Uber·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

May 2026

Summary

Uber SWE interview with a dynamic programming / optimization problem that took me a while to see clearly. The problem was clever enough that I'd probably still be staring at it if I hadn't thought to binary search on the answer.

Questions Asked (1)

You have two parallel arrays representing N services in a pipeline: one for throughput increment per scaling step and one for cost per scaling step. Services are chained so end-to-end throughput is the minimum across all services. You can scale each service any number of times, each time paying its cost and gaining its throughput increment. Given a total budget, maximize the final end-to-end throughput.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

My first instinct was greedy, which went nowhere fast.

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AI HintsAI Generated

Suggested Approach

Recognize that the end-to-end throughput is the minimum across services, so the goal is to raise the lowest service's throughput as high as possible within budget. Use binary search on the target throughput T, and for each T, compute the minimum cost to make every service's throughput at least T; if total cost ≤ budget, T is feasible. Then find the maximum feasible T.

Pro tip: Mention that scaling decisions are independent per service once T is fixed, and that the cost function is monotonic in T, enabling binary search. Also note that if a service's initial throughput already meets T, its cost is zero.

1. Clarify the problem and constraints

Restate the problem: N services in series, each with a current throughput, an increment per scaling step, and a cost per step. Budget B. Maximize the minimum throughput after scaling. Ask about constraints (N, budget, increments, costs) to determine feasible complexity.

2. Identify the monotonic property

Observe that if a target throughput T is achievable within budget, any T' < T is also achievable. This monotonicity allows binary search on T.

3. Design the feasibility check

For a given T, compute for each service the minimum number of scaling steps needed to reach at least T: steps_i = max(0, ceil((T - current_i) / increment_i)). The cost for service i is steps_i * cost_i. Sum costs; if ≤ B, T is feasible.

4. Binary search for the optimal T

Set low = min(current throughputs), high = min(current_i + (B / cost_i) * increment_i) or a safe upper bound. While low < high, mid = (low + high + 1) // 2; if feasible(mid), low = mid; else high = mid - 1. Return low.

5. Analyze complexity and edge cases

Time: O(N log(maxT)) where maxT is the upper bound. Space: O(1). Discuss edge cases: budget insufficient to scale any service, services already above target, large numbers requiring 64-bit integers, and potential overflow in cost calculation.

Key Points to Mention

The end-to-end throughput is the minimum across services, so the bottleneck is the lowest service.
Binary search on the answer (target throughput) because feasibility is monotonic.
For a fixed target, each service's required scaling is independent and computed greedily.
Cost calculation: steps = ceil((T - current) / increment), cost = steps * cost_per_step.
Use 64-bit integers to avoid overflow when summing costs or computing steps.
Time complexity O(N log(maxT)) and space O(1), which is efficient for large N.

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