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Microsoft·Software Engineer·Technical Phone Screen·Intermediate

IntermediatePrefer not to say
May 2026

Summary

Microsoft SWE interview with a classic interval merging problem. Pretty standard algorithmic round, nothing too surprising, but the complexity discussion at the end was where things got interesting.

Questions Asked (1)

Q1

Given an array of possibly overlapping and unsorted intervals, merge all overlapping ones and return a sorted list of non-overlapping intervals covering the same ranges. Also discuss the time and space complexity of your approach.

Algorithms & Data Structures
Author's notes

Sorting first is the move and I knew that, but I second-guessed myself for a minute wondering if there was some O(n) trick I was missing.

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AI HintsAI Generated

Suggested Approach

Start by clarifying assumptions (e.g., interval inclusivity, input format) and edge cases. Then propose sorting intervals by start time and merging in a single pass, explaining the algorithm step-by-step. Finally, analyze time and space complexity, and discuss potential optimizations or trade-offs.

Pro tip: Mention that sorting is the bottleneck and that if intervals are already sorted or can be sorted in linear time (e.g., using counting sort for bounded ranges), the merge can be done in O(n). Also, discuss how to handle edge cases like empty input or single interval.

1. Clarify requirements and edge cases

Ask about interval inclusivity (e.g., [1,3] and [3,5] overlap?), input format, and expected output. Consider edge cases: empty array, single interval, all overlapping, none overlapping.

2. Sort intervals by start time

Sort the intervals based on their start values. This ensures that any overlapping intervals are adjacent, simplifying the merge process.

3. Merge overlapping intervals

Iterate through sorted intervals, maintaining a current merged interval. If the next interval's start is <= current end, update the end to max(current end, next end); otherwise, add current to result and start a new merged interval.

4. Analyze complexity

Time complexity: O(n log n) due to sorting, plus O(n) for merging. Space complexity: O(n) for the output (or O(log n) if sorting in-place and ignoring output).

5. Discuss optimizations and trade-offs

Mention that if intervals are already sorted, time is O(n). If memory is tight, merge in-place. Also, note that the algorithm is optimal for comparison-based sorting.

Key Points to Mention

  • Sorting by start time is crucial for linear merge.
  • Merge condition: next.start <= current.end (assuming inclusive intervals).
  • Time complexity: O(n log n) due to sorting; space complexity: O(n) for output.
  • Edge cases: empty input, single interval, intervals with same start, touching intervals.
  • In-place merging possible if input can be modified, reducing auxiliary space.
  • If intervals are pre-sorted, time complexity reduces to O(n).

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