The greedy approach is pretty natural once you accept that the header has to stay whole.
First, clarify the constraints: header size, max chunk size, and whether the header must appear in every chunk or only once. Then, model the problem as packing the header and payload into chunks, ensuring the header is never split and each chunk's total size ≤ max. Finally, derive an optimal greedy strategy: if the header fits in a chunk, fill the rest with as much payload as possible; otherwise, handle the header separately.
Pro tip: Mention that the optimal solution often involves a greedy approach where each chunk (except possibly the first) is filled to the maximum with payload, and the header is placed in the first chunk if it fits; otherwise, the header occupies its own chunk. This demonstrates understanding of bin packing and greedy optimality.
Ask about header size, max chunk size, whether header must be repeated in each chunk, and if chunks can be empty. Confirm that the header is fixed-size and unsplittable, and payload is variable-length.
Model as: given H (header size), M (max chunk size), and L (payload length), partition the header and payload into chunks such that each chunk size ≤ M, header is not split, and number of chunks is minimized.
If H ≤ M, place header in first chunk and fill remaining space with payload; subsequent chunks contain only payload up to M. If H > M, the header cannot fit in any chunk, so the problem is infeasible unless header can be split (contradiction), so assume H ≤ M. Then the minimum number of chunks is 1 + ceil((L - (M - H)) / M) if L > M - H, else 1.
Consider cases where payload is empty, header exactly fills a chunk, or payload length is zero. Verify that the formula yields correct chunk count and that no chunk exceeds M.
Mention that if header must be repeated in each chunk, the problem changes: each chunk has H bytes overhead, so payload per chunk is M - H, and number of chunks is ceil(L / (M - H)). Compare trade-offs between repeating header vs. not.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.