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.

class Solution {
private:
    bool search(vector<vector<char>>& board,int i,int j)
    {
        unordered_set<int> hash;
        for(int k=0;k<9;k++)
            if(board[i][k]!='.')
                hash.insert(board[i][k]-'0'); 
        for(int k=0;k<9;k++)
            if(board[k][j]!='.')
                hash.insert(board[k][j]-'0');
        for(int x=i/3*3;x<i/3*3+3;x++)
            for(int y=j/3*3;y<j/3*3+3;y++)
                if(board[x][y]!='.')
                    hash.insert(board[x][y]-'0');        
        if(hash.size()==9) return false;
        
        int newi=-1;
        int newj=-1;    
        for(newi=0;newi<9;newi++)
        {
            for(newj=0;newj<9;newj++)
                if((newi!=i || newj!=j) && board[newi][newj]=='.')                                                                               
                {
                    for(char k='1';k<='9';k++)
                        if(hash.find(k-'0')==hash.end())
                        {
                            board[i][j]=k;
                            if(search(board,newi,newj)) return true;
                        }
                    board[i][j]='.';
                    return false;
                }
        }         
        for(char k='1';k<='9';k++)
            if(hash.find(k-'0')==hash.end())
            {
                    board[i][j]=k;    
            }
        return true;
    }
public:
    void solveSudoku(vector<vector<char> > &board) 
    {
        int x=0;
        int y=0;
        for(int i=0;i<9;i++)
        {
            int j;
            for(j=0;j<9;j++)
                if(board[i][j]=='.')
                {
                    x=i;
                    y=j;
                    break;
                }
                if(j!=9) break;
        }
        search(board,x,y);
    }
};