I started with a plain dict mapping category to a list of prices and sorted on checkout.
Clarify the operations and data structures needed, then design a solution using a min-heap keyed by insurance value to efficiently retrieve the least valuable books for checkout. Process operations sequentially, updating the heap and total value as needed, and return the total insurance value for each checkout.
Pro tip: Discuss trade-offs between different data structures (e.g., heap vs. balanced BST) and mention that lazy deletion can handle reclassify operations efficiently without immediate heap updates.
Ask questions to confirm operation types, input format, and constraints. Discuss edge cases like checking out more books than available or reclassifying a book that doesn't exist.
Select a min-heap (priority queue) ordered by insurance value to efficiently retrieve the least valuable books. Consider auxiliary structures like a hash map for book lookup and a set for lazy deletion.
For acquisition, add the book to the heap and map. For checkout, pop the minimum value books, skipping any marked as deleted, and sum their values. For reclassify, update the book's category and mark the old entry as deleted, then insert a new entry if needed.
Iterate through the operations in order, applying the handlers and collecting the total insurance value for each checkout operation. Return the list of totals.
Explain the time complexity: O(log n) per operation for heap insertions and deletions, with lazy deletion adding amortized O(log n). Space complexity O(n). Discuss potential optimizations if needed.
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