# Leetcode - Valid Sudoku Solution

Determine if a `9 x 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 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 or`'.'`

.

## Solution in Python

```
class Solution:
def isValidSudoku(self, board: List[List[str]]) -> bool:
for row in board:
c = set()
for n in row:
if n!= "." and n in c:
return False
else:
c.add(n)
for i in range(9):
c = set()
for j in range(9):
n = board[j][i]
if n != "." and n in c:
return False
else:
c.add(n)
p = [[0,1,2], [3,4,5], [6,7,8]]
for x in p:
for y in p:
box = product(x,y)
c = set()
for i, j in box:
n = board[j][i]
if n != "." and n in c:
return False
else:
c.add(n)
return True
```