row 2")
};
// Act
var solutions = new Dlx().Solve(data, d => d, r => r.Item1, c => c == 'X').ToList();
// Assert
Assert.That(solutions, Has.Count.EqualTo(1));
Assert.That(solutions.Select(s => s.RowIndexes), Contains.Item(new[] { 0, 1, 2 }));
}
public void SolveWithMatrixOfInt()
{
// Arrange
var matrix = new[, ]
{
{ 1, 0, 0 },
{ 0, 1, 0 },
{ 0, 0, 1 }
};
var dlx = new Dlx();
// Act
var solutions = dlx.Solve(matrix).ToList();
// Assert
Assert.That(solutions, Has.Count.EqualTo(1));
Assert.That(solutions.Select(s => s.RowIndexes), Contains.Item(new[] { 0, 1, 2 }));
}
public void SolveWithArbitraryDataStucture()
{
// Arrange
var data = new List <Tuple <int[], string> >
{
Tuple.Create(new[] { 1, 0, 0 }, "Some data associated with row 0"),
Tuple.Create(new[] { 0, 1, 0 }, "Some data associated with row 1"),
Tuple.Create(new[] { 0, 0, 1 }, "Some data associated with row 2")
};
// Act
var solutions = new Dlx().Solve(data, d => d, r => r.Item1).ToList();
// Assert
AssertSolutions(solutions, new[] {
new[] { 0, 1, 2 }
});
}
public void SolveWithArbitraryDataStuctureAndCustomPredicate()
{
// Arrange
var data = new List <Tuple <char[], string> >
{
Tuple.Create(new[] { 'X', 'O', 'O' }, "Some data associated with row 0"),
Tuple.Create(new[] { 'O', 'X', 'O' }, "Some data associated with row 1"),
Tuple.Create(new[] { 'O', 'O', 'X' }, "Some data associated with row 2")
};
// Act
var solutions = new Dlx().Solve(data, d => d, r => r.Item1, c => c == 'X').ToList();
// Assert
AssertSolutions(solutions, new[] {
new[] { 0, 1, 2 }
});
}
public void CancelledEventFiresUsingCancellationToken()
{
var matrix = new bool[0, 0];
var cancellationTokenSource = new CancellationTokenSource();
var dlx = new Dlx(cancellationTokenSource.Token);
var cancelledEventHasBeenRaised = false;
dlx.Cancelled += (_, __) => cancelledEventHasBeenRaised = true;
dlx.Started += (_, __) => cancellationTokenSource.Cancel();
// ReSharper disable once ReturnValueOfPureMethodIsNotUsed
var thread = new Thread(() => dlx.Solve(matrix).FirstOrDefault());
thread.Start();
thread.Join();
Assert.That(cancelledEventHasBeenRaised, Is.True, "Expected the Cancelled event to have been raised");
}
public void ExactCoverProblemsWithSingleSolutionTest()
{
Func <int, string> makeLabel = numSolutions => string.Format(
"Expected exactly one solution but got {0}",
numSolutions);
var arbMatrix = Arb.From(GenMatrixOfIntWithSingleSolution());
var property = Prop.ForAll(arbMatrix, matrix =>
{
var solutions = new Dlx().Solve(matrix).ToList();
var p1 = (solutions.Count() == 1).Label(makeLabel(solutions.Count()));
var p2 = CheckSolutions(solutions, matrix);
return(FsCheckUtils.And(p1, p2));
});
Check.One(Config, property);
}
public void SolveWithMatrixOfCharAndCustomPredicate()
{
// Arrange
var matrix = new[, ]
{
{ 'X', 'O', 'O' },
{ 'O', 'X', 'O' },
{ 'O', 'O', 'X' }
};
var dlx = new Dlx();
// Act
var solutions = dlx.Solve(matrix, c => c == 'X').ToList();
// Assert
Assert.That(solutions, Has.Count.EqualTo(1));
Assert.That(solutions.Select(s => s.RowIndexes), Contains.Item(new[] { 0, 1, 2 }));
}
public void Solve()
{
var internalRows = BuildInternalRows(_puzzle);
var dlxRows = BuildDlxRows(internalRows);
var dlx = new Dlx(_cancellationToken);
dlx.SearchStep += (_, args) =>
{
_searchStepCount++;
var searchStepInternalRows = args.RowIndexes
.Select(rowIndex => internalRows[rowIndex])
.ToImmutableList();
var eventArgs = new SearchStepEventArgs(_searchStepCount, searchStepInternalRows);
var handler = SearchStep;
handler?.Invoke(this, eventArgs);
};
var firstSolution = dlx.Solve(dlxRows, d => d, r => r).FirstOrDefault();
if (firstSolution != null)
{
var solutionInternalRows = firstSolution.RowIndexes
.Select(rowIndex => internalRows[rowIndex])
.ToImmutableList();
var eventArgs = new SolutionFoundEventArgs(_searchStepCount, solutionInternalRows);
var handler = SolutionFound;
handler?.Invoke(this, eventArgs);
}
else
{
var eventArgs = new NoSolutionFoundEventArgs(_searchStepCount);
var handler = NoSolutionFound;
handler?.Invoke(this, eventArgs);
}
}
private static void Main()
{
// http://puzzles.telegraph.co.uk/site/search_puzzle_number?id=27744
var grid = new Grid(ImmutableList.Create(
"6 4 9 7 3",
" 3 6 ",
" 18",
" 18 9",
" 43 ",
"7 39 ",
" 7 ",
" 4 8 ",
"9 8 6 4 5"));
grid.Draw();
var internalRows = BuildInternalRowsForGrid(grid);
var dlxRows = BuildDlxRows(internalRows);
var solutions = new Dlx()
.Solve(dlxRows, d => d, r => r)
.Where(solution => VerifySolution(internalRows, solution))
.ToImmutableList();
Console.WriteLine();
if (solutions.Any())
{
Console.WriteLine($"First solution (of {solutions.Count}):");
Console.WriteLine();
DrawSolution(internalRows, solutions.First());
Console.WriteLine();
}
else
{
Console.WriteLine("No solutions found!");
}
}
private void SolvePuzzleInBackground()
{
var rooms = _puzzle.Rooms;
var initialValues = _puzzle.InitialValues;
var numRows = rooms.SelectMany(r => r.Cells).Max(c => c.Row) + 1;
var numCols = rooms.SelectMany(r => r.Cells).Max(c => c.Col) + 1;
var maxValue = rooms.Max(r => r.Cells.Count);
var internalRows1 = rooms.SelectMany(room => BuildInternalRowsForRoom(rooms, initialValues, room));
var internalRows2 = initialValues.Select(t => BuildInternalRow(rooms, t.Item1, t.Item2, true));
var internalRows = internalRows1.Concat(internalRows2).ToImmutableList();
var dlxRows = BuildDlxRows(rooms, numRows, numCols, maxValue, internalRows);
var numRowColPrimaryColumns = numRows * numCols;
var numCellWithinRoomPrimaryColumns = rooms.Sum(r => r.Cells.Count);
var numPrimaryColumns = numRowColPrimaryColumns + numCellWithinRoomPrimaryColumns;
var dlx = new Dlx(_cancellationToken);
dlx.SearchStep += (_, searchStepEventArgs) =>
{
var subsetOfInternalRows = searchStepEventArgs.RowIndexes.Select(idx => internalRows[idx]).ToImmutableList();
_synchronizationContext.Post(_onSearchStep, subsetOfInternalRows);
};
var firstSolution = dlx.Solve(dlxRows, d => d, r => r, numPrimaryColumns).FirstOrDefault();
if (firstSolution != null)
{
var subsetOfInternalRows = firstSolution.RowIndexes.Select(idx => internalRows[idx]).ToImmutableList();
_synchronizationContext.Post(_onSolutionFound, subsetOfInternalRows);
}
}
private static Grid Solve(SamplePuzzle samplePuzzle)
{
var rooms = samplePuzzle.Rooms;
var initialValues = samplePuzzle.InitialValues;
var numRows = rooms.SelectMany(r => r.Cells).Max(c => c.Row) + 1;
var numCols = rooms.SelectMany(r => r.Cells).Max(c => c.Col) + 1;
var maxValue = rooms.Max(r => r.Cells.Count);
var internalRows1 = rooms.SelectMany(room => BuildInternalRowsForRoom(rooms, initialValues, room));
var internalRows2 = initialValues.Select(t => BuildInternalRow(rooms, t.Item1, t.Item2, true));
var internalRows = internalRows1.Concat(internalRows2).ToImmutableList();
var dlxRows = BuildDlxRows(rooms, numRows, numCols, maxValue, internalRows);
var numRowColPrimaryColumns = numRows * numCols;
var numCellWithinRoomPrimaryColumns = rooms.Sum(r => r.Cells.Count);
var numPrimaryColumns = numRowColPrimaryColumns + numCellWithinRoomPrimaryColumns;
var dlx = new Dlx();
var solutions = dlx.Solve(dlxRows, d => d, r => r, numPrimaryColumns).ToList();
Console.WriteLine($"Number of solutions found: {solutions.Count}");
var firstSolution = solutions.FirstOrDefault();
if (firstSolution == null) return null;
var subsetOfInternalRows = firstSolution.RowIndexes.Select(idx => internalRows[idx]).ToImmutableList();
var orderedSubsetOfInternalRows = subsetOfInternalRows.OrderBy(t => t.Item1.Row).ThenBy(t => t.Item1.Col);
var rowStrings = Enumerable.Range(0, numRows).Select(row => string.Join("", orderedSubsetOfInternalRows.Skip(row * numCols).Take(numRows).Select(t => t.Item2)));
var grid = new Grid(rowStrings.ToImmutableList());
return grid;
}