Applied intuition·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

May 2026

Summary

Interviewed for a software engineering role at Applied Intuition and got a computational geometry problem that felt way more niche than the typical leetcode grind. The core challenge was merging overlapping line segments in a plane, which sounds straightforward until you actually sit down and think through all the edge cases.

Questions Asked (1)

Given a list of planar line segments defined by their endpoints, merge any segments that overlap. Two segments overlap if they are collinear and their projections onto the shared line intersect or touch. Return the minimal set of merged segments.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

I knew the 1D interval merge part cold (basically the classic merge intervals problem), but grouping segments by their actual line identity tripped me up.

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AI HintsAI Generated

Suggested Approach

Normalize each segment by ordering its endpoints and representing it with a canonical line equation (slope and intercept) plus a 1D interval along that line. Group segments by line, sort intervals within each group, and merge overlapping or touching intervals to produce the minimal set of merged segments.

Pro tip: Mention that using exact rational arithmetic or a normalized integer representation for slopes and intercepts avoids floating-point precision issues when grouping collinear segments.

1. Normalize and Canonicalize

For each segment, order its endpoints lexicographically and compute a canonical representation of its supporting line (e.g., normalized slope and intercept as exact rationals).

2. Group by Line

Use a hash map keyed by the canonical line representation to group all segments that lie on the same infinite line.

3. Project to 1D Intervals

For each group, project each segment onto a 1D coordinate along the line (e.g., using the x-coordinate if the line is not vertical, otherwise y-coordinate) to obtain closed intervals.

4. Sort and Merge Intervals

Sort the intervals by start point, then iterate and merge overlapping or touching intervals (where next.start <= current.end) into a single interval.

5. Reconstruct Segments

Convert each merged interval back to a planar segment using the line's parametric equation and the interval endpoints.

Key Points to Mention

Handling collinearity: two segments overlap only if they lie on the same infinite line, so grouping by line is essential.
Exact arithmetic: use rational numbers or integer cross-multiplication to avoid floating-point errors in slope/intercept comparisons.
Interval merging: after projection, the problem reduces to the classic merge intervals algorithm, which is O(n log n) overall.
Edge cases: vertical lines, zero-length segments (points), and segments that only touch at endpoints.
Complexity analysis: O(n log n) time due to sorting, O(n) space for grouping and output.
Output format: return the minimal set of merged segments, ensuring no two output segments overlap or touch.

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