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)。

 1 class Solution {
 2 public:
 3     bool isValidSudoku(vector<vector<char>>& board) {
 4         int map[10] ={0};
 5         int i,j;
 6         //row
 7         for(i=0; i<9; i++) {
 8             memset(map,0,10*sizeof(int));
 9             for(j=0;j<9;j++){
10                 if(board[i][j]=='.') continue;
11                 if(map[board[i][j]-'0']) return false;
12                 map[board[i][j]-'0'] = 1;
13             }     
14         }
15         //column
16         for(j=0; j<9; j++) {
17             memset(map,0,10*sizeof(int));
18             for(i=0; i<9; i++) {
19                  if(board[i][j]=='.') continue;
20                 if(map[board[i][j]-'0']) return false;
21                 map[board[i][j]-'0'] = 1;
22             }
23         }
24        //3x3 subbox
25         for(i=0; i<9; i=i+3) {
26             for(j=0; j<9; j=j+3) {
27                 memset(map, 0, 10*sizeof(int));
28                 for(int m=i; m<i+3; m++) {
29                     for(int n=j; n<j+3; n++) {
30                         if(board[m][n]=='.') continue;
31                         if(map[board[m][n]-'0']) return false;
32                         map[board[m][n]-'0'] = 1;
33                     }
34                 }
35             }
36         }
37 
38         return true;
39         
40     }
41 };