leetcode 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.

A partially filled sudoku which is valid.

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.

题目大意：验证一个数独是否是有效的：某一行/一列/3x3的子格子数字不能重复。 

class Solution {
public:
    bool isValidSudoku(vector<vector<char>>& board) {
        //map<int, map<char, int> > row, col, grid;
        vector<vector<int> > row(9, vector<int>(10, 0)), col(9, vector<int>(10, 0)), grid(9, vector<int>(10, 0));
        for (int i = 0; i < 9; i++) {
            for (int j = 0; j < 9; j++) {
                char tmp = board[i][j];
                if (tmp != '.') {
                    int num = tmp - '0';
                    if (row[i][num] != 0) {
                        return false;
                    } else {
                        row[i][num] = 1;
                    }
                    
                    if (col[j][num] != 0) {
                        return false;
                    } else {
                        col[j][num] = 1;
                    }
                    // 从左往右，从上至下，3x3格子分别从0-8编号。
                    if (grid[(i / 3) * 3 + (j / 3)][num] != 0) {
                        return false;
                    } else {
                        grid[(i / 3) * 3 + (j / 3)][num] = 1;
                    }
                }
                
            }
        }
        return true;
    }
};