public void Solve(Grid grid)
{
// Need to have a column after so only check first 8 cols
for (var firstColIdx = 0; firstColIdx < 8; ++ firstColIdx)
{
var firstPossibleLocations = GetPossibleLocations(grid, firstColIdx);
// Find digits that have exactly two possible locations - possible rectangle
var potentialRectangleLocations = firstPossibleLocations.Where(pl => pl.Value.Count == 2);
foreach (var potentialRectangleLocation in potentialRectangleLocations)
{
var digitToMatch = potentialRectangleLocation.Key;
var topRowToMatch = potentialRectangleLocation.Value[0];
var bottomRowToMatch = potentialRectangleLocation.Value[1];
for (var secondColIdx = firstColIdx + 1; secondColIdx < 9; ++ secondColIdx)
{
var secondPossibleLocations = GetPossibleLocations(grid, secondColIdx);
if (!secondPossibleLocations.ContainsKey(digitToMatch) ||
secondPossibleLocations[digitToMatch].Count != 2) continue;
if (!secondPossibleLocations[digitToMatch].Contains(topRowToMatch) ||
!secondPossibleLocations[digitToMatch].Contains(bottomRowToMatch)) continue;
// Have found a rectangle, now remove the digit (if it exists) from any other columns in the top and bottom rows
for (var colToRemoveIdx = 0; colToRemoveIdx < 9; ++ colToRemoveIdx)
{
// Avoid removing it from the rectangle
if (colToRemoveIdx == firstColIdx || colToRemoveIdx == secondColIdx) continue;
if (!grid.Squares[topRowToMatch, colToRemoveIdx].IsSolved)
{
grid.CheckIfTestCase(topRowToMatch, colToRemoveIdx, digitToMatch);
grid.Squares[topRowToMatch, colToRemoveIdx].RemovePossibleDigit(digitToMatch);
}
if (!grid.Squares[bottomRowToMatch, colToRemoveIdx].IsSolved)
{
grid.CheckIfTestCase(bottomRowToMatch, colToRemoveIdx, digitToMatch);
grid.Squares[bottomRowToMatch, colToRemoveIdx].RemovePossibleDigit(digitToMatch);
}
}
}
}
}
}
/// <summary>
/// Given that you need to place a certain digit in two of the three boxes in a row (i.e. it has already been placed in one box)
/// Can you eliminate one of the rows because all three squares within a particular box have been filled with other digits?
///
/// e.g.
/// 100 920 000
/// 524 017 009
/// 000 004 271
///
/// - in this the digit 5 has only been positioned once (the middle row). So theoretically in the other two boxes
/// it will appear in either the top or the bottom row. However it can't appear in the bottom row in the third box
/// because all three squares have been taken. Therefore despite not knowing which of the top row squares in the third box
/// it will appear in, you know that it can't appear in the top row in the middle box and therefore it must be in
/// the bottom row for the middle box
/// i.e. the only remaining possibilities for 5 are marked as ? and it can be removed as a possibility from the square X
/// 100 92X ???
/// 524 017 009
/// 000 ??4 271
/// </summary>
/// <param name="grid"></param>
public void Solve(Grid grid)
{
var boxCols = grid.GetBoxColumns();
var boxRows = grid.GetBoxRows();
for (var digit = 1; digit <= 9; ++digit)
{
// Top box row then middle box row then bottom box row (of 3x3 squares)
for (var boxRow = 1; boxRow <= 3; ++boxRow)
{
// Square rows within the box row
var topSquareRow = boxRows[boxRow].Item1;
var middleSquareRow = boxRows[boxRow].Item1 + 1;
var bottomSquareRow = boxRows[boxRow].Item2;
// Key is the box number (i.e. left, middle, right) and value is the row
// in which the digit is found (if at all)
var rowInBox = grid.FindTheDigitWithinEachBoxInTheBoxRow(boxCols, digit, topSquareRow, middleSquareRow, bottomSquareRow);
// If the current digit has been placed in exactly one box in the current box row
// then there is potential to eliminate it as a possibility from one of the square rows
// in the remaining two boxes
var numberOfBoxesPlaced = rowInBox.Count(kvp => kvp.Value != GridDigitInBoxExtensions.NotFound);
if (numberOfBoxesPlaced != 1) continue;
var digitPlacedBoxCombo = rowInBox.First(kvp => kvp.Value != GridDigitInBoxExtensions.NotFound);
var boxWhereDigitPlaced = digitPlacedBoxCombo.Key;
var digitPlacedInRow = digitPlacedBoxCombo.Value;
int firstRowToCheck;
int secondRowToCheck;
if (digitPlacedInRow == topSquareRow)
{
firstRowToCheck = middleSquareRow;
secondRowToCheck = bottomSquareRow;
}
else if (digitPlacedInRow == middleSquareRow)
{
firstRowToCheck = topSquareRow;
secondRowToCheck = bottomSquareRow;
}
else
{
firstRowToCheck = topSquareRow;
secondRowToCheck = middleSquareRow;
}
// Key is box number, value is whether or not all squares in that
var completeFirstRowInBox = new Dictionary<int, int> {{1, 0}, {2, 0}, {3, 0}};
var completeSecondRowInBox = new Dictionary<int, int> { { 1, 0 }, { 2, 0 }, { 3, 0 } };
for (var boxCol = 1; boxCol <= 3; ++boxCol)
{
if (rowInBox[boxCol] != GridDigitInBoxExtensions.NotFound)
{
continue;
}
var firstRowSolvedSquares = 0;
var secondRowSolvedSquares = 0;
for (var colIdx = boxCols[boxCol].Item1; colIdx <= boxCols[boxCol].Item2; ++colIdx)
{
if (grid.Squares[firstRowToCheck, colIdx].IsSolved)
{
firstRowSolvedSquares++;
}
if (grid.Squares[secondRowToCheck, colIdx].IsSolved)
{
secondRowSolvedSquares++;
}
}
if (firstRowSolvedSquares == 3)
{
completeFirstRowInBox[boxCol] = boxCol;
}
if (secondRowSolvedSquares == 3)
{
completeSecondRowInBox[boxCol] = boxCol;
}
}
var boxToClear = 0;
var rowToClear = 0;
// If there is any row within a box (unsolved for the digit) that is complete
// then there is no room for the digit and then for that row it *must* be in the third box
if (completeFirstRowInBox.Any(kvp => kvp.Value != 0))
{
rowToClear = secondRowToCheck;
var boxWhereComplete = completeFirstRowInBox.First(kvp => kvp.Value != 0).Key;
boxToClear = FindBoxToClear(boxWhereDigitPlaced, boxWhereComplete);
}
if (completeSecondRowInBox.Any(kvp => kvp.Value != 0))
{
rowToClear = firstRowToCheck;
var boxWhereComplete = completeSecondRowInBox.First(kvp => kvp.Value != 0).Key;
boxToClear = FindBoxToClear(boxWhereDigitPlaced, boxWhereComplete);
}
if (boxToClear != 0)
{
for (var colIdx = boxCols[boxToClear].Item1; colIdx <= boxCols[boxToClear].Item2; ++colIdx)
{
grid.CheckIfTestCase(rowToClear, colIdx, digit);
grid.Squares[rowToClear, colIdx].RemovePossibleDigit(digit);
}
}
}
}
}