public bool TrySolveBox(int index, out Solution solution)
{
if (_puzzle.SolvedForBox[index] == _effectiveCount &&
TrySolveLine(_puzzle.GetBoxAsLine(index), out int lineIndex, out int value))
{
var(row, column) = Puzzle.GetLocationForBoxCell(index, lineIndex);
solution = new Solution(
row,
column,
value,
nameof(NakedSinglesSolver),
null
);
return(true);
}
solution = null;
return(false);
}
public Solution Solve(int index)
{
var box = _puzzle.GetBox(index);
// adjacent neighboring boxes
// first two values in array are horizontal neighbors
// second two values in array are vertical neighbors
var offset = (index / 3) * 3;
int[] avn = new int[]
{
(index + 1) % 3 + offset,
(index + 2) % 3 + offset,
(index + 3) % 9,
(index + 6) % 9
};
// get adjacent neighboring boxes
var ahnb1 = _puzzle.GetBox(avn[0]);
var ahnb2 = _puzzle.GetBox(avn[1]);
var avnb1 = _puzzle.GetBox(avn[2]);
var avnb2 = _puzzle.GetBox(avn[3]);
// iterate over the three rows in the box
for (int i = 0; i < 3; i++)
{
// for each row, the neighboring rows are the same
// the columns differ per cell
var row1Index = i;
var row2Index = (i + 1) % 3;
var row3Index = (i + 2) % 3;
// there are nine row to consider (three boxes)
// baseline box
var row2 = box.GetRow(row2Index);
var row3 = box.GetRow(row3Index);
// horizontal adjacent box 1 -- rows
var ahnb1Row2 = ahnb1.GetRow(row2Index);
var ahnb1Row3 = ahnb1.GetRow(row3Index);
// horizontal adjacent box 2 -- rows
var ahnb2Row2 = ahnb2.GetRow(row2Index);
var ahnb2Row3 = ahnb2.GetRow(row3Index);
// determine union of values of rows
var row2Union = ahnb1Row2.Union(ahnb2Row2);
var row3Union = ahnb1Row3.Union(ahnb2Row3);
// get complete row that includes the the first row of box
var firstRowIndex = box.GetRowOffsetForBox() + i;
var firstRow = _puzzle.GetRow(firstRowIndex);
// the boundaries of the adjacent boxes don't matter
// the appropriate rows have been merged (Union) at this point
// determine union of values of row 1 -- these values are all off-limits
// get complete row that includes the the first row of box
var boxValues = box.AsValues();
// determine disjoint set with baseline rows -- box row values are off-limits
// determine disjoint set with baseline rows -- box row values are off-limits
var row2Values = row2Union.DisjointSet(boxValues);
var row3Values = row3Union.DisjointSet(boxValues);
// determine disjoint set with baseline row -- looking for values now in that row
var row2Candidates = row2Values.DisjointSet(firstRow.Segment);
var row3Candidates = row3Values.DisjointSet(firstRow.Segment);
// row candidates -- values in both row 2 and 3 but not in row 1 or in the box
ReadOnlySpan <int> rowCandidates = new int[] {};
if (row2[0] == 0 && row3[0] == 0)
{
rowCandidates = row2Candidates.Intersect(row3Candidates);
}
else if (row2[0] == 0)
{
rowCandidates = row2Candidates;
}
else if (row3[0] == 0)
{
rowCandidates = row3Candidates;
}
if (rowCandidates.Length == 0)
{
continue;
}
// cells
for (int y = 0; y < 3; y++)
{
var col1Index = y;
var col2Index = (y + 1) % 3;
var col3Index = (y + 2) % 3;
// baseline box
var col1 = box.GetColumn(col1Index);
var col2 = box.GetColumn(col2Index);
var col3 = box.GetColumn(col3Index);
// vertical adjacent box 1 -- cols
var avnb1Col1 = avnb1.GetColumn(col1Index);
var avnb1Col2 = avnb1.GetColumn(col2Index);
var avnb1Col3 = avnb1.GetColumn(col3Index);
// vertical adjacent box 2 -- cols
var avnb2Col1 = avnb2.GetColumn(col1Index);
var avnb2Col2 = avnb2.GetColumn(col2Index);
var avnb2Col3 = avnb2.GetColumn(col3Index);
// get complete column that includes the the first column of box
var firstColIndex = box.GetColumnOffsetForBox() + y;
var firstCol = _puzzle.GetColumn(firstColIndex);
// determine union of values of cols
var col2Union = avnb1Col2.Union(avnb2Col2);
var col3Union = avnb1Col3.Union(avnb2Col3);
// determine disjoint set with baseline cols -- box col values are off-limits
var col2Values = col2Union.DisjointSet(boxValues);
var col3Values = col3Union.DisjointSet(boxValues);
// determine disjoint set with baseline col -- looking for values now in that col
var col2Candidates = col2Values.DisjointSet(firstCol.Segment);
var col3Candidates = col3Values.DisjointSet(firstCol.Segment);
ReadOnlySpan <int> colCandidates = new int[] { };
if (col2[0] == 0 && col3[0] == 0)
{
colCandidates = col2Candidates.Intersect(col3Candidates);
}
else if (col2[0] == 0)
{
colCandidates = col2Candidates;
}
else if (col3[0] == 0)
{
colCandidates = col3Candidates;
}
// col candidates -- values in both col 2 and 3 but not in col 1 or in the box
//var colCandidates = col2Candidates.Intersect(col3Candidates);
if (colCandidates.Length == 0)
{
continue;
}
var candidates = colCandidates.Intersect(rowCandidates);
if (candidates.Length == 1)
{
(var row, var column) = Puzzle.GetLocationForBoxCell(index, (i * 3) + y);
return(new Solution
{
Solved = true,
Value = candidates[0],
Row = row,
Column = column,
Solver = this
});
}
}
}
return(new Solution
{
Solved = false
});
}
public Solution Solve(int index)
{
var box = _puzzle.GetBox(index);
// adjacent neighboring boxes
// first two values in array are horizontal neighbors
// second two values in array are vertical neighbors
var offset = (index / 3) * 3;
int[] avn = new int[]
{
(index + 1) % 3 + offset,
(index + 2) % 3 + offset,
(index + 3) % 9,
(index + 6) % 9
};
// get adjacent neighboring boxes
var ahnb1 = _puzzle.GetBox(avn[0]);
var ahnb2 = _puzzle.GetBox(avn[1]);
var avnb1 = _puzzle.GetBox(avn[2]);
var avnb2 = _puzzle.GetBox(avn[3]);
// iterate over the three rows in the box
// goal is to solve a cell in this row (not other rows)
// ititial logic (body of first for loop) can solve any row cell using
// horizontal adjacent rows as input
// later logic (body of embedded for loop) can solve a given cell, one at a time
// using rows and/or columns as input
for (int i = 0; i < 3; i++)
{
// calculate rows for i
var row1Index = i;
var row2Index = (i + 1) % 3;
var row3Index = (i + 2) % 3;
// target box
var boxRow1 = box.GetRow(row1Index);
if (!boxRow1.ContainsValue(0))
{
continue;
}
var boxRow2 = box.GetRow(row2Index);
var boxRow3 = box.GetRow(row3Index);
// neighboring boxess
// horizontal adjacent box 1 -- rows
var ahnb1Row1 = ahnb1.GetRow(row1Index);
var ahnb1Row2 = ahnb1.GetRow(row2Index);
var ahnb1Row3 = ahnb1.GetRow(row3Index);
// horizontal adjacent box 2 -- rows
var ahnb2Row1 = ahnb1.GetRow(row1Index);
var ahnb2Row2 = ahnb2.GetRow(row2Index);
var ahnb2Row3 = ahnb2.GetRow(row3Index);
// determine union of values of rows
var adjRow2Union = ahnb1Row2.Union(ahnb2Row2);
var adjRow3Union = ahnb1Row3.Union(ahnb2Row3);
// get complete row that includes current row of box
var currentRowIndex = box.GetRowOffsetForBox() + i;
//TODO: consider an overload that only returns non-zero values
var currentRow = _puzzle.GetRow(currentRowIndex);
// get all values in box
var boxLine = box.AsLine();
//var boxValues = box.AsValues();
// calculate full set of illegal values for row 1
var boxRow1IllegalValues = boxLine.Union(currentRow);
// determine disjoint set with baseline row -- looking for values in that row
var row2Candidates = adjRow2Union.DisjointSet(boxRow1IllegalValues);
var row3Candidates = adjRow3Union.DisjointSet(boxRow1IllegalValues);
var boxRow1Candidates = row2Candidates.Intersect(row3Candidates);
// determine if rows on their own present a solution
if (boxRow1Candidates.Length == 1)
{
(var justOne, var column) = boxRow1.IsJustOneElementUnsolved();
if (justOne)
{
var solverKind = nameof(Strategy.RowSolver);
return(GetSolution(index, i, column, boxRow1Candidates[0], solverKind));
}
}
// interate over columns for row
// mostly targets row[column] cell
for (int y = 0; y < 3; y++)
{
if (boxRow1[y] != 0)
{
continue;
}
var col1Index = y;
var col2Index = (y + 1) % 3;
var col3Index = (y + 2) % 3;
// baseline box
var boxCol1 = box.GetColumn(col1Index);
var boxCol2 = box.GetColumn(col2Index);
var boxCol3 = box.GetColumn(col3Index);
// vertical adjacent box 1 -- cols
var avnb1Col1 = avnb1.GetColumn(col1Index);
var avnb1Col2 = avnb1.GetColumn(col2Index);
var avnb1Col3 = avnb1.GetColumn(col3Index);
// vertical adjacent box 2 -- cols
var avnb2Col1 = avnb2.GetColumn(col1Index);
var avnb2Col2 = avnb2.GetColumn(col2Index);
var avnb2Col3 = avnb2.GetColumn(col3Index);
// get complete column that includes the the first column of box
var currentColIndex = box.GetColumnOffsetForBox() + y;
var currentCol = _puzzle.GetColumn(currentColIndex);
// calculate full set of illegal values for col 1
var boxCol1IllegalValues = boxLine.Union(currentCol);
// determine union of values of cols
var col2Union = avnb1Col2.Union(avnb2Col2);
var col3Union = avnb1Col3.Union(avnb2Col3);
// determine disjoint set with baseline col -- looking for values now in that col
var col2Candidates = col2Union.DisjointSet(boxCol1IllegalValues);
var col3Candidates = col3Union.DisjointSet(boxCol1IllegalValues);
var boxCol1Candidates = col2Candidates.Intersect(col3Candidates);
// determine if columns on their own present a solution
// can solve any cell in given box column
if (boxCol1Candidates.Length == 1)
{
(var justOne, var row) = boxCol1.IsJustOneElementUnsolved();
if (justOne)
{
var solverKind = nameof(Strategy.ColumnSolver);
return(GetSolution(index, row, y, boxCol1Candidates[0], solverKind));
}
}
// determine if rows and columns together present a solution
// test: SolutionAllSlotsEmpty
var rowAndColumnCandidates = boxRow1Candidates.Intersect(boxCol1Candidates);
if (rowAndColumnCandidates.Length == 1)
{
if (boxCol1[i] == 0)
{
var solverKind = nameof(Strategy.RowColumnSolver);
return(GetSolution(index, i, y, rowAndColumnCandidates[0], solverKind));
}
}
// determine if various combinations of rows and columns present a solution
// col1[row] is candidate for all following cases
// the following set of cases involve a row or a column with:
// a candidate, one cell == 0 and the other non zero
// the cases are looking for a set of rows and columns
// that project the same value except for the row or column with
// the non-zero value (which doesn't require a projected value)
// check rows
if (boxRow1Candidates.Length > 0)
{
bool solved;
Solution solution;
var solverKind1 = nameof(Strategy.Column2CandidateColumn3BlockedRowSolver);
// row1[col3] has a value, so col3 don't need to participate in providing a candidate
if (col2Candidates.Length > 0 &&
boxRow1[col2Index] == 0 && boxRow1[col3Index] != 0 &&
((solved, solution) = CheckForIntersectionCandidates(boxRow1Candidates, col2Candidates, solverKind1)).solved)
{
return(solution);
}
var solverKind2 = nameof(Strategy.Column2BlockedColumn3CandidateRowSolver);
// row1[col2] has a value, so col2 don't need to participate in providing a candidate
if (col3Candidates.Length > 0 &&
boxRow1[col2Index] != 0 && boxRow1[col3Index] == 0 &&
((solved, solution) = CheckForIntersectionCandidates(boxRow1Candidates, col3Candidates, solverKind2)).solved)
{
return(solution);
}
}
// check columns
if (boxCol1Candidates.Length > 0)
{
bool solved;
Solution solution;
var solver1 = nameof(Strategy.Row2CandidateRow3BlockedColumnSolver);
// col1[row3] has a value, so row3 don't need to participate in providing a candidate
if (row2Candidates.Length > 0 &&
boxCol1[row2Index] == 0 && boxCol1[row3Index] != 0 &&
((solved, solution) = CheckForIntersectionCandidates(boxCol1Candidates, row2Candidates, solver1)).solved)
{
return(solution);
}
var solver2 = nameof(Strategy.Row2BlockedRow3CandidateColumnSolver);
// col1[row2] has a value, so row2 don't need to participate in providing a candidate
// test: SolutionTwoSlotsEmptyInColumn
if (row3Candidates.Length > 0 &&
boxCol1[row2Index] != 0 && boxCol1[row3Index] == 0 &&
((solved, solution) = CheckForIntersectionCandidates(boxCol1Candidates, row3Candidates, solver2)).solved)
{
return(solution);
}
}
// the following set of cases involve a row or column with:
// all cells filled, such that a row or column doesn't need to participate in providing a candidate
// col3 is blocked, so col3 doesn't need to participate in providing a candidate
var col2Blocked = boxCol2.GetUnsolvedCount() == 0;
var col3Blocked = boxCol3.GetUnsolvedCount() == 0;
var row2Blocked = boxRow2.GetUnsolvedCount() == 0;
var row3Blocked = boxRow3.GetUnsolvedCount() == 0;
if (boxCol1.GetUnsolvedCount() == 1)
{
if (col3Blocked &&
col2Candidates.Length == 1)
{
var solverKind = nameof(Strategy.Column2CandidateColumn3Blocked);
return(GetSolution(index, i, y, col2Candidates[0], solverKind));
}
}
// following set of cases test hidden singles in columns or rows
// pattern
// box 1 col1 is full
// box 2 has one value not in col1
// only one slot available in col1 in current box
// means that current cell must have that value
{
var solverKind = nameof(Strategy.ColumnLastPossibleSlot);
var candidates2 = avnb2.AsLine().DisjointSet(currentCol);
foreach (var candidate in candidates2)
{
if (!boxLine.ContainsValue(candidate) &&
!currentRow.ContainsValue(candidate) &&
CheckForValueInCellOrRow(candidate, box, col1Index, row2Index, row3Index) &&
CheckForValueInCellOrRow(candidate, avnb1, col1Index, 0, 1, 2)
)
{
solverKind += "-1";
return(GetSolution(index, i, y, candidate, solverKind));
}
}
var candidates1 = avnb1.AsLine().DisjointSet(currentCol);
foreach (var candidate in candidates1)
{
if (!boxLine.ContainsValue(candidate) &&
!currentRow.ContainsValue(candidate) &&
CheckForValueInCellOrRow(candidate, box, col1Index, row2Index, row3Index) &&
CheckForValueInCellOrRow(candidate, avnb2, col1Index, 0, 1, 2)
)
{
solverKind += "-2";
return(GetSolution(index, i, y, candidate, solverKind));
}
}
}
/*
* bool solved;
* Solution solution;
*
* // start with columns
* // test each cell in avnb1.col1
* // avnb2 presents candidate
* if (((solved, solution) = CheckForDisjointCandidates(avnb2.AsLine().Segment, currentCol.Segment, solverKind)).solved &&
* !boxLine.ContainsValue(solution.Value) &&
* !currentRow.ContainsValue(solution.Value) &&
* CheckForValueInCellOrRow(solution.Value,box,col1Index,row2Index,row3Index) &&
* CheckForValueInCellOrRow(solution.Value,avnb1,col1Index,0,1,2)
* )
* {
* solution.SolverKind += "-1";
* return solution;
* }
*
* // test avnb2.col1 solved
* // avnb1 presents candidate
* if (((solved, solution) = CheckForDisjointCandidates(avnb1.AsLine().Segment, currentCol.Segment, solverKind)).solved &&
* !boxLine.ContainsValue(solution.Value) &&
* !currentRow.Segment.Contains(solution.Value) &&
* CheckForValueInCellOrRow(solution.Value,box,col1Index,row2Index,row3Index) &&
* CheckForValueInCellOrRow(solution.Value,avnb2,col1Index,0,1,2)
* )
* {
* solution.SolverKind += "-2";
* return solution;
* }
* }
*/
{
var solverKind = nameof(Strategy.RowLastPossibleSlot);
var candidates2 = ahnb2.AsLine().DisjointSet(currentRow);
foreach (var candidate in candidates2)
{
if (!boxLine.ContainsValue(candidate) &&
!currentCol.Segment.Contains(candidate) &&
CheckForValueInCellOrColumn(candidate, box, row1Index, col2Index, col3Index) &&
CheckForValueInCellOrColumn(candidate, ahnb1, row1Index, 0, 1, 2)
)
{
solverKind += "-2";
return(GetSolution(index, i, y, candidate, solverKind));
}
}
var candidates1 = ahnb1.AsLine().DisjointSet(currentRow);
foreach (var candidate in candidates1)
{
if (!boxLine.ContainsValue(candidate) &&
!currentCol.Segment.Contains(candidate) &&
CheckForValueInCellOrColumn(candidate, box, row1Index, col2Index, col3Index) &&
CheckForValueInCellOrColumn(candidate, ahnb2, row1Index, 0, 1, 2)
)
{
solverKind += "-2";
return(GetSolution(index, i, y, candidate, solverKind));
}
}
}
/*
* bool solved;
* Solution solution;
*
*
*
* // solve for rows
* // test each cell in avhb1.row1
* // avhb2 presents candidate
* if (((solved, solution) = CheckForDisjointCandidates(ahnb2.AsLine().Segment, currentRow.Segment, solverKind)).solved &&
* !boxLine.ContainsValue(solution.Value) &&
* !currentCol.Segment.Contains(solution.Value) &&
* CheckForValueInCellOrColumn(solution.Value,box,row1Index,col2Index,col3Index) &&
* CheckForValueInCellOrColumn(solution.Value,ahnb1,row1Index,0,1,2)
* )
* {
* solution.SolverKind += "-1";
* return solution;
* }
*
* // test ahnb2.row1 solved
* // ahnb1 presents candidate
* if (((solved, solution) = CheckForDisjointCandidates(ahnb1.AsLine().Segment, currentRow.Segment, solverKind)).solved &&
* !boxLine.ContainsValue(solution.Value) &&
* !currentCol.Segment.Contains(solution.Value) &&
* CheckForValueInCellOrColumn(solution.Value,box,row1Index,col2Index,col3Index) &&
* CheckForValueInCellOrColumn(solution.Value,ahnb2,row1Index,0,1,2)
* )
* {
* solution.SolverKind += "-2";
* return solution;
* }
* }
*/
// Strategy where a column or row has two empty cells and one is constrained
{
var solverKind = nameof(Strategy.ColumnLastTwoPossibleSlots);
if (currentCol.GetUnsolvedCount() == 2)
{
var missingValues = currentCol.GetMissingValues();
for (int k = 0; k < 2; k++)
{
var value = missingValues[k];
var otherValue = missingValues[(k + 1) % 2];
if (currentRow.ContainsValue(value) &&
!boxLine.ContainsValue(otherValue))
{
return(GetSolution(index, i, y, otherValue, solverKind));
}
}
}
}
{
var solverKind = nameof(Strategy.RowLastTwoPossibleSlots);
if (currentRow.GetUnsolvedCount() == 2)
{
var missingValues = currentRow.GetMissingValues();
for (int k = 0; k < 2; k++)
{
var value = missingValues[k];
var otherValue = missingValues[(k + 1) % 2];
if (currentCol.ContainsValue(value) &&
!boxLine.ContainsValue(otherValue))
{
return(GetSolution(index, i, y, otherValue, solverKind));
}
}
}
}
bool CheckRowForValue(int searchValue, Box box, int row)
{
// get complete row that includes current row of box
var rowIndex = box.GetRowOffsetForBox() + row;
//TODO: consider an overload that only returns non-zero values
var targetRow = _puzzle.GetRow(rowIndex);
return(targetRow.Segment.Contains(searchValue));
}
bool CheckForValueInCellOrColumn(int value, Box box, int row, params int[] cols)
{
foreach (int col in cols)
{
var targetColumn = box.GetColumn(col);
if (targetColumn[row] != 0 ||
CheckColumnForValue(value, box, col))
{
}
else
{
return(false);
}
}
return(true);
}
bool CheckForValueInCellOrRow(int value, Box box, int col, params int[] rows)
{
foreach (int row in rows)
{
var targetRow = box.GetRow(row);
if (targetRow[col] != 0 ||
CheckRowForValue(value, box, row))
{
}
else
{
return(false);
}
}
return(true);
}
bool CheckColumnForValue(int searchValue, Box box, int col)
{
// get complete column that includes current column of box
var colIndex = box.GetColumnOffsetForBox() + col;
//TODO: consider an overload that only returns non-zero values
var targetCol = _puzzle.GetColumn(colIndex);
return(targetCol.Segment.Contains(searchValue));
}
(bool solved, Solution solution) CheckForIntersectionCandidates(ReadOnlySpan <int> candidate1, ReadOnlySpan <int> candidate2, string solverKind)
{
var candidates = candidate1.Intersect(candidate2);
if (candidates.Length == 1)
{
return(true, GetSolution(index, i, y, candidates[0], solverKind));
}
return(false, Solution.False);
}
(bool solved, Solution solution) CheckForDisjointCandidates(ReadOnlySpan <int> line, ReadOnlySpan <int> candidate2, string solverKind)
{
var candidates = line.DisjointSet(candidate2);
if (candidates.Length == 1)
{
return(true, GetSolution(index, i, y, candidates[0], solverKind));
}
return(false, Solution.False);
}
}
Solution GetSolution(int box, int row, int column, int value, string solverKind)
{
(var r, var c) = Puzzle.GetLocationForBoxCell(index, (row * 3) + column);
return(new Solution
{
Solved = true,
Value = value,
Row = r,
Column = c,
Solver = this,
SolverKind = solverKind
});
}
}
return(new Solution
{
Solved = false
});
}
// find a box row/column with just one missing value
// find a value that is present in the other two rows/columns but not this box
// the value can be placed in the open spot if everything lines up
public Solution Solve(int index)
{
var box = _puzzle.GetBox(index);
// adjacent neighboring boxes
// first two values in array are horizontal neighbors
// second two values in array are vertical neighbors
var offset = (index / 3) * 3;
int[] avn = new int[]
{
(index + 1) % 3 + offset,
(index + 2) % 3 + offset,
(index + 3) % 9,
(index + 6) % 9
};
var ahnb1 = _puzzle.GetBox(avn[0]);
var ahnb2 = _puzzle.GetBox(avn[1]);
var avnb1 = _puzzle.GetBox(avn[2]);
var avnb2 = _puzzle.GetBox(avn[3]);
// find intersection of values for adjacent rows
for (int i = 0; i < 3; i++)
{
(var rowJustOne, var rowCandidateIndex) = box.GetRow(i).IsJustOneElementUnsolved();
if (!rowJustOne)
{
continue;
}
// calculate indexes of adjacent rows
var row2Index = (i + 1) % 3;
var row3Index = (i + 2) % 3;
// baseline box
var row2 = box.GetRow(row2Index);
var row3 = box.GetRow(row3Index);
// horizontal adjacent box 1 -- rows
var ahnb1Row2 = ahnb1.GetRow(row2Index);
var ahnb1Row3 = ahnb1.GetRow(row3Index);
// horizontal adjacent box 2 -- rows
var ahnb2Row2 = ahnb2.GetRow(row2Index);
var ahnb2Row3 = ahnb2.GetRow(row3Index);
// get complete row that includes the the first row of box
var firstRowIndex = box.GetRowOffsetForBox() + i;
var firstRow = _puzzle.GetRow(firstRowIndex);
// determine union of values of rows
var row2Union = ahnb1Row2.Union(ahnb2Row2);
var row3Union = ahnb1Row3.Union(ahnb2Row3);
// the boundaries of the adjacent boxes don't matter
// the appropriate rows have been merged (Union) at this point
// determine union of values of row 1 -- these values are all off-limits
// determine disjoint set with baseline rows -- box row values are off-limits
var row2Values = row2Union.DisjointSet(row2.Segment);
var row3Values = row3Union.DisjointSet(row3.Segment);
// determine disjoint set with baseline row -- looking for values now in that row
var row2Candidates = row2Values.DisjointSet(firstRow.Segment);
var row3Candidates = row3Values.DisjointSet(firstRow.Segment);
// row candidates -- values in both row 2 and 3 but not in row 1 or in the box
var rowCandidates = row2Candidates.Intersect(row3Candidates);
if (rowCandidates.Length == 1)
{
(var r, var c) = Puzzle.GetLocationForBoxCell(index, i * 3 + rowCandidateIndex);
return(new Solution
{
Solved = true,
Row = r,
Column = c,
Value = rowCandidates[0],
Solver = this
});
}
// find intersection of values for adjacent columns
(var colJustOne, var candidateIndex) = box.GetColumn(i).IsJustOneElementUnsolved();
if (!colJustOne)
{
continue;
}
var col1Index = i;
var col2Index = (i + 1) % 3;
var col3Index = (i + 2) % 3;
// baseline box
var col1 = box.GetColumn(col1Index);
var col2 = box.GetColumn(col2Index);
var col3 = box.GetColumn(col3Index);
// vertical adjacent box 1 -- cols
var avnb1Col1 = avnb1.GetColumn(col1Index);
var avnb1Col2 = avnb1.GetColumn(col2Index);
var avnb1Col3 = avnb1.GetColumn(col3Index);
// vertical adjacent box 2 -- cols
var avnb2Col1 = avnb2.GetColumn(col1Index);
var avnb2Col2 = avnb2.GetColumn(col2Index);
var avnb2Col3 = avnb2.GetColumn(col3Index);
// get complete column that includes the the first column of box
var firstColIndex = box.GetColumnOffsetForBox() + i;
var firstCol = _puzzle.GetColumn(firstColIndex);
// determine union of values of cols
var col2Union = avnb1Col2.Union(avnb2Col2);
var col3Union = avnb1Col3.Union(avnb2Col3);
// determine disjoint set with baseline cols -- box col values are off-limits
var col2Values = col2Union.DisjointSet(col2.Segment);
var col3Values = col3Union.DisjointSet(col3.Segment);
// determine disjoint set with baseline col -- looking for values now in that col
var col2Candidates = col2Values.DisjointSet(firstCol.Segment);
var col3Candidates = col3Values.DisjointSet(firstCol.Segment);
// col candidates -- values in both col 2 and 3 but not in col 1 or in the box
var colCandidates = col2Candidates.Intersect(col3Candidates);
if (colCandidates.Length == 1)
{
(var r, var c) = Puzzle.GetLocationForBoxCell(index, (candidateIndex % 3) * 3 + i);
return(new Solution
{
Solved = true,
Row = r,
Column = c,
Value = colCandidates[0],
Solver = this
});
}
}
return(new Solution
{
Solved = false
});
}
public bool TrySolveBox(int index, out Solution solution)
{
Box box = _puzzle.GetBox(index);
int rowOffset = box.GetRowOffset();
int columnOffset = box.GetColumnOffset();
// get adjacent neighboring boxes
Box ahnb1 = box.FirstHorizontalNeighbor;
Box ahnb2 = box.SecondHorizontalNeighbor;
Box avnb1 = box.FirstVerticalNeighbor;
Box avnb2 = box.SecondVerticalNeighbor;
// iterate over the three rows in the box
// goal is to solve a cell in the "i" row
// initial logic (body of first for loop) can solve any row cell using
// horizontal adjacent rows as input
// later logic (body of embedded for loop) can solve a given cell, one at a time
// using rows and/or columns as input
for (int i = 0; i < 3; i++)
{
// target box
Line boxRow1 = box.GetRow(i);
// check if row contains a zero
if (!boxRow1.ContainsValue(0))
{
continue;
}
// calculate rows for i
int row1Index = i;
int row2Index = (i + 1) % 3;
int row3Index = (i + 2) % 3;
Line boxRow2 = box.GetRow(row2Index);
Line boxRow3 = box.GetRow(row3Index);
// get all values in box
Line boxLine = box.AsLine();
// neighboring boxes
// horizontal adjacent box 1 -- rows
Line ahnb1Row1 = ahnb1.GetRow(row1Index);
Line ahnb1Row2 = ahnb1.GetRow(row2Index);
Line ahnb1Row3 = ahnb1.GetRow(row3Index);
// horizontal adjacent box 2 -- rows
Line ahnb2Row1 = ahnb1.GetRow(row1Index);
Line ahnb2Row2 = ahnb2.GetRow(row2Index);
Line ahnb2Row3 = ahnb2.GetRow(row3Index);
// determine union of values of rows
ReadOnlySpan <int> adjRow2Union = ahnb1Row2.Union(ahnb2Row2);
ReadOnlySpan <int> adjRow3Union = ahnb1Row3.Union(ahnb2Row3);
// get complete row that includes current row of box
int currentRowIndex = rowOffset + i;
Line currentRow = _puzzle.GetRow(currentRowIndex);
// calculate full set of illegal values for row 1
ReadOnlySpan <int> boxRow1IllegalValues = boxLine.Union(currentRow);
// determine disjoint set with baseline row -- looking for values in that row
ReadOnlySpan <int> row2Candidates = adjRow2Union.DisjointSet(boxRow1IllegalValues);
ReadOnlySpan <int> row3Candidates = adjRow3Union.DisjointSet(boxRow1IllegalValues);
ReadOnlySpan <int> boxRow1Candidates = row2Candidates.Intersect(row3Candidates);
// determine if rows on their own present a solution
if (boxRow1Candidates.Length == 1)
{
if (boxRow1.IsJustOneElementUnsolved(out int column))
{
solution = GetSolution(index, i, column, boxRow1Candidates[0], nameof(Strategy.RowSolver));
return(true);
}
}
// iterate over columns for row
// mostly targets row[column] cell
for (int y = 0; y < 3; y++)
{
// check if current value is 0
if (boxRow1[y] != 0)
{
continue;
}
int col1Index = y;
int col2Index = (y + 1) % 3;
int col3Index = (y + 2) % 3;
// baseline box
Line boxCol1 = box.GetColumn(col1Index);
Line boxCol2 = box.GetColumn(col2Index);
Line boxCol3 = box.GetColumn(col3Index);
// vertical adjacent box 1 -- cols
Line avnb1Col1 = avnb1.GetColumn(col1Index);
Line avnb1Col2 = avnb1.GetColumn(col2Index);
Line avnb1Col3 = avnb1.GetColumn(col3Index);
// vertical adjacent box 2 -- cols
Line avnb2Col1 = avnb2.GetColumn(col1Index);
Line avnb2Col2 = avnb2.GetColumn(col2Index);
Line avnb2Col3 = avnb2.GetColumn(col3Index);
// get complete column that includes the the first column of box
int currentColIndex = columnOffset + y;
Line currentCol = _puzzle.GetColumn(currentColIndex);
// calculate full set of illegal values for col 1
ReadOnlySpan <int> boxCol1IllegalValues = boxLine.Union(currentCol);
// determine union of values of cols
ReadOnlySpan <int> col2Union = avnb1Col2.Union(avnb2Col2);
ReadOnlySpan <int> col3Union = avnb1Col3.Union(avnb2Col3);
// determine disjoint set with baseline col -- looking for values now in that col
ReadOnlySpan <int> col2Candidates = col2Union.DisjointSet(boxCol1IllegalValues);
ReadOnlySpan <int> col3Candidates = col3Union.DisjointSet(boxCol1IllegalValues);
ReadOnlySpan <int> boxCol1Candidates = col2Candidates.Intersect(col3Candidates);
// determine if columns on their own present a solution
// can solve any cell in given box column
if (boxCol1Candidates.Length == 1)
{
if (boxCol1.IsJustOneElementUnsolved(out int row))
{
solution = GetSolution(index, row, y, boxCol1Candidates[0], nameof(Strategy.ColumnSolver));
return(true);
}
}
// determine if rows and columns together present a solution
// test: SolutionAllSlotsEmpty
ReadOnlySpan <int> rowAndColumnCandidates = boxRow1Candidates.Intersect(boxCol1Candidates);
if (rowAndColumnCandidates.Length == 1)
{
if (boxCol1[i] == 0)
{
solution = GetSolution(index, i, y, rowAndColumnCandidates[0], nameof(Strategy.RowColumnSolver));
return(true);
}
}
// determine if various combinations of rows and columns present a solution
// col1[row] is candidate for all following cases
// the following set of cases involve a row or a column with:
// a candidate, one cell == 0 and the other non zero
// the cases are looking for a set of rows and columns
// that project the same value except for the row or column with
// the non-zero value (which doesn't require a projected value)
// check rows
if (boxRow1Candidates.Length > 0)
{
var solverKind = nameof(Strategy.ColumnCandidateColumnBlockedRowSolver);
// row1[col3] has a value, so col3 don't need to participate in providing a candidate
if (col2Candidates.Length > 0 &&
boxRow1[col2Index] == 0 && boxRow1[col3Index] != 0 &&
TrySolveForIntersectionCandidates(boxRow1Candidates, col2Candidates, solverKind, out solution))
{
return(true);
}
// row1[col2] has a value, so col2 don't need to participate in providing a candidate
if (col3Candidates.Length > 0 &&
boxRow1[col2Index] != 0 && boxRow1[col3Index] == 0 &&
TrySolveForIntersectionCandidates(boxRow1Candidates, col3Candidates, solverKind, out solution))
{
return(true);
}
}
// check columns
if (boxCol1Candidates.Length > 0)
{
var solverKind = nameof(Strategy.RowCandidateRowBlockedColumnSolver);
// col1[row3] has a value, so row3 don't need to participate in providing a candidate
if (row2Candidates.Length > 0 &&
boxCol1[row2Index] == 0 && boxCol1[row3Index] != 0 &&
TrySolveForIntersectionCandidates(boxCol1Candidates, row2Candidates, solverKind, out solution))
{
return(true);
}
// col1[row2] has a value, so row2 don't need to participate in providing a candidate
// test: SolutionTwoSlotsEmptyInColumn
if (row3Candidates.Length > 0 &&
boxCol1[row2Index] != 0 && boxCol1[row3Index] == 0 &&
TrySolveForIntersectionCandidates(boxCol1Candidates, row3Candidates, solverKind, out solution))
{
return(true);
}
}
// the following set of cases involve a row or column with:
// all cells filled, such that a row or column doesn't need to participate in providing a candidate
// col3 is blocked, so col3 doesn't need to participate in providing a candidate
bool col2Blocked = boxCol2.GetUnsolvedCount() == 0;
bool col3Blocked = boxCol3.GetUnsolvedCount() == 0;
bool row2Blocked = boxRow2.GetUnsolvedCount() == 0;
bool row3Blocked = boxRow3.GetUnsolvedCount() == 0;
if (boxCol1.GetUnsolvedCount() == 1)
{
var solverKind = nameof(Strategy.ColumnCandidateColumnBlocked);
// Column 1 one slot open, column 2 blocked, column 3 offers a candidate
if (col2Blocked &&
col3Candidates.Length == 1)
{
solution = GetSolution(index, i, y, col3Candidates[0], solverKind);
return(true);
}
// Column 1 one slot open, column 2 offers a candidate, column 3 blocked
if (col3Blocked &&
col2Candidates.Length == 1)
{
solution = GetSolution(index, i, y, col2Candidates[0], solverKind);
return(true);
}
}
if (boxRow1.GetUnsolvedCount() == 1)
{
var solverKind = nameof(Strategy.RowCandidateRowBlocked);
// Row 1 one slot open, row 2 blocked, row 3 offers a candidate
if (row2Blocked &&
row3Candidates.Length == 1)
{
solution = GetSolution(index, i, y, row3Candidates[0], solverKind);
return(true);
}
// Column 1 one slot open, column 2 offers a candidate, column 3 blocked
if (row3Blocked &&
row2Candidates.Length == 1)
{
solution = GetSolution(index, i, y, row2Candidates[0], solverKind);
return(true);
}
}
// following set of cases test hidden singles in columns or rows
// pattern
// box 1 col1 is full
// box 2 has one value not in col1
// only one slot available in col1 in current box
// means that current cell must have that value
{
var solverKind = nameof(Strategy.ColumnLastPossibleSlot);
var candidates1 = avnb1.AsLine().DisjointSet(currentCol);
foreach (var candidate in candidates1)
{
if (!boxLine.ContainsValue(candidate) &&
!currentRow.ContainsValue(candidate) &&
CheckForValueInCellOrRow(candidate, box, col1Index, row2Index, row3Index) &&
CheckForValueInCellOrRow(candidate, avnb2, col1Index, 0, 1, 2)
)
{
solution = GetSolution(index, i, y, candidate, solverKind);
return(true);
}
}
var candidates2 = avnb2.AsLine().DisjointSet(currentCol);
foreach (var candidate in candidates2)
{
if (!boxLine.ContainsValue(candidate) &&
!currentRow.ContainsValue(candidate) &&
CheckForValueInCellOrRow(candidate, box, col1Index, row2Index, row3Index) &&
CheckForValueInCellOrRow(candidate, avnb1, col1Index, 0, 1, 2)
)
{
solution = GetSolution(index, i, y, candidate, solverKind);
return(true);
}
}
}
{
var solverKind = nameof(Strategy.RowLastPossibleSlot);
var candidates1 = ahnb1.AsLine().DisjointSet(currentRow);
foreach (var candidate in candidates1)
{
if (!boxLine.ContainsValue(candidate) &&
!currentCol.Segment.Contains(candidate) &&
CheckForValueInCellOrColumn(candidate, box, row1Index, col2Index, col3Index) &&
CheckForValueInCellOrColumn(candidate, ahnb2, row1Index, 0, 1, 2)
)
{
solution = GetSolution(index, i, y, candidate, solverKind);
return(true);
}
}
var candidates2 = ahnb2.AsLine().DisjointSet(currentRow);
foreach (var candidate in candidates2)
{
if (!boxLine.ContainsValue(candidate) &&
!currentCol.Segment.Contains(candidate) &&
CheckForValueInCellOrColumn(candidate, box, row1Index, col2Index, col3Index) &&
CheckForValueInCellOrColumn(candidate, ahnb1, row1Index, 0, 1, 2)
)
{
solution = GetSolution(index, i, y, candidate, solverKind);
return(true);
}
}
}
// Strategy where a column or row has two empty cells and one is constrained
{
var solverKind = nameof(Strategy.ColumnLastTwoPossibleSlots);
if (currentCol.GetUnsolvedCount() == 2)
{
var missingValues = currentCol.GetMissingValues();
for (int k = 0; k < 2; k++)
{
var value = missingValues[k];
var otherValue = missingValues[(k + 1) % 2];
if (currentRow.ContainsValue(value) &&
!boxLine.ContainsValue(otherValue))
{
solution = GetSolution(index, i, y, otherValue, solverKind);
return(true);
}
}
}
}
{
var solverKind = nameof(Strategy.RowLastTwoPossibleSlots);
if (currentRow.GetUnsolvedCount() == 2)
{
var missingValues = currentRow.GetMissingValues();
for (int k = 0; k < 2; k++)
{
var value = missingValues[k];
var otherValue = missingValues[(k + 1) % 2];
if (currentCol.ContainsValue(value) &&
!boxLine.ContainsValue(otherValue))
{
solution = GetSolution(index, i, y, otherValue, solverKind);
return(true);
}
}
}
}
{
var solverKind = nameof(Strategy.LastInRowOrColumn);
(var valuesFound, var values) = FindMissingValues(currentCol, currentRow);
for (var j = 1; j < 10; j++)
{
if (values[j])
{
continue;
}
var columnIndex = box.GetColumnOffset() + y;
var rowIndex = box.GetRowOffset() + i;
var foundSolution = 0;
// try with columns for the row
for (int l = 0; l < 9; l++)
{
var cell = currentRow[l];
if (cell != 0 || l == columnIndex)
{
continue;
}
if (_puzzle.GetColumn(l).ContainsValue(j))
{
foundSolution = j;
}
else
{
foundSolution = 0;
break;
}
}
if (foundSolution != 0)
{
solution = GetSolution(index, i, y, foundSolution, solverKind);
return(true);
}
// try with rows for the column
for (int l = 0; l < 9; l++)
{
var cell = currentCol[l];
if (cell != 0 || l == columnIndex)
{
continue;
}
if (_puzzle.GetRow(l).ContainsValue(j))
{
foundSolution = j;
}
else
{
foundSolution = 0;
break;
}
}
if (foundSolution != 0)
{
solution = GetSolution(index, i, y, foundSolution, solverKind);
return(true);
}
}
}
bool CheckRowForValue(int searchValue, Box box, int row)
{
// get complete row that includes current row of box
var rowIndex = box.GetRowOffset() + row;
//TODO: consider an overload that only returns non-zero values
var targetRow = _puzzle.GetRow(rowIndex);
return(targetRow.Segment.Contains(searchValue));
}
bool CheckForValueInCellOrColumn(int value, Box box, int row, params int[] cols)
{
foreach (int col in cols)
{
var targetColumn = box.GetColumn(col);
if (targetColumn[row] != 0 ||
ColumnContainsValue(value, box, col))
{
}
else
{
return(false);
}
}
return(true);
}
bool CheckForValueInCellOrRow(int value, Box box, int col, params int[] rows)
{
foreach (int row in rows)
{
var targetRow = box.GetRow(row);
if (targetRow[col] != 0 ||
CheckRowForValue(value, box, row))
{
}
else
{
return(false);
}
}
return(true);
}
// assumes lines are of the same length
(int valuesFound, bool[] values) FindMissingValues(Line line1, Line line2)
{
int valuesFound = 0;
bool[] values = new bool[10];
for (int i = 0; i < line1.Length; i++)
{
Update(line1[i]);
Update(line2[i]);
}
return(valuesFound, values);
void Update(int value)
{
if (value != 0 && !values[value])
{
values[value] = true;
valuesFound++;
}
}
}
bool ColumnContainsValue(int searchValue, Box box, int col)
{
// get complete column that includes current column of box
var colIndex = box.GetColumnOffset() + col;
var targetCol = _puzzle.GetColumn(colIndex);
return(targetCol.Segment.Contains(searchValue));
}
bool TrySolveForIntersectionCandidates(ReadOnlySpan <int> candidate1, ReadOnlySpan <int> candidate2, string solverKind, out Solution solution)
{
var candidates = candidate1.Intersect(candidate2);
if (candidates.Length == 1)
{
solution = GetSolution(index, i, y, candidates[0], solverKind);
return(true);
}
solution = null;
return(false);
}
}
Solution GetSolution(int box, int row, int column, int value, string solverKind)
{
(var r, var c) = Puzzle.GetLocationForBoxCell(index, (row * 3) + column);
return(new Solution(
r,
c,
value,
nameof(HiddenSinglesSolver),
solverKind));
}
}
solution = null;
return(false);
}
public Solution SolveBox(int index)
{
var box = _puzzle.GetBox(index);
var solution = new Solution
{
Solved = false
};
var values = new bool[10];
var unsolvedCells = 0;
var unsolvedCell = 99;
for (int i = 0; i < 9; i++)
{
int value;
if (i < 3)
{
value = box.FirstRow[i];
}
else if (i < 6)
{
value = box.InsideRow[i - 3];
}
else
{
value = box.LastRow[i - 6];
}
if (value > 0)
{
values[value] = true;
}
else
{
unsolvedCells++;
unsolvedCell = i;
}
if (unsolvedCells > 1)
{
return(solution);
}
}
if (unsolvedCells == 0)
{
return(solution);
}
for (int i = 1; i < 10; i++)
{
if (!values[i])
{
solution.Value = i;
break;
}
}
(var row, var column) = Puzzle.GetLocationForBoxCell(index, unsolvedCell);
solution.Solved = true;
solution.Row = row;
solution.Column = column;
solution.Solver = this;
return(solution);
}