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Backtracking was the obvious move but I spent probably too long trying to be clever about constraint propagation before just committing to the recursive approach.
Use backtracking with constraint propagation: recursively try digits 1-9 in each empty cell, checking validity against row, column, and box constraints, and backtrack when no valid digit fits. Optimize by selecting the empty cell with the fewest candidates (MRV heuristic) and using bitmasks to track used digits for O(1) validity checks.
Pro tip: Mention that while backtracking is standard, for production systems you might use a constraint satisfaction solver or exact cover (Dancing Links) for guaranteed performance, and always discuss time/space complexity and potential optimizations.
Confirm that the input is a 9x9 grid with digits 1-9 and empty cells represented by '.' or 0, and that a solution is guaranteed to exist. Discuss whether to modify in-place or return a new board.
Select backtracking as the base algorithm, and explain how to incorporate heuristics like Minimum Remaining Values (MRV) and bitmasking for efficiency. Mention alternative approaches like exact cover if relevant.
Design helper functions to check if placing a digit is valid by ensuring no duplicates in the current row, column, and 3x3 sub-box. Use arrays or bitmasks to track used digits for O(1) checks.
Write a recursive function that finds the next empty cell (preferably with MRV), tries digits 1-9, and recurses if valid. If no digit works, backtrack by resetting the cell and returning false.
Discuss time complexity (worst-case exponential but typically fast for 9x9) and space complexity (O(1) extra space). Walk through a small example or edge cases like an already solved board.
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