Uber·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

May 2026

Summary

Uber SWE interview with a pipeline throughput optimization problem. The question was algorithmically interesting and I think I got through it okay, but it took me a minute to see why binary search even applied here.

Questions Asked (1)

You have a serial pipeline where overall throughput is bottlenecked by the slowest service. Each service can be scaled up at a per-unit cost, and scaling a service by x multiplies its throughput by (1+x). Given a fixed total budget, maximize the pipeline's throughput.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

Took me a beat to recognize this as a binary search on the answer problem rather than a greedy or DP thing.

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AI HintsAI Generated

Suggested Approach

Recognize that the pipeline throughput is the minimum of the scaled service throughputs, so the goal is to maximize this minimum subject to the budget. Formulate as an optimization problem: allocate budget to services to equalize their throughputs as much as possible, using binary search on the target throughput to check feasibility. Then discuss the greedy or binary search approach, complexity, and trade-offs.

Pro tip: Mention that in practice, services may have different scaling costs and diminishing returns, so the optimal allocation often involves balancing marginal gains—this shows you think beyond the idealized model.

1. Model the problem

Define variables: let x_i be the scaling factor for service i, with cost c_i * x_i. Throughput of service i becomes T_i * (1 + x_i). Overall throughput = min_i T_i * (1 + x_i).

2. Formulate optimization

Maximize min_i T_i * (1 + x_i) subject to sum_i c_i * x_i <= B and x_i >= 0. This is a convex optimization problem (maximizing a concave function? Actually min of linear is concave, so maximizing concave is convex).

3. Solve via binary search

Binary search on target throughput T. For a given T, compute required scaling for each service: x_i = max(0, T/T_i - 1). Check if total cost sum c_i * x_i <= B. If yes, T is feasible; increase lower bound.

4. Analyze complexity and edge cases

Binary search takes O(log(precision)) iterations, each O(n). Discuss precision, integer constraints, and if services can be scaled continuously or discretely.

5. Discuss trade-offs and extensions

Mention alternative greedy approach: repeatedly scale the bottleneck service until budget exhausted, but note it may not be optimal. Discuss real-world factors like latency, dependencies, and non-linear scaling.

Key Points to Mention

Pipeline throughput is determined by the slowest service (min of throughputs).
Scaling a service by x multiplies throughput by (1+x), so cost is linear in x.
The optimization problem is to maximize the minimum throughput subject to budget.
Binary search on the target throughput is an efficient way to find the optimal allocation.
Feasibility check for a target T: sum of required scaling costs <= budget.
Complexity: O(n log(1/epsilon)) for binary search with precision epsilon.
Real-world considerations: non-linear scaling, different costs, and dependencies.

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