0036._Valid_Sudoku.md

36. Valid Sudoku

难度: Medium

刷题内容

原题连接

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

内容描述

Determine if a 9x9 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: 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.

解题方案

思路 1 - 时间复杂度: O(N^2)- 空间复杂度: O(N)******

sb题没什么好说的, beats 83.27%

class Solution:
    def isValidSudoku(self, board):
        """
        :type board: List[List[str]]
        :rtype: bool
        """
        for i in range(9):
            lookup_row = {}
            lookup_col = {}
            for j in range(9):
                if board[i][j] != '.':
                    if board[i][j] in lookup_row or not 1 <= int(board[i][j]) <= 9:
                        return False
                lookup_row[board[i][j]] = 1
                if board[j][i] != '.':
                    if board[j][i] in lookup_col or not 1 <= int(board[j][i]) <= 9:
                        return False
                lookup_col[board[j][i]] = 1
                
        for i in range(0, 9, 3):
            for j in range(0, 9, 3):
                if not self.check(i, j, board):
                    return False
                
        return True
                
    def check(self, x, y, board):
        lookup = {}
        for i in range(x, x + 3):
            for j in range(y, y + 3):
                if board[i][j] != '.':
                    if board[i][j] in lookup or not 1 <= int(board[i][j]) <= 9:
                        return False
                lookup[board[i][j]] = 1
        return True