/// <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>Evaluates the difficulty level of a particular puzzle.</summary>
/// <param name="state">The puzzle to evaluate.</param>
/// <returns>The perceived difficulty level of the puzzle.</returns>
public static PuzzleDifficulty EvaluateDifficulty(PuzzleState state)
{
if (state == null)
{
throw new ArgumentNullException("state");
}
SolverOptions options = new SolverOptions();
foreach (PuzzleDifficulty diff in new PuzzleDifficulty[] { PuzzleDifficulty.Easy, PuzzleDifficulty.Medium, PuzzleDifficulty.Hard, PuzzleDifficulty.VeryHard })
{
GeneratorOptions go = GeneratorOptions.Create(diff);
if (state.NumberOfFilledCells < go.MinimumFilledCells)
{
continue;
}
options.AllowBruteForce = !go.MaximumNumberOfDecisionPoints.HasValue;
options.EliminationTechniques = go.Techniques;
options.MaximumSolutionsToFind = options.AllowBruteForce ? 2u : 1u;
SolverResults results = Solver.Solve(state, options);
if (results.Status == PuzzleStatus.Solved &&
results.Puzzles.Count == 1)
{
return(diff);
}
}
return(PuzzleDifficulty.Invalid);
}
/// <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>
private static SolverResults SolveInternal(PuzzleState state, SolverOptions options)
{
// First, make a copy of the state and work on that copy. That way, the original
// instance passed to us by the client remains unmodified.
state = state.Clone();
// Fill cells using logic and analysis techniques until no more
// can be filled.
var totalUseOfTechniques = new Dictionary <EliminationTechnique, int>();
FastBitArray [][] possibleNumbers = FillCellsWithSolePossibleNumber(state, options.EliminationTechniques, ref totalUseOfTechniques);
// Analyze the current state of the board
switch (state.Status)
{
// If the puzzle is now solved, return it. If the puzzle is in an inconsistent state (such as
// two of the same number in the same row), return that as well as there's nothing more to be done.
case PuzzleStatus.Solved:
case PuzzleStatus.CannotBeSolved:
return(new SolverResults(state.Status, state, 0, totalUseOfTechniques));
// If the puzzle is still in progress, it means no more cells
// can be filled by elimination alone, so do a brute-force step.
// BruteForceSolve recursively calls back to this method.
default:
if (options.AllowBruteForce)
{
SolverResults results = BruteForceSolve(state, options, possibleNumbers);
if (results.Status == PuzzleStatus.Solved)
{
AddTechniqueUsageTables(results.UseOfTechniques, totalUseOfTechniques);
}
return(results);
}
else
{
return(new SolverResults(PuzzleStatus.CannotBeSolved, state, 0, null));
}
}
}
/// <summary>
/// Based on the specified GeneratorOptions, determines whether the SolverResults
/// created by solving a puzzle with a particular cell value removed represents a valid
/// new state.
/// </summary>
/// <param name="state">The puzzle state being validated.</param>
/// <param name="results">The SolverResults to be verified.</param>
/// <returns>true if the removal that led to this call is valid; false, otherwise.</returns>
private static bool IsValidRemoval(PuzzleState state, SolverResults results, GeneratorOptions options)
{
// Make sure we have a puzzle with one and only one solution
if (results.Status != PuzzleStatus.Solved || results.Puzzles.Count != 1)
{
return(false);
}
// Make sure we don't have too few cells
if (state.NumberOfFilledCells < options.MinimumFilledCells)
{
return(false);
}
// Now check to see if too many decision points were involved
if (options.MaximumNumberOfDecisionPoints.HasValue &&
results.NumberOfDecisionPoints > options.MaximumNumberOfDecisionPoints)
{
return(false);
}
// Otherwise, it's a valid removal.
return(true);
}
/// <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));
}
/// <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));
}