public bool dancingLinksAlg()
{
if (columns.Count == 0)
{
return(true);
}
int minCount = columns.Min(x => x.columnMemberCount);
if (minCount <= 0)
{
return(false);
}
DancingLinksColumnHeader c = columns.Where(x => x.columnMemberCount == minCount).ToArray()[0];
int count = c.columnMemberCount;
DancingLinksNode curNode = c.firstEntry;
//Outer loop iterates through rows intersecting the column
//Inside this, we look at a given row. Iterate through the columns intersecting that row.
while (count > 0)
{
#region Removal_and_Test
DancingLinksNode curColPivot = curNode.right;
while (curColPivot != curNode)
{
DancingLinksNode curRowPivot = curColPivot.down;
while (curRowPivot != curColPivot)
{
#region Remove_rows_Except_Pivot_Row
DancingLinksNode curRemNode = curRowPivot.right;
while (curRemNode != curRowPivot)
{
curRemNode.up.down = curRemNode.down;
curRemNode.down.up = curRemNode.up;
curRemNode.header.columnMemberCount--;
curRemNode = curRemNode.right;
}
rows.Remove(rowLookUp[curRowPivot.row]);
#endregion
//curRowPivot.right.left = curRowPivot.left;
//curRowPivot.left.right = curRowPivot.right;
curRowPivot = curRowPivot.down;
}
columns.Remove(curColPivot.header);
//We must remove the Pivot Row as well.
//Notice that we do not remove the Pivot Row from the rows list. This is intentional.
curColPivot.up.down = curColPivot.down;
curColPivot.down.up = curColPivot.up;
curColPivot = curColPivot.right;
}
//Lastly, we remove the pivot column.
columns.Remove(curNode.header);
curNode.left.right = curNode.right;
curNode.right.left = curNode.left;
DancingLinksNode colRemNode = curNode.down;
while (colRemNode != curNode)
{
colRemNode.left.right = colRemNode.right;
colRemNode.right.left = colRemNode.left;
colRemNode = colRemNode.down;
}
if (dancingLinksAlg())
{
return(true);
}
#endregion
#region Readd
else
{
//If removing this row didn't work, backtrack and undo all those row and column removals.
columns.Add(curNode.header);
curNode.right.left = curNode;
curNode.left.right = curNode;
DancingLinksNode colAddNode = curNode.down;
while (colAddNode != curNode)
{
colAddNode.left.right = colAddNode.right;
colAddNode.right.left = colAddNode.left;
colAddNode = colAddNode.down;
}
//Now, we follow the links into the inner rows and columns to restore them as well.
curColPivot = curNode.right;
while (curColPivot != curNode)
{
DancingLinksNode curRowPivot = curColPivot.down;
while (curRowPivot != curColPivot)
{
#region Add_rows_Except_Pivot_Row
DancingLinksNode curAddNode = curRowPivot.right;
while (curAddNode != curRowPivot)
{
curAddNode.up.down = curAddNode;
curAddNode.down.up = curAddNode;
curAddNode.header.columnMemberCount++;
curAddNode = curAddNode.right;
}
rows.Add(rowLookUp[curRowPivot.row]);
#endregion
//curRowPivot.right.left = curRowPivot.left;
//curRowPivot.left.right = curRowPivot.right;
curRowPivot = curRowPivot.down;
}
columns.Add(curColPivot.header);
//We must Add the Pivot Row as well.
curColPivot.up.down = curColPivot;
curColPivot.down.up = curColPivot;
curColPivot = curColPivot.right;
}
}
#endregion
curNode = curNode.down;
count--;
}
return(false);
}
public DancingLinks(SudokuGrid s)
{
rowLookUp = new Dictionary <Triple <int>, SudokuRowHeader>();
if (s.Validate())
{
columns = new List <DancingLinksColumnHeader>();
rows = new List <SudokuRowHeader>();
//Initialise blank Sudoku Grid.
for (int i = 1; i <= 9; i++)
{
for (int j = 1; j <= 9; j++)
{
columns.Add(new DancingLinksColumnHeader(new Tuple <int, int>(i, j), DancingLinksColumnHeader.ColumnType.Cell));
columns.Add(new DancingLinksColumnHeader(new Tuple <int, int>(i, j), DancingLinksColumnHeader.ColumnType.Row));
columns.Add(new DancingLinksColumnHeader(new Tuple <int, int>(i, j), DancingLinksColumnHeader.ColumnType.Square));
columns.Add(new DancingLinksColumnHeader(new Tuple <int, int>(i, j), DancingLinksColumnHeader.ColumnType.Column));
for (int k = 1; k <= 9; k++)
{
SudokuRowHeader r = new SudokuRowHeader(new Triple <int>(i, j, k));
rows.Add(r);
rowLookUp.Add(new Triple <int>(i, j, k), r);
}
}
}
//Convention: for cell numbers, x is the row and y is the column. This is reversed for square numbering. This is an artefact of how I am visualising the objects.
//Column Linking
foreach (DancingLinksColumnHeader column in columns)
{
column.columnMemberCount = 9;
if (column.type == DancingLinksColumnHeader.ColumnType.Cell)
{
int content;
if (int.TryParse(s.boxes[column.constraintNum.Item1 - 1, column.constraintNum.Item2 - 1].Text, out content))
{
column.columnMemberCount = 1;
column.firstEntry = new DancingLinksNode(column, column.constraintNum.Item1, column.constraintNum.Item2, content);
column.firstEntry.up = column.firstEntry;
column.firstEntry.down = column.firstEntry;
if (rowLookUp.ContainsKey(new Triple <int>(column.constraintNum.Item1, column.constraintNum.Item2, content)))
{
rowLookUp[new Triple <int>(column.constraintNum.Item1, column.constraintNum.Item2, content)].firstNode.left.right = column.firstEntry;
rowLookUp[new Triple <int>(column.constraintNum.Item1, column.constraintNum.Item2, content)].firstNode.left = column.firstEntry;
}
else
{
SudokuRowHeader r = new SudokuRowHeader(new Triple <int>(column.constraintNum.Item1, column.constraintNum.Item2, content));
rows.Add(r);
rowLookUp.Add(new Triple <int>(column.constraintNum.Item1, column.constraintNum.Item2, content), r);
r.firstNode = column.firstEntry;
}
}
else
{
column.firstEntry = new DancingLinksNode(column, column.constraintNum.Item1, column.constraintNum.Item2, 1);
DancingLinksNode curNode = column.firstEntry;
if (rowLookUp.ContainsKey(new Triple <int>(column.constraintNum.Item1, column.constraintNum.Item2, 1)))
{
rowLookUp[new Triple <int>(column.constraintNum.Item1, column.constraintNum.Item2, 1)].firstNode.left.right = curNode;
rowLookUp[new Triple <int>(column.constraintNum.Item1, column.constraintNum.Item2, 1)].firstNode.left = curNode;
}
else
{
SudokuRowHeader r = new SudokuRowHeader(new Triple <int>(column.constraintNum.Item1, column.constraintNum.Item2, 1));
rows.Add(r);
rowLookUp.Add(new Triple <int>(column.constraintNum.Item1, column.constraintNum.Item2, 1), r);
r.firstNode = curNode;
}
for (int i = 2; i <= 9; i++)
{
curNode.down = new DancingLinksNode(column, column.constraintNum.Item1, column.constraintNum.Item2, i);
curNode.down.up = curNode;
curNode = curNode.down;
if (i == 9)
{
column.firstEntry.up = curNode;
curNode.down = column.firstEntry;
}
if (rowLookUp.ContainsKey(new Triple <int>(column.constraintNum.Item1, column.constraintNum.Item2, i)))
{
rowLookUp[new Triple <int>(column.constraintNum.Item1, column.constraintNum.Item2, i)].firstNode.left.right = curNode;
rowLookUp[new Triple <int>(column.constraintNum.Item1, column.constraintNum.Item2, i)].firstNode.left = curNode;
}
else
{
SudokuRowHeader r = new SudokuRowHeader(new Triple <int>(column.constraintNum.Item1, column.constraintNum.Item2, i));
rows.Add(r);
rowLookUp.Add(new Triple <int>(column.constraintNum.Item1, column.constraintNum.Item2, i), r);
r.firstNode = curNode;
}
}
}
}
if (column.type == DancingLinksColumnHeader.ColumnType.Column)
{
int content;
int rowNum = 0;
bool isInColumn = false;
for (int i = 1; i <= 9 && !isInColumn; i++)
{
if (int.TryParse(s.boxes[i - 1, column.constraintNum.Item1 - 1].Text, out content))
{
if (content == column.constraintNum.Item2)
{
isInColumn = true;
}
rowNum = i;
}
}
if (isInColumn)
{
column.columnMemberCount = 1;
column.firstEntry = new DancingLinksNode(column, rowNum, column.constraintNum.Item1, column.constraintNum.Item2);
column.firstEntry.up = column.firstEntry;
column.firstEntry.down = column.firstEntry;
}
else
{
column.firstEntry = new DancingLinksNode(column, 1, column.constraintNum.Item1, column.constraintNum.Item2);
DancingLinksNode curNode = column.firstEntry;
for (int i = 2; i <= 9; i++)
{
curNode.down = new DancingLinksNode(column, i, column.constraintNum.Item1, column.constraintNum.Item2);
curNode.down.up = curNode;
curNode = curNode.down;
if (i == 9)
{
column.firstEntry.up = curNode;
curNode.down = column.firstEntry;
}
}
}
}
if (column.type == DancingLinksColumnHeader.ColumnType.Row)
{
int content;
int colNum = 0;
bool isInColumn = false;
for (int i = 1; i <= 9 && !isInColumn; i++)
{
if (int.TryParse(s.boxes[column.constraintNum.Item1 - 1, i - 1].Text, out content))
{
if (content == column.constraintNum.Item2)
{
isInColumn = true;
}
colNum = i;
}
}
if (isInColumn)
{
column.columnMemberCount = 1;
column.firstEntry = new DancingLinksNode(column, column.constraintNum.Item1, colNum, column.constraintNum.Item2);
column.firstEntry.up = column.firstEntry;
column.firstEntry.down = column.firstEntry;
}
else
{
column.firstEntry = new DancingLinksNode(column, column.constraintNum.Item1, 1, column.constraintNum.Item2);
DancingLinksNode curNode = column.firstEntry;
for (int i = 2; i <= 9; i++)
{
curNode.down = new DancingLinksNode(column, column.constraintNum.Item1, i, column.constraintNum.Item2);
curNode.down.up = curNode;
curNode = curNode.down;
if (i == 9)
{
column.firstEntry.up = curNode;
curNode.down = column.firstEntry;
}
}
}
}
if (column.type == DancingLinksColumnHeader.ColumnType.Square)
{
int squareX = column.constraintNum.Item1 % 3 - 1;
if (squareX < 0)
{
squareX += 3;
}
int squareY = (column.constraintNum.Item1 - (squareX + 1)) / 3;
int rowNum = 0;
int colNum = 0;
bool isInSquare = false;
for (int i = 1; i <= 3; i++)
{
for (int j = 1; j <= 3; j++)
{
int content;
if (int.TryParse(s.boxes[squareY * 3 + i - 1, squareX * 3 + j - 1].Text, out content))
{
if (content == column.constraintNum.Item2)
{
isInSquare = true;
rowNum = squareY * 3 + i;
colNum = squareX * 3 + j;
}
}
}
}
if (isInSquare)
{
column.columnMemberCount = 1;
column.firstEntry = new DancingLinksNode(column, rowNum, colNum, column.constraintNum.Item2);
column.firstEntry.up = column.firstEntry;
column.firstEntry.down = column.firstEntry;
}
else
{
column.firstEntry = new DancingLinksNode(column, squareY * 3 + 1, squareX * 3 + 1, column.constraintNum.Item2);
DancingLinksNode curNode = column.firstEntry;
for (int i = 1; i <= 3; i++)
{
for (int j = 1; j <= 3; j++)
{
if (i != 1 || j != 1)
{
curNode.down = new DancingLinksNode(column, squareY * 3 + i, squareX * 3 + j, column.constraintNum.Item2);
curNode.down.up = curNode;
curNode = curNode.down;
}
if (i == 3 && j == 3)
{
column.firstEntry.up = curNode;
curNode.down = column.firstEntry;
}
}
}
}
}
}
}
}