LeetCode-036-有效的数独

Posted on | In | Views:

1. 题目：

有效的数独

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。

img

上图是一个部分填充的有效的数独。

数独部分空格内已填入了数字，空白格用 '.' 表示。

示例 1:

1
2
3
4
5
6
7
8
9
10
11
12
13
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:

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
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。

说明:

  • 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。
  • 给定数独序列只包含数字 1-9 和字符 '.' 。
  • 给定数独永远是 9x9 形式的。

2. 解题：

本题要求比较简单只需要判断给出的数独是否有效即可。

大体思路分为三部分：

  1. 每行中不能出现重复的数字；
  2. 每列中不能出现重复的数字；
  3. 每个3*3方格中不能出现重复数字。

因此我们使用Set来判断是否有重复的数字。

代码：

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
class Solution {
    public boolean isValidSudoku(char[][] board) {
        Set<Character> cols = new HashSet<>();
        Set<Character> rows = new HashSet<>();
        Set<Character> blocks = new HashSet<>();
        int row = board.length;
        int col = board[0].length;
        for (int i = 0; i < row; i++) {
            for (int j = 0; j < col; j++) {
                //检查行
                if (board[i][j] != '.') {
                    if (rows.contains(board[i][j])) {
                        return false;
                    } else {
                        rows.add(board[i][j]);
                    }
                }
                //检查列
                if (board[j][i] != '.') {
                    if (cols.contains(board[j][i])) {
                        return false;
                    } else {
                        cols.add(board[j][i]);
                    }
                }
            }
            rows.clear();
            cols.clear();
        }
        //检查方块
        for (int i = 0; i < 3; i++) {
            for (int j = 0; j< 3; j++) {
                for (int m = i * 3; m < i * 3 + 3; m++) {
                    for (int n = j * 3; n < j * 3 + 3; n++) {
                        if (board[m][n] != '.') {
                            if (blocks.contains(board[m][n])) {
                                return false;
                            } else {
                                blocks.add(board[m][n]);
                            }
                        }
                    }
                }
                blocks.clear();
            }
        }
        return true;
    }
}