MathWorks·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Apr 2026

Summary

MathWorks software engineer interview with a computational geometry problem that looks straightforward but has some real complexity hiding in the constraints.

Questions Asked (1)

Given a list of n segments on a number line, each defined by a start and end point, return an array where each entry is the count of other segments that intersect with that segment (touching at a single point counts as an intersection).

Algorithms & Data Structures

Author's notes

My first instinct was brute force O(n^2) and I said so out loud, which I think was fine.

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AI HintsAI Generated

Suggested Approach

Clarify the problem constraints (n, coordinate ranges, whether segments are inclusive) and discuss a sweep-line algorithm with a Fenwick tree to count intersections efficiently. Explain how to handle active segments and compute counts for each segment, then analyze time and space complexity.

Pro tip: Mention that sorting events by coordinate and processing starts before ends ensures touching endpoints are counted as intersections, avoiding off-by-one errors. Also, note that the problem can be solved in O(n log n) time, which is optimal for comparison-based sorting.

1. Clarify requirements and constraints

Ask about input size, coordinate ranges, whether segments can overlap completely, and if touching endpoints count. Confirm output format and edge cases.

2. Choose an efficient algorithm

Propose a sweep-line approach: sort all endpoints, use a Fenwick tree (BIT) to maintain active segments, and count intersections for each segment.

3. Detail the sweep-line process

Process events in order: for a start event, query the BIT for active segments that intersect; for an end event, update the BIT. Handle ties by processing starts before ends.

4. Compute counts and handle duplicates

For each segment, count intersections with active segments, ensuring each pair is counted once. Adjust for self-counting and duplicate segments if necessary.

5. Analyze complexity and test

State O(n log n) time and O(n) space. Walk through a small example to verify correctness, including edge cases like nested or touching segments.

Key Points to Mention

Sweep-line algorithm with event sorting
Fenwick tree (Binary Indexed Tree) for dynamic prefix sums
Handling of touching endpoints by processing starts before ends
Time complexity O(n log n) and space complexity O(n)
Edge cases: duplicate segments, fully nested segments, single-point segments
Alternative approaches like interval trees or divide-and-conquer, and their trade-offs

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