Two Sigma·Software Engineer·Technical Phone Screen·Intermediate

IntermediatePrefer not to say

Jun 2026

Summary

Two Sigma software engineer round, one algorithmic problem the whole time. The problem itself was well-constructed and I can see why they like it, but I went in underprepared for the greedy heap approach and paid for it.

Questions Asked (1)

You have a startup with initial capital w and a list of n projects, each with a capital threshold and a profit. You can complete at most k projects (one at a time, in any order), and profit is added to your capital immediately after each project. Find the maximum capital you can end up with.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

My first instinct was brute force: at each step, scan all projects, pick the highest-profit one you can afford, repeat.

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AI HintsAI Generated

Suggested Approach

Model the problem as a greedy selection where at each step you choose the most profitable project among those affordable with current capital. Use a min-heap to efficiently track affordable projects and a max-heap to select the best profit, ensuring O(n log n) time. Explain why greedy works here: always taking the highest profit available maximizes future capital and never hurts.

Pro tip: Mention that this is a classic 'IPO' problem and that the greedy choice is optimal because profits are non-negative and capital only increases. Also, discuss edge cases like k=0 or no affordable projects.

1. Clarify and Restate

Restate the problem in your own words, confirming constraints: initial capital w, at most k projects, each project requires capital threshold and yields profit. Ask about input sizes and whether profits can be zero.

2. Identify Greedy Strategy

Explain that at each step, among all projects with capital requirement ≤ current capital, pick the one with maximum profit. This maximizes capital for subsequent steps.

3. Design Efficient Data Structures

Sort projects by capital requirement. Use a min-heap to add projects as they become affordable, and a max-heap to select the highest profit. Repeat up to k times.

4. Analyze Complexity and Trade-offs

Time: O(n log n) due to sorting and heap operations. Space: O(n). Compare with brute-force O(n^k) and discuss why greedy is optimal.

5. Test with Edge Cases

Walk through examples: k=0, no affordable projects, multiple projects with same profit, and large k. Verify correctness and handle integer overflow if needed.

Key Points to Mention

Greedy choice property: always pick the most profitable affordable project.
Use of min-heap to manage projects by capital requirement and max-heap for profit selection.
Time complexity O(n log n) and space O(n).
Proof of optimality: by induction, greedy maximizes capital after each step.
Handling edge cases: k=0, no affordable projects, and large capital values.
Comparison with alternative approaches like dynamic programming or brute force.

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