# LeetCode 36. Valid Sudoku

## Description

https://leetcode.com/problems/valid-sudoku/

Determine if a 9×9 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 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`.

Accepted

## Explanation

To satisfy the following:

• There is no rows with duplicates.
• There is no columns with duplicates.
• There is no sub-boxes with duplicates.

## Python Solution

``````class Solution:
def isValidSudoku(self, board: List[List[str]]) -> bool:
rows = [{} for i in range(9)]
columns = [{} for i in range(9)]
boxes = [{} for i in range(9)]

for i in range(9):
for j in range(9):
num = board[i][j]
if num != '.':
box_index = (i //  3) * 3 + j // 3

rows[i][num] = rows[i].get(num, 0) + 1
columns[j][num] = columns[j].get(num, 0) + 1
boxes[box_index][num] = boxes[box_index].get(num, 0) + 1

if rows[i][num] > 1 or columns[j][num] > 1 or boxes[box_index][num] > 1:
return False

return True``````
• Time complexity: O(1). Only one iteration over the board with 81 cells.
• Space complexity : O(1).