题目

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。

示例 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

示例 2:

输入:[  ["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。

示例 3:

输入: [1,3,5,6], 7输出: 4

示例 4:

输入: [1,3,5,6], 0输出: 0

思路解析

这道题因为需要判断数值是否存在，所以用 Hash Map 是一个很好的选择。因为每一行、每一列、每一格都是需要单独进行判断的，所以需要建立三个长度为9的HashMap数组，分别存放行、列、格的数值。

通过一个二层循环遍历这个 9*9 的数组,把当前格的数值存放到对应的HashMap中，判断之前是否已经存放过了，如果已经存放过那就退出，返回 false，如果是.的话那就跳过，这样只需要遍历一边就可以了。

动画理解

代码实现

//时间复杂度：O(n)//空间复杂度：O(1)class Solution {    public boolean isValidSudoku(char[][] board) {        HashMap[] row = new HashMap[9];        HashMap[] column = new HashMap[9];        HashMap[] box = new HashMap[9];        for (int i = 0; i < 9; i++) {            row[i] = new HashMap(9);            column[i] = new HashMap(9);            box[i] = new HashMap(9);        }        for (int i = 0; i < 9; i++) {            for (int j = 0; j < 9; j++) {                if (board[i][j] == '.') {                    continue;                }                int boxIndex=i / 3 * 3 + j / 3;                if ((boolean) row[i].getOrDefault(board[i][j], true)) {                    return false;                }                if ((boolean) column[j].getOrDefault(board[i][j], true)) {                    return false;                }                if ((boolean) box[boxIndex].getOrDefault(board[i][j], true)) {                    return false;                }                row[i].put(board[i][j], false);                column[j].put(board[i][j], false);                box[boxIndex].put(board[i][j], false);            }        }
        return true;    }}

LeetCode 图解 | 36.有效的数独

题目

思路解析

动画理解

代码实现

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