The add/remove part was fine, pretty standard set operations.
Start by clarifying requirements and assumptions, then design data structures to efficiently track recipes and ingredient counts. Implement the cart operations using hash maps for O(1) updates, and compute discounts based on overlapping ingredient quantities. Discuss trade-offs and potential optimizations.
Pro tip: Mention that you would use a hash map to count ingredient occurrences across recipes, enabling O(1) updates and efficient discount calculation. Also, clarify the discount rule (e.g., threshold per ingredient) before coding.
Ask about discount rules (e.g., threshold quantity per ingredient, discount percentage), whether recipes can be added multiple times, and if ingredient quantities matter. Confirm expected operations and constraints.
Use a map to store recipes (recipe ID to ingredient list) and another map to track total quantity per ingredient across all recipes. This allows efficient updates and discount calculation.
For add_recipe, increment ingredient counts and add recipe to cart. For remove_recipe, decrement counts and remove recipe. For get_total_discount, iterate over ingredient counts and apply discount rule.
Discuss time complexity: add/remove O(k) where k is number of ingredients per recipe; get_total_discount O(m) where m is number of unique ingredients. Space O(n + m) for recipes and counts.
Mention potential optimizations like caching discount totals, handling concurrent updates, or supporting different discount tiers. Also consider edge cases like removing non-existent recipes.
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