The bottleneck part is what trips you up first.
Model the problem as maximizing the minimum throughput across services under a budget constraint, where each service's throughput is a function of its scale-ups. Use binary search on the target throughput to check feasibility, then allocate budget to the bottleneck service until it's no longer the bottleneck, repeating until budget is exhausted.
Pro tip: Emphasize that the optimal solution often involves balancing services to similar throughput levels rather than over-scaling one service, and mention that greedy allocation works when scale-up gains are diminishing.
For each service, create a function that maps the number of scale-ups to its throughput, considering the gain and cost of each scale-up. The overall pipeline throughput is the minimum of these functions.
Binary search over possible throughput values. For a given target T, compute the minimum cost to make each service achieve at least T throughput, then sum these costs and check if it's within budget.
For each service, determine the cheapest set of scale-ups that reaches T. Since scale-ups have varying gains and costs, use a greedy approach (e.g., sort by gain per cost) or dynamic programming if scale-ups are discrete and small in number.
The binary search yields the maximum feasible T. Then, for that T, output the specific scale-ups chosen for each service to achieve T within budget.
Analyze time complexity (e.g., O(N log(maxT) * K) where K is scale-ups per service) and mention that if scale-ups are continuous, a greedy water-filling approach may be more efficient.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.