Given a partially filled 9×9 Sudoku board, fill in every empty cell so that each digit 1–9 appears exactly once in every row, every column, and every 3×3 box. The puzzle is guaranteed to have exactly one valid completion. Scanning the whole board from the start to find the next empty cell, and checking a candidate digit by walking the entire row, column, and box arrays, both work — but repeat information the search already had. Passing the next position down directly, and maintaining a table of which digits are already used in each row, column, and box, turns both of those repeated derivations into a single lookup: the exact same tree of choices gets explored, just without re-deriving facts about the board that hadn't changed.