Sudoku Solver

Solving a Sudoku puzzle is another perfect application of the backtracking algorithm. The goal is to fill a 9×9 grid with digits so that each column, each row, and each of the nine 3×3 subgrids that compose the grid contain all of the digits from 1 to 9. The backtracking approach systematically tries to fill the empty cells (often represented by a 0 or '.') one by one. The algorithm can be structured as follows: First, find an empty cell in the grid. If no empty cells exist, the puzzle is solved, and we have found a solution. This is our base case. If we find an empty cell at `(row, col)`, we then try to place each digit from 1 to 9 in that cell. For each digit `d` we try, we must first check if placing `d` at `(row, col)` is valid according to Sudoku rules. A placement is valid if the same digit does not already exist in the current row, the current column, or the current 3×3 subgrid. If the placement is valid, we place the digit in the cell and make a recursive call to our solver function to continue filling the rest of the grid. If this recursive call eventually leads to a solution (returns true), then we also return true. If it doesn't lead to a solution (returns false), it means our current choice of digit `d` was wrong. In this case, we must backtrack: we reset the cell at `(row, col)` to be empty and try the next digit (e.g., `d+1`). If we try all digits from 1 to 9 and none of them lead to a solution, we return false, triggering backtracking in the previous call.