/// <summary>Attempts to solve a Sudoku puzzle.</summary>
/// <param name="state">The state of the puzzle to be solved.</param>
/// <param name="options">Options to use for solving.</param>
/// <returns>The result of the solve attempt.</returns>
/// <remarks>No changes are made to the parameter state.</remarks>
public static SolverResults Solve(PuzzleState state, SolverOptions options)
{
// Validate parameters
if (state == null)
{
throw new ArgumentNullException("state");
}
if (options == null)
{
throw new ArgumentNullException("options");
}
options = options.Clone();
if (options.EliminationTechniques.Count == 0)
{
options.EliminationTechniques.Add(new NakedSingleTechnique());
}
// Turn off the raising of changed events while solving,
// though it probably doesn't matter as the first thing
// SolveInternal does is make a clone, and RaiseStateChangedEvent
// is not cloned (on purpose).
bool raiseChangedEvent = state.RaiseStateChangedEvent;
state.RaiseStateChangedEvent = false;
// Attempt to solve the puzzle
SolverResults results = SolveInternal(state, options);
// Reset whether changed events should be raised
state.RaiseStateChangedEvent = raiseChangedEvent;
// Return the solver results
return(results);
}
/// <summary>Uses brute-force search techniques to solve the puzzle.</summary>
/// <param name="state">The state to be solved.</param>
/// <param name="options">The options to use in solving.</param>
/// <param name="possibleNumbers">The possible numbers off of which to base the search.</param>
/// <returns>The result of the solve attempt.</returns>
/// <remarks>Changes may be made to the parameter state.</remarks>
private static SolverResults BruteForceSolve(PuzzleState state, SolverOptions options, FastBitArray [][] possibleNumbers)
{
// A standard brute-force search would take way, way, way too long to solve a Sudoku puzzle.
// Luckily, there are ways to significantly trim the search tree to a point where
// brute-force is not only possible, but also very fast. The idea is that not every number
// can be put into every cell. In fact, using elimination techniques, we can narrow down the list
// of numbers for each cell, such that only those need be are tried. Moreover, every time a new number
// is entered into a cell, other cell's possible numbers decrease. It's in our best interest
// to start the search with a cell that has the least possible number of options, thereby increasing
// our chances of "guessing" the right number sooner. To this end, I find the cell in the grid
// that is empty and that has the least number of possible numbers that can go in it. If there's more
// than one cell with the same number of possibilities, I choose randomly among them. This random
// choice allows the solver to be used for puzzle generation.
List <Point> bestGuessCells = new List <Point>();
int bestNumberOfPossibilities = state.GridSize + 1;
for (int i = 0; i < state.GridSize; i++)
{
for (int j = 0; j < state.GridSize; j++)
{
int count = possibleNumbers[i][j].CountSet;
if (!state[i, j].HasValue)
{
if (count < bestNumberOfPossibilities)
{
bestNumberOfPossibilities = count;
bestGuessCells.Clear();
bestGuessCells.Add(new Point(i, j));
}
else if (count == bestNumberOfPossibilities)
{
bestGuessCells.Add(new Point(i, j));
}
}
}
}
// If there are no cells available to fill, there's nothing we can do
// to make forward progress. If there are cells available, which should
// always be the case when this method is called, go through each of the possible
// numbers in the cell and try to solve the puzzle with that number in it.
SolverResults results = null;
if (bestGuessCells.Count > 0)
{
// Choose a random cell from amongst the possibilities found above
Point bestGuessCell = bestGuessCells[RandomHelper.GetRandomNumber(bestGuessCells.Count)];
// Get the possible numbers for that cell. For each possible number,
// fill that number into the cell and recursively call to Solve.
FastBitArray possibleNumbersForBestCell = possibleNumbers[bestGuessCell.X][bestGuessCell.Y];
for (byte p = 0; p < possibleNumbersForBestCell.Length; p++)
{
if (possibleNumbersForBestCell[p])
{
PuzzleState newState = state;
// Fill in the cell and solve the puzzle
newState[bestGuessCell] = p;
SolverOptions tempOptions = options.Clone();
if (results != null)
{
tempOptions.MaximumSolutionsToFind =
(uint)(tempOptions.MaximumSolutionsToFind.Value - results.Puzzles.Count);
}
SolverResults tempResults = SolveInternal(newState, tempOptions);
// If it could be solved, update information about the solving process
// and return the solution. Only if the user wants to find multiple
// solutions will the search continue.
if (tempResults.Status == PuzzleStatus.Solved)
{
if (results != null && results.Puzzles.Count > 0)
{
results.Puzzles.AddRange(tempResults.Puzzles);
}
else
{
results = tempResults;
results.NumberOfDecisionPoints++;
}
if (options.MaximumSolutionsToFind.HasValue &&
results.Puzzles.Count >= options.MaximumSolutionsToFind.Value)
{
return(results);
}
}
// If we're not cloning, we need to cancel out the change
newState[bestGuessCell] = null;
}
}
}
// We'll get here if the requested number of solutions could not be found, or if no
// solutions at all could be found. Either return a solution if we did get at least one,
// or return that none could be found.
return(results != null ? results : new SolverResults(PuzzleStatus.CannotBeSolved, state, 0, null));
}