← Two Sigma Interview Insights
Took me a minute to slow down and not just binary search for the exact point.
Clarify the problem constraints (e.g., sorted by x, no duplicate x, handling of boundary points) and then propose an efficient binary search to locate the segment containing the target x. Compute the interpolated y using linear interpolation, and return null if x is outside the range. Discuss trade-offs between binary search and linear scan, and mention edge cases like exact point matches and floating-point precision.
Pro tip: Explicitly state that you assume the points are sorted by x and have no duplicate x values; if duplicates exist, clarify how to handle them (e.g., return the first or average). Also, mention that you would use binary search for O(log n) time, which is crucial for large datasets.
Confirm that the list is sorted by x, contains at least two points, and has no duplicate x values. Discuss how to handle x exactly equal to a point's x, x outside the range, and floating-point precision.
Use binary search to find the segment where the target x lies, achieving O(log n) time. Alternatively, mention linear scan for small n or if the list is unsorted, but highlight the trade-offs.
Given the two endpoints (x1, y1) and (x2, y2) of the segment, compute y = y1 + (x - x1) * (y2 - y1) / (x2 - x1). Handle the case where x equals x1 or x2 to avoid division by zero.
If x is less than the first point's x or greater than the last point's x, return null. If x exactly matches a point's x, return that point's y directly.
State that binary search gives O(log n) time and O(1) space, which is optimal. Discuss potential issues with floating-point comparisons and how to mitigate them (e.g., using epsilon).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.