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Two Sigma·Software Engineer·Technical Phone Screen·Intermediate

Intermediate
May 2026

Summary

Two Sigma SWE interview with a simulation-style coding problem about dynamically scaling a server fleet. Pretty clean problem once you see what it's asking, but the edge cases around integer overflow tripped me up a bit.

Questions Asked (1)

Q1

You have a fleet of servers behind a load balancer, each with a fixed throughput limit. Given a sequence of total throughput readings, simulate adding the minimum number of servers needed after each reading so capacity stays sufficient. Return the server count after each step.

Algorithms & Data StructuresTechnical Trade-offs
Author's notes

The core logic clicked pretty fast: just do ceiling division of the reading by the limit to get how many servers you need, then take the max with the current count.

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AI HintsAI Generated

Suggested Approach

First, clarify the problem: each server has a fixed capacity, and after each throughput reading, we need to ensure total capacity >= current throughput. We can maintain a running count of servers and add the minimum number needed to cover any deficit. The key is to compute the required servers as ceil(throughput / capacity) and take the maximum with the current count, since servers are never removed.

Pro tip: Mention that servers are never removed, so the count is non-decreasing. This simplifies the solution to a single pass with O(n) time and O(1) extra space, which is optimal.

1. Clarify assumptions and constraints

Confirm that each server has a fixed throughput capacity, servers are never removed, and we need the minimum number of servers after each reading. Ask about input size and whether throughput readings are cumulative or per-interval.

2. Define the capacity condition

At any step, total capacity = server_count * capacity_per_server. We need total capacity >= current throughput reading. So the required servers = ceil(throughput / capacity_per_server).

3. Design the algorithm

Initialize server_count = 0. For each throughput reading, compute required = ceil(reading / capacity). If required > server_count, set server_count = required. Append server_count to the result list.

4. Analyze complexity and edge cases

Time complexity is O(n) for n readings, space O(1) extra (or O(n) for output). Handle edge cases: zero throughput, capacity zero (invalid), and large numbers (use integer arithmetic to avoid floating-point errors).

5. Discuss trade-offs and extensions

If servers could be removed, we might need a more complex data structure. If capacity varies per server, we'd need a different approach. Mention that the greedy approach works because capacity is additive and servers are identical.

Key Points to Mention

  • Use integer arithmetic for ceiling division: (throughput + capacity - 1) // capacity to avoid floating-point precision issues.
  • The server count is monotonically non-decreasing because servers are never removed.
  • The greedy strategy of adding only when needed is optimal because each server adds a fixed capacity.
  • Time complexity O(n) and space O(1) extra, which is optimal for a single pass.
  • Edge cases: throughput = 0 (no servers needed), throughput exactly divisible by capacity, and very large throughput values.
  • If the problem allowed server removal, a different approach (e.g., tracking active servers) would be needed.

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