public static IEnumerable <Cell[, ]> Solve(Cell[,] board)
{
board = board.Copy();
var i = 0;
var unknowns = board.Points()
.Where(s => board[s.x, s.y] == Cell.Unknown)
.ToArray();
while (i >= 0)
{
var(x, y) = unknowns[i];
var cell = board[x, y];
int nextGuessIndex = cell == Cell.Unknown ? 0 : Array.IndexOf(FillOptions, cell) + 1;
if (nextGuessIndex >= FillOptions.Length)
{
board[x, y] = Cell.Unknown;
i--;
continue;
}
board[x, y] = FillOptions[nextGuessIndex];
if (board.LegalSquare(x, y) && board.LegalNumbers(x, y))
{
if (i < unknowns.Length - 1)
{
i++;
}
else if (board[x, y] == Cell.Full && board.LegalPath(x, y) || board[x, y] != Cell.Full && board.LegalPath())
{
yield return(board.Copy());
}
}
}
}
public static bool Legal(this Cell[,] board) => board.LegalSquare() && board.LegalPath() && board.LegalNumbers();
public static bool LegalNumbers(this Cell[,] board) => !board.Points() .Any(s => board[s.x, s.y] >= 0 && !board.LegalNumbers(s.x, s.y));
public static bool LegalNumbers(this Cell[,] board, int x, int y)
{
if (!board.Contains(x, y))
{
return(true);
}
if (board[x, y] >= 0)
{
var cellNumber = (int)board[x, y];
var countUnknown = 0;
var countFull = 0;
foreach (var(dx, dy) in Cardinals)
{
var scale = 1;
var foundUnknown = false;
while (true)
{
var newX = x + dx * scale;
var newY = y + dy * scale;
if (!board.Contains(newX, newY) || board[newX, newY] == Cell.Empty || board[newX, newY] >= 0)
{
break;
}
if (foundUnknown || board[newX, newY] == Cell.Unknown)
{
foundUnknown = true;
countUnknown++;
}
else if (board[newX, newY] == Cell.Full && ++countFull > cellNumber)
{
return(false);
}
scale++;
}
}
return(countUnknown + countFull >= cellNumber && (cellNumber != 0 || countFull <= 0));
}
foreach (var(dx, dy) in Cardinals)
{
var scale = 1;
while (true)
{
var newX = x + dx * scale;
var newY = y + dy * scale;
if (!board.Contains(newX, newY))
{
break;
}
if (board[newX, newY] >= 0)
{
if (!board.LegalNumbers(newX, newY))
{
return(false);
}
break;
}
scale++;
}
}
return(true);
}
public static bool Legal(this Cell[,] board, int x, int y) => board.LegalSquare(x, y) && board.LegalNumbers(x, y);
