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Two Sigma·Software Engineer·Technical Phone Screen·Intermediate

IntermediatePrefer not to say
May 2026

Summary

Two Sigma coding round, one classic problem that I thought I knew cold going in. Turns out knowing the problem and explaining it cleanly under pressure are two different things.

Questions Asked (1)

Q1

Given an array of non-negative integers representing bar heights in an elevation map, calculate the total volume of water trapped between the bars after rain.

Algorithms & Data StructuresTechnical Trade-offs
Author's notes

I knew this problem.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the problem and walking through a small example to demonstrate understanding. Then present a solution using precomputed left and right maximum arrays, explaining the O(n) time and O(n) space complexity. If time permits, discuss the two-pointer optimization to O(1) space, highlighting the trade-offs.

Pro tip: At Two Sigma, interviewers value clean, efficient code and the ability to discuss trade-offs. After presenting your solution, proactively mention edge cases like empty arrays or all equal heights, and offer to optimize space if needed.

1. Clarify and Confirm

Ask clarifying questions about input constraints (e.g., array size, height range) and confirm the expected output. Restate the problem in your own words to ensure alignment.

2. Brute Force Baseline

Briefly describe a naive O(n^2) approach: for each bar, find the maximum height to its left and right, then add the minimum of those minus the current height. This shows you can start simple.

3. Optimize with Precomputation

Explain how to precompute left and right maximum arrays in O(n) time, then compute trapped water in a single pass. This reduces time complexity to O(n) with O(n) space.

4. Further Optimize with Two Pointers

If asked for better space, describe the two-pointer technique: maintain left and right pointers and track max left/right seen so far, computing water on the fly. This achieves O(n) time and O(1) space.

5. Analyze Trade-offs and Edge Cases

Compare the approaches in terms of time/space complexity and code simplicity. Discuss edge cases such as empty array, single bar, strictly increasing/decreasing heights, and large inputs.

Key Points to Mention

  • Time and space complexity of each approach (brute force O(n^2), precomputed O(n) time/O(n) space, two-pointer O(n) time/O(1) space).
  • The formula for water trapped at each index: min(max_left, max_right) - height[i].
  • How precomputing left and right maximum arrays works and why it's efficient.
  • The two-pointer technique and why it correctly computes trapped water without extra space.
  • Edge cases: empty array, single element, all bars same height, strictly increasing/decreasing heights.
  • Potential follow-up: how to handle very large arrays or streaming input (e.g., if data doesn't fit in memory).

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