LinkedIn·Machine Learning Engineer·Technical Phone Screen·Senior

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May 2026Remote

Summary

LinkedIn MLE interview with a meaty algorithms problem centered on interval coverage. The question had multiple layers and I don't think I fully nailed the follow-up on the dynamic segment tree variant.

Questions Asked (2)

Given a list of half-open integer intervals [l, r), compute the total length covered by at least one interval. Implement a sort-and-merge line sweep approach and analyze its time and space complexity.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

The sort-and-merge part I handled fine.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the problem: half-open intervals [l, r) and the goal to compute the total length covered by at least one interval. Then describe the sort-and-merge line sweep: sort intervals by start, iterate while merging overlapping or adjacent intervals, and accumulate the lengths of merged intervals. Finally, analyze time complexity O(n log n) due to sorting and space complexity O(n) for the merged list (or O(1) extra if done in-place).

Pro tip: Mention that half-open intervals simplify merging because touching intervals (e.g., [1,2) and [2,3)) can be merged without double-counting the boundary, and highlight that the algorithm is optimal for comparison-based sorting.

1. Clarify the problem and edge cases

Confirm that intervals are half-open [l, r) and that we need the total length covered by at least one interval. Discuss edge cases: empty list, single interval, intervals with zero length (l == r), and unsorted input.

2. Sort intervals by start

Sort the list of intervals by their start coordinate. If starts are equal, sorting by end is optional but can help with consistency.

3. Merge overlapping intervals

Initialize a merged list with the first interval. For each subsequent interval, if its start is less than or equal to the end of the last merged interval, extend the last merged interval's end to the maximum of the two ends; otherwise, add the interval to the merged list.

4. Compute total covered length

Sum the lengths of all intervals in the merged list: total += (end - start) for each merged interval. Return the total.

5. Analyze complexity

Time complexity: O(n log n) due to sorting, where n is the number of intervals. Space complexity: O(n) for the merged list (or O(1) extra if merging in-place and only tracking total length).

Key Points to Mention

Sorting is the bottleneck; the merge step is linear.
Half-open intervals allow merging when next.start <= current.end (touching intervals merge without overlap).
Edge cases: empty input, zero-length intervals, and intervals that are completely contained within others.
In-place merging can reduce space complexity to O(1) beyond the input.
The algorithm is optimal for comparison-based sorting; if intervals are already sorted, time is O(n).
Use long integers for total length to avoid overflow if coordinates are large.

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

Extend the interval coverage problem to support incremental add and remove operations, returning the total covered length after each update. Implement this using a segment tree or interval tree, and discuss coordinate compression for large coordinate ranges.

Algorithms & Data StructuresSystem DesignTechnical Trade-offs

Author's notes

This is where things got harder.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the problem constraints (coordinate range, number of operations, update types) and then propose a segment tree with lazy propagation over compressed coordinates. Explain how each node tracks covered length and cover count, enabling O(log n) updates and O(1) total covered length retrieval. Discuss trade-offs between segment tree and interval tree, and justify coordinate compression for large ranges.

Pro tip: Mention that coordinate compression must include both endpoints and possibly midpoints (e.g., for open intervals) to avoid off-by-one errors, and that the segment tree should store cover count and covered length per node to handle overlapping intervals correctly.

1. Clarify requirements and constraints

Ask about coordinate range, number of operations, interval types (closed/open), and whether updates are online. This determines if coordinate compression is necessary and the segment tree design.

2. Design data structure with coordinate compression

Collect all possible coordinates from initial intervals and future updates, sort and deduplicate to create compressed indices. Map each original coordinate to its compressed index.

3. Implement segment tree with lazy propagation

Build a segment tree over compressed coordinates. Each node stores cover count (number of active intervals fully covering the node's range) and covered length (total length covered by at least one interval). Update cover count and covered length on add/remove.

4. Handle updates and query total covered length

For each add/remove operation, update the segment tree in O(log n) by adjusting cover counts on the relevant nodes. After each update, the total covered length is the root's covered length.

5. Analyze complexity and discuss trade-offs

Explain time complexity: O(log n) per update, O(1) query. Space: O(n). Compare with interval tree (which may be simpler but less efficient for this problem) and discuss when coordinate compression is beneficial.

Key Points to Mention

Coordinate compression reduces large coordinate ranges to a manageable size, enabling efficient segment tree operations.
Segment tree nodes store cover count and covered length; cover count determines if the node's range is fully covered.
Lazy propagation is not strictly needed if updates are point updates on compressed coordinates, but can be used for range updates.
Total covered length is maintained at the root and updated after each operation.
Time complexity: O(log n) per update, O(1) query; space O(n).
Trade-offs: interval tree may be simpler but less efficient for frequent updates; segment tree with compression is optimal for this problem.

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