LeetCode第三十六题-判断九宫格是否有效

Valid Sudoku

问题简介：确定9x9数独格是否有效, 只需要根据以下规则验证已填充的单元格：

1.每行必须包含数字1-9而不重复

2.每列必须包含数字1-9而不重复

3.网格的9个3x3子框中的每一个必须包含数字1-9而不重复

注：

1.数独板(部分填充)可能有效,但不一定是可解决的

2.只需要根据上述规则验证已填充的单元格

3.给定的板只包含数字1-9和字符’.’

4.给定的电路板尺寸始终为9x9

举例：

1:

输入:

[

[“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

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”]

]

输出: false

解释: 左上角的3*3里有两个8所以答案为false

解法一：

通过set集合对每行每列的元素进行判断,这里的难点是在小的33九宫格里,要注意小九宫格坐标的计算,观察：

观察行号规律：

第 i=0 个九宫格：000111222; 第1个九宫格：000111222; 第2个九宫格：000111222；第3个九宫格：333444555; 第4个九宫格：333444555; 第5个九宫格：333444555;第6个九宫格：666777888; 第7个九宫格：666777888; 第8个九宫格：666777888;

可见对于每三个九宫格行号增3；即可表示为对3作商,因此第i个九宫格的第j个格点的行号加偏移量可表示为i/33+j/3

观察列号规律：

第0个九宫格：012012012; 第1个九宫格：345345345; 第2个九宫格：678678678;第3个九宫格：012012012; 第4个九宫格：345345345; 第5个九宫格：678678678;第6个九宫格：012012012; 第7个九宫格：345345345; 第8个九宫格：678678678;

可见对于下个九宫格列号增3，循环周期为3；对于单个九宫格，每个格点行号增1，周期也为3。因此第i个九宫格的第j个格点的列号加偏移量可表示为i%3*3+j%3

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