Uber·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Apr 2026

Summary

Uber SWE interview with a pipeline throughput optimization problem. The core challenge was figuring out the right algorithmic approach under pressure, and binary search on the answer wasn't the first thing that came to mind.

Questions Asked (1)

You have a series of services running in sequence where the overall throughput is bottlenecked by the slowest service. Each service has a base throughput and can be scaled up at a cost proportional to the scale factor. Given a fixed budget, how do you maximize the overall pipeline throughput?

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

Took me a while to see the binary search angle.

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AI HintsAI Generated

Suggested Approach

Model the pipeline throughput as the minimum of the scaled throughputs of all services, then formulate an optimization problem to allocate the budget across services to maximize this minimum. Use binary search on the target throughput to check feasibility, or solve via greedy allocation based on marginal gains.

Pro tip: Emphasize that the optimal allocation often equalizes the throughputs of all services, and mention that in practice, services may have discrete scaling options or non-linear costs, so a greedy approach with a priority queue can be more practical.

1. Define the problem mathematically

Let each service i have base throughput T_i and scale factor s_i ≥ 1, with cost c_i(s_i) = k_i * s_i (or proportional). The pipeline throughput is min_i (T_i * s_i). Given budget B, maximize min_i (T_i * s_i) subject to sum_i c_i(s_i) ≤ B.

2. Identify the bottleneck and scaling trade-offs

The slowest service determines throughput. To increase overall throughput, you must increase the throughput of the current bottleneck, but this may shift the bottleneck to another service. The goal is to balance the scaled throughputs.

3. Choose an optimization strategy

For continuous scaling and linear costs, the optimal solution equalizes all scaled throughputs. You can binary search on the target throughput X: for each service, compute required scale s_i = X / T_i and check if total cost ≤ B. For discrete or non-linear costs, use a greedy approach: repeatedly invest in the service with the lowest current throughput until budget exhausted.

4. Analyze complexity and edge cases

Binary search runs in O(n log(precision)) time. Greedy with a priority queue runs in O(B log n) if budget is discrete, or O(n log n) with marginal cost analysis. Consider cases where some services cannot be scaled (s_i = 1) or have maximum scale limits.

5. Discuss practical considerations and extensions

Mention that in real systems, scaling may have diminishing returns, latency constraints, or dependencies. Also, consider that throughput might not be perfectly linear with scale factor due to contention or overhead.

Key Points to Mention

The pipeline throughput is determined by the slowest service (min of scaled throughputs).
The optimization problem: maximize min_i (T_i * s_i) subject to sum_i (k_i * s_i) ≤ B, s_i ≥ 1.
For linear costs, the optimal solution equalizes all scaled throughputs (water-filling).
Binary search on the target throughput is an efficient way to find the maximum feasible throughput.
Greedy allocation based on marginal gain works well for discrete or non-linear scaling costs.
Consider practical constraints: discrete scaling steps, maximum capacity, non-linear costs, and latency.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.