## Description

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

1. Each row must contain the digits 1-9 without repetition.
2. Each column must contain the digits 1-9 without repetition.
3. 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)