36. Valid Sudoku

Description

Determine if a 9x9 Sudoku board is valid. Only the filled cells need to be validated according to the following rules:

Each row must contain the digits 1-9 without repetition.
Each column must contain the digits 1-9 without repetition.
Each of the 9 3x3 sub-boxes of the grid must contain the digits 1-9 without repetition.

A partially filled sudoku which is valid.

The Sudoku board could be partially filled, where empty cells are filled with the character '.'.

Example 1:

Input:
[
  ["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: true

Example 2:

Input:
[
  ["8","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: false
Explanation: Same as Example 1, except with the 5 in the top left corner being 
    modified to 8. Since there are two 8's in the top left 3x3 sub-box, it is invalid.

Note:

A Sudoku board (partially filled) could be valid but is not necessarily solvable.
Only the filled cells need to be validated according to the mentioned rules.
The given board contain only digits 1-9 and the character '.'.
The given board size is always 9x9.

Solutions

1. Hash Table

# Time: O(9n)
# Space: O(n)
class Solution:
    def isValidSudoku(self, board: List[List[str]]) -> bool:
        return (self.is_row_valid(board) and
            self.is_col_valid(board) and
            self.is_square_valid(board))

    def is_row_valid(self, board):
        for row in board:
            if not self.is_unit_valid(row):
                return False
        return True

    def is_col_valid(self, board):
        for col in zip(*board):
            if not self.is_unit_valid(col):
                return False
        return True
        
    def is_square_valid(self, board):
        for i in (0, 3, 6):
            for j in (0, 3, 6):
                square = [board[x][y] for x in range(i, i + 3) for y in range(j, j + 3)]
                if not self.is_unit_valid(square):
                    return False
        return True
        
    def is_unit_valid(self, unit):
        unit = [i for i in unit if i != '.']
        return len(set(unit)) == len(unit)
# 504/504 cases passed (88 ms)
# Your runtime beats 96.72 % of python3 submissions
# Your memory usage beats 100 % of python3 submissions (12.7 MB)

References

36. Valid Sudoku