My first instinct was to just sort everything by points descending and grab the top 3, which obviously breaks the moment you have duplicate categories.
Clarify the problem constraints and edge cases, then propose an efficient algorithm that groups books by category and selects the top books from distinct categories. Discuss time and space complexity, and consider alternative approaches like dynamic programming or greedy with sorting.
Pro tip: Demonstrate awareness of real-world data science applications by mentioning how this problem relates to feature selection or recommendation systems, and always test with edge cases like fewer than 3 categories or negative points.
Restate the problem in your own words, ask clarifying questions about input format, constraints (e.g., number of books, point range), and edge cases (e.g., fewer than 3 categories, ties).
Consider brute force (check all combinations of up to 3 books from distinct categories) and optimized approaches like sorting books by points within each category and then selecting the best combination across categories.
Select an efficient approach: group books by category, sort each group descending by points, then either use a priority queue to pick top books from distinct categories or dynamic programming to maximize points with at most 3 books from distinct categories.
State time and space complexity (e.g., O(n log n) for sorting, O(n) space). Discuss handling cases with fewer than 3 categories, negative points (if allowed), and ties.
Walk through a small example to verify correctness, including edge cases, and optionally write pseudocode or actual code if requested.
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