<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) {

        solve(board);

    }
    bool checkColumn(const std::vector<std::vector<char>>& board, int colIdx, char val) {
        set<char> seen;
        for (int i = 0; i < board.size(); i++) {
            if (board[i][colIdx] != '.') {
                seen.insert(board[i][colIdx]);
            }
        }
        return seen.find(val) == seen.end(); // Return true if val is not in the column
    }

    bool checkRow(const std::vector<std::vector<char>>& board, int rowIdx, char val) {
        set<char> seen;
        for (int i = 0; i < board[rowIdx].size(); i++) {
            if (board[rowIdx][i] != '.') {
                seen.insert(board[rowIdx][i]);
            }
        }
        return seen.find(val) == seen.end(); // Return true if val is not in the row
    }
    bool check3x3(const std::vector<std::vector<char>>& board, int idx, char val) {
        int row_start = (idx / 3) * 3;
        int col_start = (idx % 3) * 3;
        std::set<char> seen; // Use std::set to track seen characters
        char temp; // Corrected data type

        for (int i = row_start; i < row_start + 3; i++) {
            for (int j = col_start; j < col_start + 3; j++) {
                temp = board[i][j];
                if (temp != '.') {
                    seen.insert(temp);
                }
            }
        }

        return seen.find(val) == seen.end(); 
    }
    //combines all the functions all together
    bool isValid(const std::vector<std::vector<char>>& board, int row, int col, char val) {
        return checkRow(board, row, val) &&
               checkColumn(board, col, val) &&
               check3x3(board, (row / 3) * 3 + (col / 3), val);
    }

    bool solve(std::vector<std::vector<char>>& board) {
        // Find the next empty cell
        for (int i = 0; i < 9; i++) {
            for (int j = 0; j < 9; j++) {
                if (board[i][j] == '.') {
                    // Try all possible numbers
                    for (char num = '1'; num <= '9'; num++) {
                        // Check if placing num is valid
                        if (isValid(board, i, j, num)) {
                            board[i][j] = num; // Place num

                            //try to solve the rest of the board
                            if (solve(board)) {
                                return true;
                            }

                            //back track
                            board[i][j] = '.'; //num was not the correct value so we undo our modification
                        }
                    }
                    return false; //we will never come here but just to make sure
                }
            }
        }
        return true; //we solved the board
    }

};
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