LeetCode 36. Valid Sudoku (Medium)

题目

Determine if a 9 x 9 Sudoku board is valid. Only the filled cells need to be validated according to the following rules:

1.Each row must contain the digits 1-9 without repetition.

2.Each column must contain the digits 1-9 without repetition.

3.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 '.'.

---

思路

方法1 （Java）

设置一个Set集合，遍历数独表二维数组，将当前遍历到的位置的元素以3个字符串形式记录下它所在的行，列和九宫格信息，并加入Set集合。若Set集合中存在某一元素的任意行/列/九宫格信息，则认为该表不符合规则。

设当前元素值为val，位置为(i, j)，位于第i/3*3+j/3个九宫格（从0开始），则该元素的信息可以设置为：

行信息："val in row i"

列信息："val in col j"

九宫格信息："val in box i/3*3+j/3"

class Solution {
    public boolean isValidSudoku(char[][] board) {
        HashSet<String> set = new HashSet<>();
        for(int i = 0; i < 9; i++){
            for(int j = 0; j < 9; j++){
                if(board[i][j] == '.') continue;
                String row = board[i][j] + " in row " + i;
                String col = board[i][j] + " in col " + j;
                String box = board[i][j] + " in box " + (i/3*3+j/3);
                if(set.contains(row) || set.contains(col) || set.contains(box)) return false;
                set.add(row);
                set.add(col);
                set.add(box);
            }
        }
        return true;
    }
}

方法2（Java）

从0-8，对每一个i，设置3个boolean数组分别检测第i行、第i列和第i个九宫格，数组的index代表被检测的值。

对于每个i的值，j从0-8意味着检测：

第i行, 第j个数是否已位于行i中；

第i列，第j个数是否已位于列i中；

第i个九宫格中，该九宫格从左上角到右下角的第j数是否已位于该九宫格中。

 

设置3个数组，

boolean[] checkRow 检查位置(i, j)的值是否已存在第i行

boolean[] checkCol 检查位置(j, i)的值是否已存在第i列

boolean[] checkBox 检查位置(i/3*3+j/3, j%3*3+j%3)的值是否已存在第i个九宫格中

例如当i为4，j从0-8，对应行、列、九宫格的遍历过程

  0 1 2   3 4 5   6 7 8
0 o o o | o 1 o | o o o
1 o o o | o 2 o | o o o
2 o o o | o 3 o | o o o
------------------------
3 o o o | o 4 o | o o o
4 1 2 3 | 4 5 6 | 7 8 9
5 o o o | o 6 o | o o o
------------------------
6 o o o | o 7 o | o o o
7 o o o | o 8 o | o o o
8 o o o | o 9 o | o o o

第4个九宫格中
1 2 3
4 5 6
7 8 9

class Solution {
    public boolean isValidSudoku(char[][] board) {
        for(int i = 0; i < 9; i++){
            boolean[] checkRow = new boolean[9];
            boolean[] checkCol = new boolean[9];
            boolean[] checkBox = new boolean[9];
            for(int j = 0; j < 9; j++){
                if(board[i][j] == '.') {}
                else if(checkRow[board[i][j]-'1']) return false;
                else checkRow[board[i][j]-'1'] = true;

                if(board[j][i] == '.'){}
                else if(checkCol[board[j][i]-'1']) return false;
                else checkCol[board[j][i]-'1'] = true;

                int m = i/3*3+j/3, n = i%3*3+j%3;
                if(board[m][n] == '.'){}
                else if(checkBox[board[m][n]-'1']) return false;
                else checkBox[board[m][n]-'1'] = true;
            }
        }
        return true;
    }
}