Two Sigma·Software Engineer·Technical Phone Screen·Intermediate

IntermediatePrefer not to say

Apr 2026

Summary

Two Sigma coding round, one algorithmic problem the whole session. The problem itself was well-designed and I actually enjoyed it once I figured out the core insight, though getting there took longer than I'd like to admit.

Questions Asked (1)

You start with w capital and have n projects, each with a required minimum capital and a profit value. You can complete at most k projects, picking any available one whose capital requirement you currently meet and collecting its profit. What's the maximum capital you can end up with?

Algorithms & Data Structures

Author's notes

Took me a bit to stop thinking about this as a DP problem.

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AI HintsAI Generated

Suggested Approach

Model the problem as a greedy selection with a priority queue: at each step, among all projects whose capital requirement is ≤ current capital, pick the one with the highest profit. Sort projects by capital requirement and use a max-heap to efficiently retrieve the best available project, repeating up to k times.

Pro tip: Clarify edge cases upfront (e.g., no affordable projects, k=0, or multiple projects with same capital) and mention that the greedy choice is optimal because capital only increases, so a project affordable now remains affordable later. This shows you understand the exchange argument and can handle interviewer follow-ups.

1. Understand the problem and constraints

Restate the problem: start with capital w, choose at most k projects, each project i requires capital[i] and gives profit[i]. You can only pick a project if current capital ≥ capital[i]. Goal: maximize final capital.

2. Identify the greedy strategy

At any point, the best choice is the affordable project with the highest profit, because taking it increases capital and never reduces future options. This greedy choice is optimal due to the monotonic nature of capital.

3. Design the algorithm with sorting and a max-heap

Sort projects by required capital. Use a max-heap to store profits of all projects whose capital requirement ≤ current capital. For up to k iterations, add newly affordable projects to the heap, then if heap is non-empty, pop the max profit and add it to capital.

4. Analyze complexity and edge cases

Time complexity: O(n log n) for sorting + O(n log n) for heap operations (each project added/removed once). Space: O(n). Handle edge cases: no affordable projects, k=0, or fewer than k projects available.

5. Walk through an example and conclude

Trace a small example to verify correctness. Conclude that the algorithm returns the maximum possible capital after at most k projects.

Key Points to Mention

Greedy choice property: always pick the highest profit among affordable projects.
Use a max-heap (priority queue) to efficiently get the maximum profit.
Sort projects by capital requirement to process them in order of affordability.
Time complexity: O(n log n) due to sorting and heap operations.
Space complexity: O(n) for the heap and sorted list.
Edge cases: k=0, no affordable projects, or fewer than k projects available.

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