class Sudoku
{
    public int[,] Numbers { get; set; }
    int x;
    int y;

    public Sudoku(int[,] num)
    {
        Numbers = num;

        for (x = 0; x < 9; x++)
        {
            for (y = 0; y < 9; y++)
            {
                if (Numbers[x, y] == 0)
                    return;
            }
        }
    }

    public bool IsCompleted { get { return x == 9 && y == 9; } }

    //計(jì)算數(shù)獨(dú)，返回null表示無法計(jì)算
    public Sudoku CaluSudoKu()
    {
        if (IsCompleted)
            return this;

        foreach (var num in GetAvaibleNumbers())
        {
            var tmpData = Numbers.Clone() as int[,];
            tmpData[x, y] = num;

            var sudouku = new Sudoku(tmpData);
            var ret = sudouku.CaluSudoKu();

            if (ret != null)
                return ret;
        }

        return null;
    }

    int[] GetAvaibleNumbers()
    {
        var set = new HashSet<int>(new int[] { 1, 2, 3, 4, 5, 6, 7, 8, 9 });
        for (int i = 0; i < 9; i++)
        {
            set.Remove(Numbers[x, i]);
            set.Remove(Numbers[i, y]);
        }

        int xStart = x - x % 3;
        int yStart = y - y % 3;

        for (int i = 0; i < 3; i++)
        {
            for (int j = 0; j < 3; j++)
            {
                set.Remove(Numbers[i + xStart, j + yStart]);
            }
        }

        return set.ToArray();
    }
}