// Chronological backtracking algorithm
static private Tuple <Sudoku, int> ChronologicalBacktracking(Sudoku sudoku)
{
// Counting the amount of expansions
int expansionCount = 0;
Stack <Sudoku> stack = new Stack <Sudoku>();
// Initial push
stack.Push(sudoku);
Sudoku newSudoku = sudoku.Clone();
while (!sudoku.IsSolution())
{
newSudoku = sudoku.Clone();
// Get new variable, the first empty one
Tuple <int, int> newVariable = newSudoku.EmptyVariable(0);
List <int> domain = newSudoku.domains[newVariable.Item1, newVariable.Item2];
newSudoku[newVariable.Item1, newVariable.Item2] = domain[sudoku.domainCounter];
// Check if the new sudoku is a partial solution, if so, push to stack
if (newSudoku.IsPartialSolution(newVariable))
{
stack.Push(newSudoku);
}
// Domain and expansion counter
sudoku.domainCounter++;
expansionCount++;
// Backtrack step
if (sudoku.domainCounter >= domain.Count)
{
sudoku = stack.Pop();
}
}
return(new Tuple <Sudoku, int>(sudoku, expansionCount));
}
// Forward checking algorithm
static private Tuple <Sudoku, int> ForwardChecking(Sudoku sudoku)
{
int expansionCount = 0;
Stack <Sudoku> stack = new Stack <Sudoku>();
stack.Push(sudoku);
Sudoku newSudoku = sudoku.Clone();
while (!sudoku.IsSolution())
{
newSudoku = sudoku.Clone();
bool alreadyPopped = false;
// Generate and push successor
Tuple <int, int> newVariable = newSudoku.EmptyVariable(0);
List <int> domain = newSudoku.domains[newVariable.Item1, newVariable.Item2];
newSudoku[newVariable.Item1, newVariable.Item2] = domain[sudoku.domainCounter];
if (newSudoku.IsPartialSolution(newVariable))
{
stack.Push(newSudoku);
}
// Domain counter goes up
sudoku.domainCounter++;
expansionCount++;
/*
* Update constraints where this sudoku is a part of.
* Find all constraints that should be updated and update them
* check all constraints in constraintset.
* If V_i has value, get all constraints C_ji where V_j not instantiated, and make them consistent.
*/
foreach (Tuple <Tuple <int, int>, Tuple <int, int> > constraint in newSudoku.constraintSet)
{
if (constraint.Item2.Equals(newVariable))
{
// If V_j is not fixed (not instantiated)
if (!newSudoku.fixedNumbers.Contains(new Tuple <int, int>(constraint.Item1.Item1, constraint.Item1.Item2)))
{
// Remove the value of V_i from domains of V_j
newSudoku.domains[constraint.Item1.Item1, constraint.Item1.Item2].Remove(domain[newSudoku.domainCounter]);
// If new domain of a location is empty, it should step back.
// Problem with double backtrack step (if also sudoku.domaincounter >= domain.count), therefor we added extra check at backtrack step
if (newSudoku.domains[constraint.Item1.Item1, constraint.Item1.Item2].Count == 0)
{
// Get previous sudoku
sudoku = stack.Pop();
Console.WriteLine("empty domain, step back to previous sudoku");
// Set alreadyPopped to true, so we don't pop twice.
alreadyPopped = true;
break;
}
}
}
}
// Backtrack step (make sure stack isn't popped yet)
if (sudoku.domainCounter >= domain.Count && alreadyPopped == false)
{
sudoku = stack.Pop();
Console.WriteLine("backtrack-step");
}
}
return(new Tuple <Sudoku, int>(sudoku, expansionCount));
}
