Sudoku Solver

Write a program to solve a Sudoku puzzle by filling the empty cells.

Empty cells are indicated by the character '.'.

You may assume that there will be only one unique solution.

A sudoku puzzle...

...and its solution numbers marked in red.

Runtime: 72ms.

class Solution {
public:
    void solveSudoku(vector<vector<char>>& board) {
        if(board.empty() || board.size() != 9 || board[0].size() != 9)  return;
        
        solve(board, 0, 0);
    }
    
    bool solve(vector<vector<char> >& board, int i, int j){
        if(j >= 9) //reaches to the last column
            return solve(board, i + 1, 0);
        
        if(i == 9) //reaches to the last row
            return true;
            
        if(board[i][j] == '.'){//fill 0~9 recursively
            for(int k = 1; k <= 9; k++){
                board[i][j] = k + '0';
                if(isValid(board, i, j)){
                    if(solve(board, i, j + 1))
                        return true;
                }
                board[i][j] = '.'; //this line is important?
            }
        }
        else
            return solve(board, i, j + 1);
        
        return false;
    }
    
    bool isValid(vector<vector<char> >& board, int i, int j){
        for(int row = 0; row < 9; row++){
            if(row != i && board[row][j] == board[i][j])
                return false;
        }
        
        for(int col = 0; col < 9; col++){
            if(col != j && board[i][col] == board[i][j])
                return false;
        }
        
        for(int row = i / 3 * 3; row < i / 3 * 3 + 3; row++){
            for(int col = j / 3 * 3; col < j / 3 * 3 + 3; col++){
                if((row != i || col != j) && board[row][col] == board[i][j])
                    return false;
            }
        }
        
        return true;
    }
};