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 '.'.

思考：先检查每一行，再检查每一列，最后检查9个子方块，时间复杂度为n2+n2+n2=O(n2)。

class Solution {
public:
    bool isValidSudoku(vector<vector<char>>& board) {
        int map[10] ={0};
        int i,j;
        //row
        for(i=0; i<9; i++) {
            memset(map,0,10*sizeof(int));
            for(j=0;j<9;j++){
                if(board[i][j]=='.') continue;
                if(map[board[i][j]-'0']) return false;
                map[board[i][j]-'0'] = 1;
            }     
        }
        //column
        for(j=0; j<9; j++) {
            memset(map,0,10*sizeof(int));
            for(i=0; i<9; i++) {
                 if(board[i][j]=='.') continue;
                if(map[board[i][j]-'0']) return false;
                map[board[i][j]-'0'] = 1;
            }
        }
       //3x3 subbox
        for(i=0; i<9; i=i+3) {
            for(j=0; j<9; j=j+3) {
                memset(map, 0, 10*sizeof(int));
                for(int m=i; m<i+3; m++) {
                    for(int n=j; n<j+3; n++) {
                        if(board[m][n]=='.') continue;
                        if(map[board[m][n]-'0']) return false;
                        map[board[m][n]-'0'] = 1;
                    }
                }
            }
        }

        return true;
        
    }
};