36. Valid Sudoku

Medium (Trung bình) Python 🔗 Xem trên LeetCode

📋 Đề Bài

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 1-9 or '.'.

🧠 Thuật Toán & Kỹ Thuật

Matrix (Ma trận)
⏱️ Thời gian O(n²)
💾 Không gian O(n)

💻 Lời Giải

Python 0036-valid-sudoku.py 
class Solution:
    def isValidSudoku(self, board: List[List[str]]) -> bool:
        n = len(board)
        
        for i in range(n):
            row = set()
            for j in range(n):
                if board[i][j] in row:
                    return False
                if '0' <= board[i][j] <= '9':
                    row.add(board[i][j]) 
                
        for j in range(n):
            col = set()
            for i in range(n):
                if board[i][j] in col:
                    return False
                if '0' <= board[i][j] <= '9':
                    col.add(board[i][j])  
        
        for i in range(0, n - 2, 3):
            for j in range(0, n - 2, 3):
                mat = set()
                for x in range(i, i + 3):
                    for y in range(j, j + 3):
                        if board[x][y] in mat:
                            return False
                        if '0' <= board[x][y] <= '9':
                            mat.add(board[x][y]) 
        
        return True