My first instinct was to reach for combinations and just brute force it, which would've been fine for small inputs but they flagged upfront that the list could be large.
Clarify the problem constraints and edge cases, then propose an efficient algorithm. For each category, keep only the top 3 book values, then use a greedy or dynamic programming approach to select up to 3 books from distinct categories that maximize total points.
Pro tip: Mention that since we can select at most 3 books, we can optimize by reducing each category to its top 3 values, and then use a priority queue or sorting to combine them efficiently. This shows awareness of practical optimization.
Ask questions to confirm constraints: Can we select fewer than 3 books? Are point values positive? What if there are fewer than 3 categories? This ensures you understand the requirements.
Discuss a naive solution: generate all combinations of up to 3 books from distinct categories and compute the maximum. This establishes a baseline and shows you can think simply.
Observe that for each category, only the top 3 book values matter because we can pick at most 3 books total. Extract these top values per category.
Use a greedy approach: sort all candidate books by value descending, then iterate and pick books from distinct categories until 3 are chosen. Alternatively, use dynamic programming over categories with state (number of books chosen, total points).
State time and space complexity (e.g., O(N log N) for sorting). Test with cases like fewer than 3 categories, negative values, or ties.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.