My first instinct was to just sort the packages descending and greedily assign them to the highest-capacity truck available.
Clarify the problem constraints and edge cases, then propose a greedy algorithm that assigns the heaviest package to the truck with the largest remaining capacity, halving that truck's capacity after each assignment. Analyze the time complexity and discuss potential optimizations or alternative approaches.
Pro tip: Mention that using a max-heap for truck capacities allows efficient retrieval of the largest capacity, and emphasize the importance of handling multiple test scenarios by resetting data structures between cases.
Ask clarifying questions to confirm assumptions: Are packages indivisible? Can trucks be used multiple times? Is the halving applied after each delivery? What are the constraints on number of trucks, packages, and weights?
Propose a greedy strategy: sort packages in descending order, use a max-heap for truck capacities, and for each package, assign it to the truck with the largest capacity, then halve that capacity and reinsert into the heap.
State that the time complexity is O(P log T) where P is number of packages and T is number of trucks, due to heap operations, and space complexity is O(T) for the heap.
Discuss edge cases: no packages (return 1), no trucks (return 0 if packages exist), packages heavier than any initial capacity (return 0), and multiple test scenarios requiring reinitialization.
Compare greedy with other approaches like dynamic programming or backtracking, explaining why greedy is optimal here and its efficiency for large inputs.
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