Sudoku Solver

Problem: Fill empty cells so each row, column, and $3 \times 3$ box has digits $1$-$9$ exactly once.

Approach: For each empty cell, try digits $1$-$9$. Check validity (no duplicate in row, column, box). If valid, place and recurse. Backtrack if no digit works.

Time: $O(9^{empty})$ worst case, constraints prune heavily.

Space: $O(empty)$ for recursion.

See the implementation unit for code.