/// <summary>
/// Constructs a constraint that will enforce that the given <paramref name="squares"/> are
/// magic squares based on the rows, columns, and, optionally, the diagonals.
/// </summary>
/// <param name="possibleValues">
/// The possible values that can be in the magic squares.
/// </param>
/// <param name="squares">
/// The locations of the magic squares.
/// </param>
/// <param name="includeDiagonals">
/// If true, values along the diagonals of the square must also sum to the magic number.
/// </param>
/// <exception cref="ArgumentException">
/// If the any of the given <paramref name="squares"/>' sizes are not compatible with the
/// length of <paramref name="possibleValues"/>.
/// </exception>
public MagicSquaresConstraint(ReadOnlySpan <int> possibleValues, IEnumerable <Box> squares, bool includeDiagonals = true)
{
_size = possibleValues.Length;
_magicSquares = squares.ToArray();
_squareSize = Boxes.IntSquareRoot(_size);
_includeDiagonals = includeDiagonals;
if (_magicSquares.Any(
b =>
b.TopLeft.Row < 0 || b.TopLeft.Column < 0 ||
b.TopLeft.Row + b.Size > _size || b.TopLeft.Column + b.Size > _size ||
b.Size != _squareSize))
{
throw new ArgumentException(
$"Based on the {nameof(possibleValues)}, {nameof(squares)} must fit in a puzzle of size {_size} and have size {_squareSize}.");
}
_allPossibleValues = new BitVector();
for (int i = 0; i < possibleValues.Length; ++i)
{
if (_allPossibleValues.IsBitSet(possibleValues[i]))
{
throw new ArgumentException("Values must be unique.");
}
_allPossibleValues.SetBit(possibleValues[i]);
}
_possibleSets = MagicSquares.ComputeSets(possibleValues, _squareSize, _allPossibleValues);
}
/// <inheritdoc/>
public bool TryInitFor(IReadOnlyPuzzleWithMutablePossibleValues puzzle)
{
_boxSize = Boxes.IntSquareRoot(puzzle.Size);
_puzzle = puzzle;
_helper = new UniqueInXHelper(puzzle);
return(true);
}
/// <inheritdoc/>
public override bool TryInit(IReadOnlyPuzzle puzzle, BitVector uniquePossibleValues)
{
_boxSize = Boxes.IntSquareRoot(puzzle.Size);
_puzzle = puzzle;
if (!base.TryInit(puzzle, uniquePossibleValues))
{
_puzzle = null;
return(false);
}
return(true);
}
internal static void AssertMagicSquaresSatisfied(
IReadOnlyPuzzle puzzle, int expectedSum, bool verifyDiagonals)
{
int boxSize = Boxes.IntSquareRoot(puzzle.Size);
var boxes = new Box[puzzle.Size];
for (int boxIdx = 0; boxIdx < boxes.Length; ++boxIdx)
{
boxes[boxIdx] = new Box(Boxes.GetStartingBoxCoordinate(boxIdx, boxSize), boxSize);
}
AssertMagicSquaresSatisfied(puzzle, boxes, expectedSum, verifyDiagonals);
}
/// <inheritdoc/>
public bool TryInit(IReadOnlyPuzzleWithMutablePossibleValues puzzle)
{
int size = puzzle.Size;
_puzzle = puzzle;
_boxSize = Boxes.IntSquareRoot(puzzle.Size);
_unsetRowValues = new BitVector[size];
_unsetRowValues.AsSpan().Fill(_puzzle.UniquePossibleValues);
Span <BitVector> possibleValues = _unsetRowValues.AsSpan();
_unsetColumnValues = possibleValues.ToArray();
_unsetBoxValues = possibleValues.ToArray();
int boxIdx;
for (int row = 0; row < size; row++)
{
for (int col = 0; col < size; col++)
{
boxIdx = Boxes.CalculateBoxIndex(new Coordinate(row, col), _boxSize);
int?val = puzzle[row, col];
if (!val.HasValue)
{
continue;
}
if (!_unsetRowValues[row].IsBitSet(val.Value) ||
!_unsetColumnValues[col].IsBitSet(val.Value) ||
!_unsetBoxValues[boxIdx].IsBitSet(val.Value))
{
return(false);
}
_unsetRowValues[row].UnsetBit(val.Value);
_unsetColumnValues[col].UnsetBit(val.Value);
_unsetBoxValues[boxIdx].UnsetBit(val.Value);
}
}
foreach (Coordinate c in puzzle.GetUnsetCoords())
{
_puzzle.IntersectPossibleValues(in c, _GetPossibleValues(in c));
if (_puzzle.GetPossibleValues(in c).IsEmpty)
{
return(false);
}
}
return(true);
}
/// <inheritdoc/>
public bool TryInit(IReadOnlyPuzzle puzzle, BitVector uniquePossibleValues)
{
int size = puzzle.Size;
_boxSize = Boxes.IntSquareRoot(size);
if (size != _unsetRowValues?.Length)
{
_unsetRowValues = new BitVector[size];
_unsetRowValues.AsSpan().Fill(uniquePossibleValues);
_unsetColValues = _unsetRowValues.AsSpan().ToArray();
_unsetBoxValues = _unsetRowValues.AsSpan().ToArray();
}
else
{
_unsetRowValues.AsSpan().Fill(uniquePossibleValues);
_unsetColValues.AsSpan().Fill(uniquePossibleValues);
_unsetBoxValues.AsSpan().Fill(uniquePossibleValues);
}
int boxIdx = 0;
for (int row = 0; row < size; row++)
{
for (int col = 0; col < size; col++)
{
if (col == 0)
{
boxIdx = (row / _boxSize) * _boxSize;
}
else if (col % _boxSize == 0)
{
boxIdx++;
}
int?val = puzzle[row, col];
if (!val.HasValue)
{
continue;
}
if (!_unsetRowValues[row].IsBitSet(val.Value) ||
!_unsetColValues ![col].IsBitSet(val.Value) ||
public void GetPossibleValues_MatchesGetPossibleBoxValues()
{
var puzzle = new PuzzleWithPossibleValues(new int?[][] {
new int?[] { 1, null /* 4 */, null /* 3 */, 2 },
new int?[] { null /* 2 */, null /* 3 */, null /* 1 */, 4 },
new int?[] { null /* 4 */, 1, null /* 2 */, 3 },
new int?[] { 3, null /* 2 */, null /* 4 */, 1 }
});
var rule = new MaxCountPerBoxRule();
Assert.True(rule.TryInit(puzzle, puzzle.UniquePossibleValues));
for (int row = 0; row < puzzle.Size; row++)
{
for (int column = 0; column < puzzle.Size; column++)
{
int box = Boxes.CalculateBoxIndex(new(row, column), Boxes.IntSquareRoot(puzzle.Size));
Assert.Equal(
rule.GetMissingValuesForBox(box),
rule.GetPossibleValues(new Coordinate(row, column)));
}
}
}
public void GetPossibleValues_MatchesGetPossibleBoxValues()
{
var puzzle = new PuzzleWithPossibleValues(new int?[][] {
new int?[] { 1, null /* 4 */, null /* 3 */, 2 },
new int?[] { null /* 2 */, null /* 3 */, null /* 1 */, 4 },
new int?[] { null /* 4 */, 1, null /* 2 */, 3 },
new int?[] { 3, null /* 2 */, null /* 4 */, 1 }
});
var rule = new BoxUniquenessRule();
Assert.True(rule.TryInit(puzzle, puzzle.UniquePossibleValues));
IList <BitVector> possibleValuesByBox = _GetPossibleValuesByBox(puzzle.Size, rule);
for (int row = 0; row < puzzle.Size; row++)
{
for (int column = 0; column < puzzle.Size; column++)
{
int box = Boxes.CalculateBoxIndex(new(row, column), Boxes.IntSquareRoot(puzzle.Size));
Assert.Equal(
possibleValuesByBox[box],
rule.GetPossibleValues(new Coordinate(row, column)));
}
}
}
internal static void AssertStandardPuzzleSolved(IReadOnlyPuzzle puzzle)
{
Assert.Equal(0, puzzle.NumEmptySquares);
var alreadyFound = new HashSet <int>(puzzle.Size);
for (int row = 0; row < puzzle.Size; row++)
{
alreadyFound.Clear();
for (int col = 0; col < puzzle.Size; col++)
{
Assert.True(alreadyFound.Add(puzzle[row, col].Value), $"Value at ({row}, {col}) clashed with another value in that row!");
}
}
for (int col = 0; col < puzzle.Size; col++)
{
alreadyFound.Clear();
for (int row = 0; row < puzzle.Size; row++)
{
Assert.True(alreadyFound.Add(puzzle[row, col].Value), $"Value at ({row}, {col}) clashed with another value in that col!");
}
}
int boxSize = Boxes.IntSquareRoot(puzzle.Size);
for (int box = 0; box < puzzle.Size; box++)
{
alreadyFound.Clear();
(int startRow, int startCol) = Boxes.GetStartingBoxCoordinate(box, boxSize);
for (int row = startRow; row < startRow + boxSize; row++)
{
for (int col = startCol; col < startCol + boxSize; col++)
{
Assert.True(alreadyFound.Add(puzzle[row, col].Value), $"Value at ({row}, {col}) clashed with another value in that box!");
}
}
}
}
public void IntSquareRoot_WithInvalidSize_Throws(int puzzleSize)
{
Assert.Throws <ArgumentException>(() => Boxes.IntSquareRoot(puzzleSize));
}
public void IntSquareRoot_WithValidSizes_IsCorrect(int puzzleSize, int expectedBoxSize)
{
Assert.Equal(expectedBoxSize, Boxes.IntSquareRoot(puzzleSize));
}