Leetcode -- Sudoku Solver

Ideas:

DFS + Sudoku game rules.

The rule of the sudoku game is:

Duplicate numbers are not allowed in the same column of the same row, and duplicate numbers are not allowed in every 9 intrauterine devices.

 1 class Solution { 2 public: 3     bool isValid(vector<vector<char> > &board, int a, int b) { 4         int i,j; 5         for(i = 0; i < 9; i++) 6             if(i != a && board[i][b] == board[a][b]) 7                 return false; 8  9         for(j = 0; j < 9; j++)10             if(j != b && board[a][j] == board[a][b])11                 return false;12 13         int x = a/3*3;14         int y = b/3*3;15         for(i = 0; i < 3; i++)16             for(j = 0; j< 3; j++)17                 if(x+i != a && y+j != b && board[x+i][y+j] == board[a][b])18                     return false;19         return true;20     }21     bool solveSudokudfs(vector<vector<char> > &board)22     {23         for(int i = 0; i < 9; i++)24             for(int j = 0; j < 9; j++)25             {26                 if(board[i][j] == ‘.‘)27                 {28                     for(int k = 1; k <= 9; k++)29                     {30                         board[i][j] = ‘0‘ + k;31                         if(isValid(board,i,j) && solveSudokudfs(board))32                             return true;33                         board[i][j] = ‘.‘;34                     }35                     return false;36                 }37             }38         return true;39     }40     void solveSudoku(vector<vector<char> > &board) {41         // Note: The Solution object is instantiated only once.42         solveSudokudfs(board);43     }44 };