Two Sigma·Data Scientist·Technical Phone Screen·Intermediate

Intermediate

Jun 2026

Summary

Got a coding question for a Data Scientist role at Two Sigma that felt more like a software engineering problem than anything stats-related. The core of it was implementing interpolation and extrapolation on a polyline built from unsorted 2D points. Interesting problem, made me think harder about edge cases than I expected.

Questions Asked (1)

Given an unsorted list of distinct 2D points, sort them by x-coordinate to form a polyline, then implement a function that takes a query x value and returns the corresponding y value using exact match, linear interpolation between adjacent points, or extrapolation beyond the endpoints.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

My first instinct was binary search after sorting, which is the right move, but I fumbled the extrapolation cases initially.

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AI HintsAI Generated

Suggested Approach

Start by clarifying requirements: input format, handling of duplicate x-values, and expected behavior for out-of-range queries. Then outline the algorithm: sort points by x, build a data structure for efficient lookup (e.g., binary search on x-coordinates), and implement the three cases (exact match, interpolation, extrapolation). Discuss trade-offs between preprocessing time and query time, and mention edge cases like single point or empty list.

Pro tip: Emphasize that sorting once and using binary search makes queries O(log n), which is crucial for repeated queries. Also, proactively discuss numerical stability and how to handle extrapolation (e.g., using the slope of the nearest segment) to show depth.

1. Clarify requirements and edge cases

Ask about input size, query frequency, and expected behavior for out-of-range x, duplicate x-values, or empty input. Confirm whether extrapolation should use the first/last segment's slope.

2. Preprocess: sort and store x-coordinates

Sort the points by x-coordinate. Store the sorted x-values in a separate array for binary search, and keep the corresponding y-values.

3. Implement query logic with binary search

Use binary search to find the position of the query x. If exact match, return y. If between two points, interpolate linearly. If outside, extrapolate using the slope of the nearest segment.

4. Analyze complexity and trade-offs

Discuss time complexity: O(n log n) preprocessing, O(log n) per query. Mention alternative approaches (e.g., hash map for exact match only) and why they are insufficient for interpolation/extrapolation.

5. Test and validate

Walk through examples: exact match, interpolation, extrapolation, and edge cases (single point, query at boundary). Mention potential floating-point precision issues and how to mitigate them.

Key Points to Mention

Sorting by x-coordinate and using binary search for O(log n) queries
Linear interpolation formula: y = y1 + (x - x1) * (y2 - y1) / (x2 - x1)
Extrapolation using the slope of the first or last segment
Handling edge cases: empty list, single point, duplicate x-values (if allowed)
Time and space complexity analysis: O(n log n) preprocessing, O(log n) query, O(n) space
Numerical stability and floating-point precision considerations

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