NURO·Software Engineer·Technical Phone Screen·Intermediate

IntermediatePrefer not to say

Jun 2026

Summary

Interviewed for a Software Engineer role at Nuro and got a coding problem about finding gaps in a union of integer intervals. Pretty clean problem once you see the pattern, but there are a few edge cases that'll trip you up if you're not careful.

Questions Asked (1)

Given a list of integer intervals, find all maximal integer ranges within the span of the input that are not covered by any interval. Return them sorted.

Algorithms & Data Structures

Author's notes

My first instinct was to treat it like a merge-intervals problem, which is basically right.

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AI HintsAI Generated

Suggested Approach

Clarify the problem: intervals are inclusive, and we need maximal gaps within the span from the minimum start to the maximum end. Sort intervals by start, merge overlapping or adjacent intervals, then compute gaps between merged intervals and at the boundaries. Return gaps sorted, which they naturally are if we process in order.

Pro tip: Explicitly discuss edge cases like empty input, single interval, and intervals that touch (e.g., [1,2] and [3,4] produce no gap if integers are discrete). Also mention that sorting dominates time complexity, so O(n log n) is optimal.

1. Clarify requirements and edge cases

Confirm whether intervals are inclusive, whether touching intervals (e.g., [1,2] and [3,4]) should be merged, and what to return for empty or fully covered input. Discuss integer discreteness.

2. Sort intervals by start

Sort the input intervals by their start value. This enables efficient merging and gap detection in a single pass.

3. Merge overlapping intervals

Iterate through sorted intervals, merging any that overlap or are adjacent. Keep track of the current merged interval's end.

4. Identify gaps between merged intervals

After merging, compute the gaps between consecutive merged intervals. Also check for gaps before the first interval and after the last interval within the overall span.

5. Return sorted gaps

Collect all gaps as intervals and return them. Since we process in sorted order, the gaps are already sorted.

Key Points to Mention

Time complexity: O(n log n) due to sorting, which is optimal for comparison-based approaches.
Space complexity: O(n) for storing merged intervals and gaps, or O(1) extra if modifying input.
Handling of inclusive vs exclusive intervals and integer discreteness (e.g., [1,2] and [3,4] may or may not have a gap).
Edge cases: empty input, single interval, intervals covering the entire span, and negative numbers.
Alternative approaches: sweep line with events, but sorting and merging is simpler and equally efficient.
Definition of 'maximal' ranges: gaps that cannot be extended without overlapping an input interval.

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