leetcode: 36. Valid Sudoku

# Determine if a Sudoku is valid,
# according to: Sudoku Puzzles - The Rules.
#
# The Sudoku board could be partially filled,
# where empty cells are filled with the character '.'.
#
# A partially filled sudoku which is valid.
#
# Note:
# A valid Sudoku board (partially filled) is not necessarily solvable.
# Only the filled cells need to be validated.

class Solution():
    def isValidSudoku(self, board):
        for i in range(9):
            if not self.isValidList([board[i][j] for j in range(9)]) or not self.isValidList([board[j][i] for j in range(9)]):
                return False
        for m in range(3):
            for n in range(3):
                if not self.isValidList([board[i][j] for i in range(m*3, m*3+3) for j in range(n*3, n*3+3)]):
                    return False
        return True

    def isValidList(self, xs):
        tmp = list(filter(lambda x : x != ".", xs))
        return len(tmp) + 1 == len(set(xs))


if __name__ == "__main__":
    board = [[1, '.', '.', '.', '.', '.', '.', '.', '.'],
             ['.', 2, '.', '.', '.', '.', '.', '.', '.'],
             ['.', '.', 3, '.', '.', '.', '.', '.', '.'],
             ['.', '.', '.', 4, '.', '.', '.', '.', '.'],
             ['.', '.', '.', '.', 5, '.', '.', '.', '.'],
             ['.', '.', '.', '.', '.', 6, '.', '.', '.'],
             ['.', '.', '.', '.', '.', '.', 7, '.', '.'],
             ['.', '.', '.', '.', '.', '.', '.', 8, '.'],
             ['.', '.', '.', '.', '.', '.', '.', '.', 9]]
    assert Solution().isValidSudoku(board)