I knew immediately it was n-queens but knowing the name and actually coding it cleanly are two different things.
Use backtracking to place queens row by row, maintaining sets for columns and diagonals to ensure O(1) validity checks. At each row, try each column, and if safe, place a queen and recurse; when a solution is found, convert the board to the required string format and add to results.
Pro tip: Emphasize the use of bitmasking to represent columns and diagonals for optimal performance, and mention that the time complexity is O(n!) but pruning makes it efficient for n ≤ 9. Also, note that the problem is a classic example of constraint satisfaction and can be related to ML hyperparameter tuning.
Confirm the input size constraints and output format. Discuss potential edge cases like n=1 or n=0.
Use sets or bitmasks to track occupied columns, diagonals (row+col), and anti-diagonals (row-col). This allows O(1) checks for queen placement.
Recursively place queens row by row. For each row, iterate over columns, check if safe, place queen, recurse to next row, then backtrack.
When a solution is found (row == n), convert the board state to a list of strings with 'Q' and '.', and add to the results list.
Discuss time complexity O(n!) and space O(n). Mention optimizations like bitmasking and symmetry reduction if needed.
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