36. Valid Sudoku

Determine if a 9x9 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 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.

在一个循环中分别遍历所有的行和所有的列以及所有的九宫格，使用哈希表判断是否有重复的数字

class Solution {
public:
    bool isValidSudoku(vector<vector<char>>& board) {
        if(board.empty() || board[0].empty()){
            return false;
        }
        int m = board.size();
        int n = board[0].size();
        
        for(int i = 0; i < m; i++){
            set<char> row;
            set<char> col;
            set<char> mat;  
            for(int j = 0; j < n; j++){
                if(board[i][j] != '.' && row.find(board[i][j]) != row.end())
                    return false;
                else
                    row.insert(board[i][j]);
                if(board[j][i] != '.' && col.find(board[j][i]) != col.end())
                    return false;
                else
                    col.insert(board[j][i]);
                int rowIndex = 3*(i/3);
                int colIndex = 3*(i%3);
                if(board[rowIndex+j/3][colIndex+j%3] != '.' && mat.find(board[rowIndex+j/3][colIndex+j%3]) != mat.end())
                    return false;
                else
                    mat.insert(board[rowIndex+j/3][colIndex+j%3]);
            }
        }
        return true;
    }
};