Two Sigma·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

May 2026

Summary

Interviewed for a Research Engineer role at Two Sigma. One coding question, pretty algorithmic in nature. The problem itself wasn't crazy hard but the efficiency angle is where they actually care.

Questions Asked (1)

You're given a set of discrete (x, y) points forming a polyline. For a query x value, compute the corresponding y using linear interpolation if x falls between two points, or extrapolation using the nearest boundary segment if x is outside the range.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

My first instinct was to just loop through all the points and find the neighbors.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the problem constraints: input format, whether x values are sorted, and expected query patterns. Then propose an efficient solution using binary search to locate the interval, followed by linear interpolation or extrapolation. Discuss trade-offs between preprocessing (e.g., sorting) and query time, and mention edge cases like duplicate x values or single-point input.

Pro tip: Emphasize the importance of handling edge cases and numerical stability, and suggest that in a real system you might preprocess the points into a data structure for faster queries. Also, mention that extrapolation should use the nearest boundary segment, not just the first/last two points, to avoid misleading results.

1. Clarify requirements and constraints

Ask about input size, whether x values are sorted, query frequency, and expected precision. Confirm that extrapolation uses the nearest boundary segment.

2. Choose data structure and algorithm

If points are sorted, use binary search to find the interval in O(log n) time. If not, consider sorting once or using a balanced tree for dynamic updates.

3. Implement interpolation/extrapolation logic

For interpolation, use the formula y = y1 + (x - x1) * (y2 - y1) / (x2 - x1). For extrapolation, apply the same formula using the nearest boundary segment (first two or last two points).

4. Handle edge cases and errors

Address cases like empty input, single point, duplicate x values, and x exactly matching a point. Discuss numerical stability and potential division by zero.

5. Analyze complexity and trade-offs

State time complexity: O(log n) per query with binary search, O(n) if linear scan. Discuss space complexity and possible optimizations for multiple queries.

Key Points to Mention

Binary search for O(log n) query time when points are sorted by x.
Linear interpolation formula and its application to extrapolation using boundary segments.
Edge cases: empty input, single point, duplicate x values, and x outside range.
Numerical stability: avoid division by zero, consider floating-point precision.
Trade-offs between preprocessing (sorting) and query efficiency.
Potential for caching or building an index for frequent queries.

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