Sudoku Solver

-----QUESTION-----

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.

-----SOLUTION-----

class Solution {public:    void solveSudoku(vector<vector<char>> &board) {        backtracking(board,0);    }    bool backtracking(vector<vector<char>> &board,int line)    {        //find first empty cell        for(int i = line; i<9; i++)        {           for(int j = 0; j<9; j++)            {                if(board[i][j]!='.') continue;                for(int k = 1; k<=9; k++) //first empty cell is found                {                    if(!isValid(board,i,j,k+'0')) continue;                    board[i][j] = k+'0';                    if(backtracking(board,i)) return true;                }                board[i][j] = '.';                return false; //if no valid value is found            }        }        return true; //if no empty cell is found    }    bool isValid(vector<vector<char>> &board, int line, int column, char value)    {        int upperBoard = line/3 * 3;        int leftBoard = column/3 * 3;        for(int i = 0; i<3; i++)        {            for(int j = 0; j<3; j++)            {                if(board[upperBoard+i][leftBoard+j] == value) return false;            }        }        for(int i = 0; i<9; i++)        {            if(board[line][i] == value) return false;        }        for(int i = 0; i<9; i++)        {            if(board[i][column] == value) return false;        }        return true;    }};