有效的数独

🎯 问题描述（来源于LeetCode）

描述：
请你判断一个 9 x 9 的数独是否有效。只需要 根据以下规则 ，验证已经填入的数字是否有效即可。

  1. 数字 1-9 在每一行只能出现一次。
  2. 数字 1-9 在每一列只能出现一次。
  3. 数字 1-9 在每一个以粗实线分隔的 3x3 宫内只能出现一次。（请参考示例图）
    说明：
  • board.length == 9
  • board[i].length == 9
  • board[i][j] 是一位数字（1-9）或者 '.'

示例：

  • 示例 1：
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输入：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"]]
输出：true
  • 示例 2：
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输入：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"]]
输出：false
解释：除了第一行的第一个数字从 **5** 改为 **8** 以外，空格内其他数字均与 示例1 相同。 但由于位于左上角的 3x3 宫内有两个 8 存在, 因此这个数独是无效的。

💻 解题思路

思路1：哈希表

思路1：代码实现

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class Solution:
    def isValidSudoku(self, board: List[List[str]]) -> bool:
        rows=[dict() for _ in range(9)]
        cols=[dict() for _ in range(9)]
        boxs=[dict() for _ in range(9)]
        for i  in range(9):
            for j in range(9):
                if board[i][j]=='.':
                    continue
                num = int(board[i][j])
                box_index=(i//3)*3+j//3
                rows_num=rows[i].get(num,0)
                cols_num=cols[j].get(num,0)
                boxs_num=boxs[box_index].get(num,0)
                if rows_num>0 or cols_num>0 or boxs_num>0:
                    return False
                rows[i][num]=1    
                cols[j][num]=1    
                boxs[box_index][num]=1
        return True

思路1：📊 性能分析

提交结果
  • 运行时间：0ms击败100.00%
  • 内存消耗：19.09MB击败55.16%
复杂度验证
  • 时间复杂度：O(1)O(1)
  • 空间复杂度：O(1)O(1)

思考