The core of this is backtracking and I knew that going in, but I fumbled the box index calculation for a bit.
Use backtracking with constraint propagation: recursively try digits 1-9 in empty cells, checking validity against row, column, and box constraints. Optimize by choosing the cell with the fewest candidates (MRV heuristic) and using bitmasks for O(1) validity checks.
Pro tip: Mention that while backtracking is standard, you can discuss advanced optimizations like Dancing Links (Algorithm X) for exact cover problems, showing depth beyond the expected solution.
Confirm that the input is a 9x9 grid with some cells pre-filled, and the goal is to fill all empty cells in-place. Ask about assumptions like guaranteed solvability and whether to modify the input or return a new grid.
Select backtracking as the core approach, and decide on optimizations such as MRV heuristic and bitmasking for constraint checks. Explain why backtracking is suitable for this constraint satisfaction problem.
Write a recursive function that finds the next empty cell, tries digits 1-9, and backtracks if a digit leads to an invalid state. Use helper functions to check row, column, and box validity efficiently.
Discuss time and space complexity: worst-case O(9^(n*n)) but with pruning it's much faster. Mention how MRV and bitmasks reduce the search space and improve performance.
Walk through a simple example to verify correctness. Consider edge cases like already solved puzzles, invalid inputs, and multiple solutions (though standard Sudoku has a unique solution).
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