36. 有效的数独-优快云博客

本文链接：https://blog.youkuaiyun.com/weixin_42529866/article/details/115655721

该博客介绍了一个用于验证9x9数独是否有效的算法。算法通过检查每行、每列和每个3x3宫格内的数字是否存在重复来确定数独的合法性。示例展示了两种情况，一种是有效的数独布局，另一种由于重复数字而无效。博客内容涉及编程和算法设计，适合对数独和编程感兴趣的读者阅读。

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题目描述

请你判断一个 9x9 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。

数字 1-9 在每一行只能出现一次。
数字 1-9 在每一列只能出现一次。
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）

数独部分空格内已填入了数字，空白格用 ‘.’ 表示。

注意：

一个有效的数独（部分已被填充）不一定是可解的。
只需要根据以上规则，验证已经填入的数字是否有效即可。

示例 1：
在这里插入图片描述

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：

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。

提示：

board.length == 9
board[i].length == 9
board[i][j] 是一位数字或者 ‘.’

来源：力扣（LeetCode）
链接：https://leetcode-cn.com/problems/valid-sudoku
著作权归领扣网络所有。商业转载请联系官方授权，非商业转载请注明出处。

思路

class Solution {
    public boolean isValidSudoku(char[][] board) {
        boolean[][] rows = new boolean[9][9];
        boolean[][] cols = new boolean[9][9];
        boolean[][][] blocks = new boolean[3][3][9];
        for(int i = 0;i < board.length;++i){
            for(int j = 0;j < board[0].length;++j){
                if(board[i][j] != '.'){
                    int digit = board[i][j] - '0' -1;
                    if(rows[i][digit] || cols[j][digit] || blocks[i/3][j/3][digit]){
                        return false;
                    }else{
                        rows[i][digit] = cols[j][digit] = blocks[i/3][j/3][digit] = true;
                    }
                }
            }
        }
        return true;
    }
}