/// <summary>Generates a random Sudoku puzzle.</summary>
/// <returns>The generated results.</returns>
private static SolverResults GenerateOne(GeneratorOptions options)
{
// Generate a full solution randomly, using the solver to solve a completely empty grid.
// For this, we'll use the elimination techniques that yield fast solving.
PuzzleState solvedState = new PuzzleState();
SolverOptions solverOptions = new SolverOptions();
solverOptions.MaximumSolutionsToFind = 1;
solverOptions.EliminationTechniques = new List <EliminationTechnique> {
new NakedSingleTechnique()
};
solverOptions.AllowBruteForce = true;
SolverResults newSolution = Solver.Solve(solvedState, solverOptions);
// Create options to use for removing filled cells from the complete solution.
// MaximumSolutionsToFind is set to 2 so that we look for more than 1, but there's no
// need in continuing once we know there's more than 1, so 2 is a find value to use.
solverOptions.MaximumSolutionsToFind = 2;
solverOptions.AllowBruteForce =
!options.MaximumNumberOfDecisionPoints.HasValue || options.MaximumNumberOfDecisionPoints > 0;
solverOptions.EliminationTechniques = solverOptions.AllowBruteForce ?
new List <EliminationTechnique> {
new NakedSingleTechnique()
} : options.Techniques; // For perf: if brute force is allowed, techniques don't matter!
// Now that we have a full solution, we want to randomly remove values from cells
// until we get to a point where there is not a unique solution for the puzzle. The
// last puzzle state that did have a unique solution can then be used.
PuzzleState newPuzzle = newSolution.Puzzle;
// Get a random ordering of the cells in which to test their removal
Point [] filledCells = GetRandomCellOrdering(newPuzzle);
// Do we want to ensure symmetry?
int filledCellCount = options.EnsureSymmetry && (filledCells.Length % 2 != 0) ? filledCells.Length - 1 : filledCells.Length;
// If ensuring symmetry...
if (options.EnsureSymmetry)
{
// Find the middle cell and put it at the end of the ordering
for (int i = 0; i < filledCells.Length - 1; i++)
{
Point p = filledCells[i];
if (p.X == newPuzzle.GridSize - p.X - 1 &&
p.Y == newPuzzle.GridSize - p.Y - 1)
{
Point temp = filledCells[i];
filledCells[i] = filledCells[filledCells.Length - 1];
filledCells[filledCells.Length - 1] = temp;
}
}
// Modify the random ordering so that paired symmetric cells are next to each other
// i.e. filledCells[i] and filledCells[i+1] are symmetric pairs
for (int i = 0; i < filledCells.Length - 1; i += 2)
{
Point p = filledCells[i];
Point sp = new Point(newPuzzle.GridSize - p.X - 1, newPuzzle.GridSize - p.Y - 1);
for (int j = i + 1; j < filledCells.Length; j++)
{
if (filledCells[j].Equals(sp))
{
Point temp = filledCells[i + 1];
filledCells[i + 1] = filledCells[j];
filledCells[j] = temp;
break;
}
}
}
// In the order of the array, try to remove each pair from the puzzle and see if it's
// still solvable and in a valid way. If it is, greedily leave those cells out of the puzzle.
// Otherwise, skip them.
byte [] oldValues = new byte[2];
for (int filledCellNum = 0;
filledCellNum < filledCellCount && newPuzzle.NumberOfFilledCells > options.MinimumFilledCells;
filledCellNum += 2)
{
// Store the old value so we can put it back if necessary,
// then wipe it out of the cell
oldValues[0] = newPuzzle[filledCells[filledCellNum]].Value;
oldValues[1] = newPuzzle[filledCells[filledCellNum + 1]].Value;
newPuzzle[filledCells[filledCellNum]] = null;
newPuzzle[filledCells[filledCellNum + 1]] = null;
// Check to see whether removing it left us in a good position (i.e. a
// single-solution puzzle that doesn't violate any of the generation options)
SolverResults newResults = Solver.Solve(newPuzzle, solverOptions);
if (!IsValidRemoval(newPuzzle, newResults, options))
{
newPuzzle[filledCells[filledCellNum]] = oldValues[0];
newPuzzle[filledCells[filledCellNum + 1]] = oldValues[1];
}
}
// If there are an odd number of cells in the puzzle (which there will be
// as everything we're doing is 9x9, 81 cells), try to remove the odd
// cell that doesn't have a pairing. This will be the middle cell.
if (filledCells.Length % 2 != 0)
{
// Store the old value so we can put it back if necessary,
// then wipe it out of the cell
int filledCellNum = filledCells.Length - 1;
byte oldValue = newPuzzle[filledCells[filledCellNum]].Value;
newPuzzle[filledCells[filledCellNum]] = null;
// Check to see whether removing it left us in a good position (i.e. a
// single-solution puzzle that doesn't violate any of the generation options)
SolverResults newResults = Solver.Solve(newPuzzle, solverOptions);
if (!IsValidRemoval(newPuzzle, newResults, options))
{
newPuzzle[filledCells[filledCellNum]] = oldValue;
}
}
}
// otherwise, it's much easier.
else
{
// Look at each cell in the random ordering. Try to remove it.
// If it works to remove it, do so greedily. Otherwise, skip it.
for (int filledCellNum = 0;
filledCellNum < filledCellCount && newPuzzle.NumberOfFilledCells > options.MinimumFilledCells;
filledCellNum++)
{
// Store the old value so we can put it back if necessary,
// then wipe it out of the cell
byte oldValue = newPuzzle[filledCells[filledCellNum]].Value;
newPuzzle[filledCells[filledCellNum]] = null;
// Check to see whether removing it left us in a good position (i.e. a
// single-solution puzzle that doesn't violate any of the generation options)
SolverResults newResults = Solver.Solve(newPuzzle, solverOptions);
if (!IsValidRemoval(newPuzzle, newResults, options))
{
newPuzzle[filledCells[filledCellNum]] = oldValue;
}
}
}
// Make sure to now use the techniques specified by the user to score this thing
solverOptions.EliminationTechniques = options.Techniques;
SolverResults finalResult = Solver.Solve(newPuzzle, solverOptions);
// Return the best puzzle we could come up with
newPuzzle.Difficulty = options.Difficulty;
return(new SolverResults(PuzzleStatus.Solved, newPuzzle, finalResult.NumberOfDecisionPoints, finalResult.UseOfTechniques));
}
