LeetCode——36. 有效的数独(Valid Sudoku)[中等]——分析及代码（Java）

一、题目

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。

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）

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：

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。

二、分析及代码

1. 模拟

（1）思路

设计布尔变量，记录各行、列、3x3 格子内各个数字的出现情况。遍历数组中的元素，根据数字在三种限定范围内的重复情况，判断数独有效性。

（2）代码

class Solution {
    
    
    public boolean isValidSudoku(char[][] board) {
    
    
        //初始化
        boolean[][] rows = new boolean[9][9];//rows[i][j]表示第i行数字j是否已出现过
        boolean[][] cols = new boolean[9][9];//cols[i][j]表示第i列数字j是否已出现过
        boolean[][][] boxes = new boolean[3][3][9];//boxes[i][j][k]表示对于3x3的格子第i行第j个中数字k是否已出现过
        for (int i = 0; i < 9; i++)
            for (int j = 0; j < 9; j++) {
    
    
                rows[i][j] = false;
                cols[i][j] = false;
            }
        for (int i = 0 ; i < 3; i++)
            for (int j = 0; j < 3; j++)
                for (int k = 0; k < 9; k++)
                    boxes[i][j][k] = false;
        
        //遍历验证
        for (int i = 0; i < 9; i++) {
    
    //遍历行
            for (int j = 0; j < 9; j++) {
    
    //遍历列
                if (board[i][j] != '.') {
    
    //判断数字是否已填入
                    int num = board[i][j] - '1';//提取数字-1的值
                    if (rows[i][num] == true || cols[j][num] == true || boxes[i / 3][j / 3][num] == true)//数字重复，数独无效
                        return false;
                    rows[i][num] = true;//更新数字出现标记
                    cols[j][num] = true;//更新数字出现标记
                    boxes[i / 3][j / 3][num] = true;//更新数字出现标记
                }
            }
        }
        return true;//无重复数字，数独有效
    }
}

（3）结果

执行用时 ：2 ms，在所有 Java 提交中击败了 70.66% 的用户；
内存消耗 ：38.5 MB，在所有 Java 提交中击败了 42.87% 的用户。

三、其他

暂无。