## 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**:

- 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:falseExplanation:Same as Example 1, except with the5in the top left corner being modified to8. 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).

## One Thought to “LeetCode 36. Valid Sudoku”