14. Sudoku Solver

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

A sudoku solution must satisfy all of the following rules:

1. Each of the digits 1-9 must occur exactly once in each row.

2. Each of the digits 1-9 must occur exactly once in each column.

3. Each of the digits 1-9 must occur exactly once in each of the 9 3x3 sub-boxes of the grid.

The '.' character indicates empty cells.

Example 1:

Input: board = [["5","3",".",".","7",".",".",".","."],["6",".",".","1","9","5",".",".","."],[".","9","8",".",".",".",".","6","."],["8",".",".",".","6",".",".",".","3"],["4",".",".","8",".","3",".",".","1"],["7",".",".",".","2",".",".",".","6"],[".","6",".",".",".",".","2","8","."],[".",".",".","4","1","9",".",".","5"],[".",".",".",".","8",".",".","7","9"]]
Output: [["5","3","4","6","7","8","9","1","2"],["6","7","2","1","9","5","3","4","8"],["1","9","8","3","4","2","5","6","7"],["8","5","9","7","6","1","4","2","3"],["4","2","6","8","5","3","7","9","1"],["7","1","3","9","2","4","8","5","6"],["9","6","1","5","3","7","2","8","4"],["2","8","7","4","1","9","6","3","5"],["3","4","5","2","8","6","1","7","9"]]
Explanation: The input board is shown above and the only valid solution is shown below:

Solution: (Backtracking)

Approach: Check if a position is empty If empty check for 1-9 and check if safe then insert To check is safe check no does not exits in row, col and block

class Solution
{
public:
    pair<int, int> findUnassigned(vector<vector<char>> &board)
    {
        for (int i = 0; i < 9; i++)
        {
            for (int j = 0; j < 9; j++)
            {
                if (board[i][j] == '.')
                {
                    return {i, j};
                }
            }
        }
        return {-1, -1};
    }

    bool isSafe(int row, int col, int num, vector<vector<char>> &board)
    {
        for (int i = 0; i < 9; i++)
        {
            if (board[row][i] == num+48)
            {
                return false;
            }
        }

        for (int i = 0; i < 9; i++)
        {
            if (board[i][col] == num+48)
            {
                return false;
            }
        }

        int rowStart = row - row % 3;
        int colStart = col - col % 3;

        for (int i = 0; i < 3; i++)
        {
            for (int j = 0; j < 3; j++)
            {
             
                if (board[i + rowStart][j + colStart] == num+48)
                {
                    return false;
                }
            }
        }

        return true;
    }

    bool solve(vector<vector<char>> &board)
    {
        pair<int, int> p = findUnassigned(board);
        int row = p.first;
        int col = p.second;
        
        if (row == -1 && col == -1)
        {
            return true;
        }

        for (int num = 1; num <= 9; num++)
        {
            if (isSafe(row, col, num, board))
            {
                
                board[row][col] = num + 48;
                if (solve(board))
                {
                    return true;
                }
                board[row][col] = '.';
            }
        }

        return false;
    }

    void solveSudoku(vector<vector<char>> &board)
    {
        if (solve(board))
        {
            return;
        }
    }
};