[LeetCode] 36. Valid Sudoku

Determine if a 9 x 9 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 nine 3 x 3 sub-boxes of the grid must contain the digits 1-9 without repetition.

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.

Example 1:

Input: 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"]]
Output: true

Example 2:
Input: 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"]]
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.

Constraints:
board.length == 9
board[i].length == 9
board[i][j] is a digit 1-9 or '.'.

有效的数独。

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。

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）

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。
空白格用 '.' 表示。

来源：力扣（LeetCode）
链接：https://leetcode.cn/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

这道题的重点是如何判断数字在他所在的行、列和 3x3 宫内只出现一次。这里我们需要三个二维数组，分别记录 9 行，9 列和 9 个 3x3 宫内数字出现的情况。其中行和列的问题比较直观，重点是如何知道某个位置上的数字是属于哪个 3x3 宫。

对于任意一个数字，他在矩阵内的坐标是(i, j)，那么他的 cubeIndex = i / 3 * 3 + j / 3

复杂度

时间O(81) - O(1)
空间O(1) - 三个 9x9 的 boolean 数组

代码

Java实现

class Solution {
    public boolean isValidSudoku(char[][] board) {
        // 数独的行、列和3x3小宫格各有9个
        int n = 9;

        // 创建3个数组，用于记录行、列和3x3小宫格中出现的数字
        boolean[][] rows = new boolean[n][n];
        boolean[][] cols = new boolean[n][n];
        boolean[][] boxes = new boolean[n][n];

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                if (board[i][j] != '.') {
                    int num = board[i][j] - '1'; // 将字符转换为0-8的数字
                    int boxIndex = (i / 3) * 3 + j / 3; // 计算小宫格索引

                    // 如果当前数字在行、列或小宫格中已存在，则返回false
                    if (rows[i][num] || cols[j][num] || boxes[boxIndex][num]) {
                        return false;
                    }

                    // 记录当前数字在行、列和小宫格中出现过
                    rows[i][num] = true;
                    cols[j][num] = true;
                    boxes[boxIndex][num] = true;
                }
            }
        }

        // 如果没有冲突，返回true
        return true;
    }
}

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