Backtracking is the obvious path here but getting the implementation clean under pressure is another thing entirely.
Start by clarifying the problem constraints (e.g., 9x9 grid, valid puzzle) and then propose a backtracking algorithm with pruning using sets or bitmasks to track used numbers in rows, columns, and boxes. Discuss time/space complexity and potential optimizations like choosing the cell with fewest possibilities (MRV heuristic) and early termination.
Pro tip: Mention that you would first check if the puzzle is valid and solvable, and consider using a constraint propagation approach (like Dancing Links) for extreme efficiency, but backtracking is usually sufficient and simpler to implement.
Ask about input format, whether the puzzle is guaranteed solvable, and if there are any performance constraints. Confirm that a standard 9x9 Sudoku is expected.
Propose backtracking as the primary approach, explaining how it explores empty cells and backtracks on invalid placements. Mention optimizations like using sets/bitmasks for O(1) validity checks.
Describe the recursive function: find an empty cell, try numbers 1-9, check validity, place, recurse, and backtrack. Emphasize using helper data structures to track used numbers.
State that worst-case time is O(9^(n*n)) but with pruning it's much faster. Discuss heuristics like MRV (minimum remaining values) and constraint propagation to improve performance.
Mention testing with a valid puzzle, an invalid puzzle, and an empty grid. Discuss handling of already solved puzzles and ensuring no infinite loops.
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