题目链接
tag:
- Medium;
question
Determine if a 9x9 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 9 3x3 sub-boxes of the grid must contain the digits 1-9 without repetition.
The Sudoku board could be partially filled, where empty cells are filled with the character '.'.
Example 1:
Input:
[
["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:
[
["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.
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.
- The given board contain only digits 1-9 and the character '.'.
- The given board size is always 9x9.
思路：
这道题让我们验证一个方阵是否为有效的数独，判断标准是看各行各列是否有重复数字，以及每个小的3x3的小方阵里面是否有重复数字，如果都无重复，则当前矩阵是数独矩阵，但不代表待数独矩阵有解，只是单纯的判断当前未填完的矩阵是否是数独矩阵。那么根据数独矩阵的定义，我们在遍历每个数字的时候，就看看包含当前位置的行和列以及3x3小方阵中是否已经出现该数字，那么我们需要三个标志矩阵，分别记录各行，各列，各小方阵是否出现某个数字，其中行和列标志下标很好对应，就是小方阵的下标需要稍稍转换一下，具体代码如下：
class Solution {
public:
bool isValidSudoku(vector > &board) {
if (board.empty() || board[0].empty()) return false;
int m = board.size(), n = board[0].size();
vector > rowFlag(m, vector(n, false));
vector > colFlag(m, vector(n, false));
vector > cellFlag(m, vector(n, false));
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j) {
if (board[i][j] >= '1' && board[i][j] <= '9') {
int c = board[i][j] - '1';
if (rowFlag[i][c] || colFlag[c][j] || cellFlag[3 * (i / 3) + j / 3][c]) return false;
rowFlag[i][c] = true;
colFlag[c][j] = true;
cellFlag[3 * (i / 3) + j / 3][c] = true;
}
}
}
return true;
}
};