36-Valid-Sudoku.md

36. Valid Sudoku

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 or '.'

Solution

from collections import defaultdict

class Solution:
    def isValidSudoku(self, board: List[List[str]]) -> bool:
        for i in range(3):
            for j in range(3):
                tmp = defaultdict(int)
                tmp[board[0+3*i][0+3*j]] += 1
                tmp[board[0+3*i][1+3*j]] += 1
                tmp[board[0+3*i][2+3*j]] += 1
                tmp[board[1+3*i][0+3*j]] += 1
                tmp[board[1+3*i][1+3*j]] += 1
                tmp[board[1+3*i][2+3*j]] += 1
                tmp[board[2+3*i][0+3*j]] += 1
                tmp[board[2+3*i][1+3*j]] += 1
                tmp[board[2+3*i][2+3*j]] += 1
                tmp['.'] = 0
                if max(tmp.values()) > 1:
                    return False
        for i in range(9):
            tmp1, tmp2 = defaultdict(int), defaultdict(int)
            for j in range(9):
                tmp1[board[i][j]] += 1
                tmp2[board[j][i]] += 1
            tmp1['.'] = tmp2['.'] = 0
            if max(tmp1.values()) > 1 or max(tmp2.values()) > 1:
                return False
        return True

Use Python dict to record each block, column and row.