Get Max Throughput

Problem Overview

• Goal: Choose how many times to scale each of n serial services to maximize the final (nth) service throughput within a given budget.
• Input/Output: arrays throughput[n], scaling_cost[n], and integer budget; return the maximum achievable end-to-end throughput (long).
• Model: Services form a pipeline; scaling service i by x raises its capacity from throughput[i] to throughput[i] * (i + x).
• Context: Data processing pipeline optimization; a coding interview problem and interview question from Citadel interviews.