<p>Write a program to solve a Sudoku puzzle by filling the empty cells.</p>

<p>A sudoku solution must satisfy <strong>all of the following rules</strong>:</p>

<ol>
	<li>Each of the digits <code>1-9</code> must occur exactly once in each row.</li>
	<li>Each of the digits <code>1-9</code> must occur exactly once in each column.</li>
	<li>Each of the digits <code>1-9</code> must occur exactly once in each of the 9 <code>3x3</code> sub-boxes of the grid.</li>
</ol>

<p>The <code>&#39;.&#39;</code> character indicates empty cells.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img src="https://upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Sudoku-by-L2G-20050714.svg/250px-Sudoku-by-L2G-20050714.svg.png" style="height:250px; width:250px" />
<pre>
<strong>Input:</strong> board = [[&quot;5&quot;,&quot;3&quot;,&quot;.&quot;,&quot;.&quot;,&quot;7&quot;,&quot;.&quot;,&quot;.&quot;,&quot;.&quot;,&quot;.&quot;],[&quot;6&quot;,&quot;.&quot;,&quot;.&quot;,&quot;1&quot;,&quot;9&quot;,&quot;5&quot;,&quot;.&quot;,&quot;.&quot;,&quot;.&quot;],[&quot;.&quot;,&quot;9&quot;,&quot;8&quot;,&quot;.&quot;,&quot;.&quot;,&quot;.&quot;,&quot;.&quot;,&quot;6&quot;,&quot;.&quot;],[&quot;8&quot;,&quot;.&quot;,&quot;.&quot;,&quot;.&quot;,&quot;6&quot;,&quot;.&quot;,&quot;.&quot;,&quot;.&quot;,&quot;3&quot;],[&quot;4&quot;,&quot;.&quot;,&quot;.&quot;,&quot;8&quot;,&quot;.&quot;,&quot;3&quot;,&quot;.&quot;,&quot;.&quot;,&quot;1&quot;],[&quot;7&quot;,&quot;.&quot;,&quot;.&quot;,&quot;.&quot;,&quot;2&quot;,&quot;.&quot;,&quot;.&quot;,&quot;.&quot;,&quot;6&quot;],[&quot;.&quot;,&quot;6&quot;,&quot;.&quot;,&quot;.&quot;,&quot;.&quot;,&quot;.&quot;,&quot;2&quot;,&quot;8&quot;,&quot;.&quot;],[&quot;.&quot;,&quot;.&quot;,&quot;.&quot;,&quot;4&quot;,&quot;1&quot;,&quot;9&quot;,&quot;.&quot;,&quot;.&quot;,&quot;5&quot;],[&quot;.&quot;,&quot;.&quot;,&quot;.&quot;,&quot;.&quot;,&quot;8&quot;,&quot;.&quot;,&quot;.&quot;,&quot;7&quot;,&quot;9&quot;]]
<strong>Output:</strong> [[&quot;5&quot;,&quot;3&quot;,&quot;4&quot;,&quot;6&quot;,&quot;7&quot;,&quot;8&quot;,&quot;9&quot;,&quot;1&quot;,&quot;2&quot;],[&quot;6&quot;,&quot;7&quot;,&quot;2&quot;,&quot;1&quot;,&quot;9&quot;,&quot;5&quot;,&quot;3&quot;,&quot;4&quot;,&quot;8&quot;],[&quot;1&quot;,&quot;9&quot;,&quot;8&quot;,&quot;3&quot;,&quot;4&quot;,&quot;2&quot;,&quot;5&quot;,&quot;6&quot;,&quot;7&quot;],[&quot;8&quot;,&quot;5&quot;,&quot;9&quot;,&quot;7&quot;,&quot;6&quot;,&quot;1&quot;,&quot;4&quot;,&quot;2&quot;,&quot;3&quot;],[&quot;4&quot;,&quot;2&quot;,&quot;6&quot;,&quot;8&quot;,&quot;5&quot;,&quot;3&quot;,&quot;7&quot;,&quot;9&quot;,&quot;1&quot;],[&quot;7&quot;,&quot;1&quot;,&quot;3&quot;,&quot;9&quot;,&quot;2&quot;,&quot;4&quot;,&quot;8&quot;,&quot;5&quot;,&quot;6&quot;],[&quot;9&quot;,&quot;6&quot;,&quot;1&quot;,&quot;5&quot;,&quot;3&quot;,&quot;7&quot;,&quot;2&quot;,&quot;8&quot;,&quot;4&quot;],[&quot;2&quot;,&quot;8&quot;,&quot;7&quot;,&quot;4&quot;,&quot;1&quot;,&quot;9&quot;,&quot;6&quot;,&quot;3&quot;,&quot;5&quot;],[&quot;3&quot;,&quot;4&quot;,&quot;5&quot;,&quot;2&quot;,&quot;8&quot;,&quot;6&quot;,&quot;1&quot;,&quot;7&quot;,&quot;9&quot;]]
<strong>Explanation:</strong>&nbsp;The input board is shown above and the only valid solution is shown below:

<img src="https://upload.wikimedia.org/wikipedia/commons/thumb/3/31/Sudoku-by-L2G-20050714_solution.svg/250px-Sudoku-by-L2G-20050714_solution.svg.png" style="height:250px; width:250px" />
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>board.length == 9</code></li>
	<li><code>board[i].length == 9</code></li>
	<li><code>board[i][j]</code> is a digit or <code>&#39;.&#39;</code>.</li>
	<li>It is <strong>guaranteed</strong> that the input board has only one solution.</li>
</ul>

class Solution {
public:
    void solveSudoku(vector<vector<char>>& board) {
        vector<vector<int>> res;
        for(int i = 0; i < 9; i++) {
            for(int j = 0; j < 9; j++) {
                if(board[i][j] == '.'){
                    res.push_back({i, j});
                }
            }
        }

        board = getAns(res, board);
        
    }

    vector<vector<char>> getAns(vector<vector<int>> res, vector<vector<char>>& board) {
        if(res.empty()){
            return board;
        }

        vector<int> fr = res.back();
        res.pop_back();

        for(int i = 1; i <= 9; i++) {
            board[fr[0]][fr[1]] = '0' + i;
            if(!isValid(board, fr)){
                continue;
            }

            vector<vector<char>> temp = getAns(res, board);
            if(!temp.empty()) {
                return temp;
            }
            board[fr[0]][fr[1]] = '.';
        }

        board[fr[0]][fr[1]] = '.';
        return {};
    }

    bool isValid(vector<vector<char>>& board, vector<int> fr) {
        int ic = fr[0]/3, jc = fr[1]/3, x = 0, y = 0;
        char ind = board[fr[0]][fr[1]];

        for(int i = 0; i < 3; i++) {
            for(int j = 0; j < 3; j++) {
                x = 3*ic + i;
                y = 3*jc + j;

                if(x == fr[0] && y == fr[1]) {
                    continue;
                }

                if(board[x][y] == ind) {
                    return false;
                }
            }
        }

        for(int i = 0; i < 9; i++){
            if(i == fr[0]){
                continue;
            }

            if(board[i][fr[1]] == ind){
                return false;
            }
        }

        for(int i = 0; i < 9; i++){
            if(i == fr[1]){
                continue;
            }

            if(board[fr[0]][i] == ind){
                return false;
            }
        }

        return true;
    }
};
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