36. Valid Sudoku

Problem Link

Description

---

Determine if a 9 x 9 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 nine 3 x 3 sub-boxes of the grid must contain the digits 1-9 without repetition.

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.

 

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: true

Example 2:

Input: board = 
[["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.

 

Constraints:

• board.length == 9
• board[i].length == 9
• board[i][j] is a digit 1-9 or '.'.

Solution

---

Python3

class Solution:
    def isValidSudoku(self, board: List[List[str]]) -> bool:
        usedRow = [[False] * 9 for _ in range(9)]
        usedCol = [[False] * 9 for _ in range(9)]
        usedSec = [[False] * 9 for _ in range(9)]
        
        for i in range(9):
            for j in range(9):
                if board[i][j] != '.':
                    num = ord(board[i][j]) - ord('0') - 1
                    k = i // 3 * 3 + j // 3
 
                    if usedRow[i][num] or usedCol[j][num] or usedSec[k][num]:
                        return False
                    
                    usedRow[i][num] = usedCol[j][num] = usedSec[k][num] = True
        
        return True