private static Grid <int> RunBacktrackingSearch(SudokuGrid puzzleGrid)
{
var nextVariable = GetNextVariable(puzzleGrid);
if (nextVariable == null)
{
return(puzzleGrid.GetValues()); // the base case: the grid is full
}
// Save the constraining variables here to avoid generating them on
// every iteration below.
var constraints = puzzleGrid.GetUnsetNeighbors(nextVariable);
foreach (int value in nextVariable.GetPossibleValues())
{
nextVariable.Value = value;
if (CheckConsistency(nextVariable, constraints))
{
var nextGrid = UpdateGridForAssignment(nextVariable, constraints, puzzleGrid);
var solution = RunBacktrackingSearch(nextGrid);
if (solution != null)
{
return(solution);
}
}
}
return(null);
}
/// <summary>
/// Makes a deep copy of a grid.
/// </summary>
/// <param name="other">the grid to copy</param>
public SudokuGrid(SudokuGrid other)
{
Validate.IsNotNull(other, "other");
Variables = new Grid <Variable>(GRID_SIZE, GRID_SIZE);
foreach (var v in other.Variables)
{
Variables[v.Location] = new Variable(v);
}
}
/*
* Deep copies the grid and propagates the constraints implied by the assigned variable.
*/
private static SudokuGrid UpdateGridForAssignment(
Variable assigned,
IEnumerable <Variable> constraints,
SudokuGrid currentGrid)
{
var newGrid = new SudokuGrid(currentGrid);
foreach (var constraint in constraints)
{
newGrid[constraint.Location].RemovePossibleValue(assigned.Value);
}
return(newGrid);
}
/*
* Returns the unset variable with the fewest remaining possible values.
*/
private static Variable GetNextVariable(SudokuGrid puzzleGrid)
{
Variable result = null;
foreach (var v in puzzleGrid.GetAllUnsetVariables())
{
if (result == null || v.PossibleValuesCount < result.PossibleValuesCount)
{
result = v;
}
}
return(result);
}
/*
* Initialize the possible values for each variable using the known
* initial values.
*/
private static SudokuGrid InitializeVariables(Grid <int> initialValues)
{
var puzzleGrid = new SudokuGrid(initialValues);
foreach (var unset in puzzleGrid.GetAllUnsetVariables())
{
foreach (var constraint in puzzleGrid.GetSetNeighbors(unset))
{
unset.RemovePossibleValue(constraint.Value);
}
}
return(puzzleGrid);
}
