Valid Sudoku

Determine if a Sudoku is valid, according to: Sudoku Puzzles - The Rules.

The Sudoku board could be partially filled, where empty cells are filled with the character '.'.

A partially filled sudoku which is valid.

Note:
A valid Sudoku board (partially filled) is not necessarily solvable. Only the filled cells need to be validated.

class Solution {
public:
     bool isValidSudoku(vector<vector< char> > &board) {
         bool exist[ 10];
         // check row
         for( int i= 0;i< 9;i++)
        {
             for( int k= 0;k< 9;k++) exist[k+ 1]= false;;
             for( int j= 0;j< 9;j++)
             if(board[i][j]!= ' . ')
            {
                  if(exist[board[i][j]- ' 0 '])  return  false;
                 exist[board[i][j]- ' 0 ']= true;
            }
        }
         // check column
         for( int i= 0;i< 9;i++)
        {
             for( int k= 0;k< 9;k++) exist[k+ 1]= false;
             for( int j= 0;j< 9;j++)
             if(board[j][i]!= ' . ')
            {
                  if(exist[board[j][i]- ' 0 '])  return  false;
                 exist[board[j][i]- ' 0 ']= true;
            }
        }
         // check square
         for( int di= 0;di< 9;di+= 3)
             for( int dj= 0;dj< 9;dj+= 3)
            {
                 for( int k= 0;k< 9;k++) exist[k+ 1]= false;
                 for( int i= 0;i< 3;i++)
                     for( int j= 0;j< 3;j++)
                    {
                         char c=board[di+i][dj+j];
                         if(c!= ' . ')
                        {
                             if(exist[c- ' 0 '])  return  false;
                            exist[c- ' 0 ']= true;
                        }
                    }
            }
         return  true;
    }
};