"""

Write a program to solve a Sudoku puzzle by filling the empty cells.

A sudoku solution must satisfy all of the following rules:

Each of the digits 1-9 must occur exactly once in each row.

Each of the digits 1-9 must occur exactly once in each column.

Each of the digits 1-9 must occur exactly once in each of the 9 3x3 sub-boxes of the grid.

The '.' character indicates empty cells.

Example 1:

Input: board = [["5","3",".",".","7",".",".",".","."],["6",".",".","1","9","5",".",".","."],[".","9","8",".",".",".",".","6","."],["8",".",".",".","6",".",".",".","3"],["4",".",".","8",".","3",".",".","1"],["7",".",".",".","2",".",".",".","6"],[".","6",".",".",".",".","2","8","."],[".",".",".","4","1","9",".",".","5"],[".",".",".",".","8",".",".","7","9"]]

Output: [["5","3","4","6","7","8","9","1","2"],["6","7","2","1","9","5","3","4","8"],["1","9","8","3","4","2","5","6","7"],["8","5","9","7","6","1","4","2","3"],["4","2","6","8","5","3","7","9","1"],["7","1","3","9","2","4","8","5","6"],["9","6","1","5","3","7","2","8","4"],["2","8","7","4","1","9","6","3","5"],["3","4","5","2","8","6","1","7","9"]]

Explanation: The input board is shown above and the only valid solution is shown below:

Constraints:

board.length == 9

board[i].length == 9

board[i][j] is a digit or '.'.

It is guaranteed that the input board has only one solution.

"""

class Solution:

def solve(self, board):

for i in range(9):

for j in range(9):

if board[i][j] == '.':

for k in range(1, 10):

if self.isValid(board, i, j, str(k)):

board[i][j] = str(k)

if self.solve(board):

return True

else:

board[i][j] = '.'

return False

return True

def solveSudoku(self, board: List[List[str]]) -> None:

"""

Do not return anything, modify board in-place instead.

"""

self.solve(board)

def isValid(self, board, i, j, k):

for m in range(9):

if board[m][j] == k:

return False

if board[i][m] == k:

return False

if board[3*(i//3)+m//3][3*(j//3)+m%3] == k:

return False

return True