36-valid-sudoku.py

"""
36. Valid Sudoku
Medium - 63.6%

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
"""

from typing import List

class Solution:
    def isValidSudoku(self, board: List[List[str]]) -> bool:
        # Use sets to track seen numbers in rows, columns, and boxes
        rows = [set() for _ in range(9)]
        cols = [set() for _ in range(9)]
        boxes = [set() for _ in range(9)]
        
        for i in range(9):
            for j in range(9):
                num = board[i][j]
                if num == '.':
                    continue
                
                # Calculate box index: (row//3)*3 + col//3
                box_index = (i // 3) * 3 + j // 3
                
                # Check if number already exists in row, column, or box
                if num in rows[i] or num in cols[j] or num in boxes[box_index]:
                    return False
                
                # Add number to respective sets
                rows[i].add(num)
                cols[j].add(num)
                boxes[box_index].add(num)
        
        return True