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Microsoft·Software Engineer·Technical Phone Screen·Intermediate

Intermediate
Jul 2026

Summary

Microsoft SWE interview with a single algorithmic question about circular arrays. Pretty standard stuff but I fumbled the setup a bit before getting to a clean solution.

Questions Asked (1)

Q1

Given a circularly sorted array, find the number of rotations that have been applied to it.

Algorithms & Data Structures
Author's notes

I knew this was a binary search problem pretty quickly but spent too long second-guessing the edge cases, like what happens when the array has duplicates or is already sorted.

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AI HintsAI Generated

Suggested Approach

Clarify that the array is sorted in ascending order and contains distinct elements, then explain that the number of rotations equals the index of the minimum element. Use binary search to find the minimum element in O(log n) time by comparing the middle element with the rightmost element.

Pro tip: Explicitly state that if the array is not rotated (i.e., already sorted), the answer is 0, and handle edge cases like empty array or single element gracefully. Also, mention that if duplicates are allowed, the problem becomes trickier and may require a modified binary search with O(n) worst-case time.

1. Clarify assumptions and edge cases

Confirm that the array is sorted in ascending order, contains distinct elements, and is rotated some number of times (possibly zero). Discuss edge cases: empty array, single element, and already sorted array.

2. Relate rotations to minimum element index

Explain that rotating a sorted array shifts elements, so the minimum element ends up at the rotation point. The number of rotations is exactly the index of the minimum element.

3. Design binary search for minimum

Use binary search: compare the middle element with the rightmost element. If mid > right, the minimum is in the right half; otherwise, it's in the left half (including mid). Narrow down until left == right.

4. Implement and test

Write clean code with proper loop conditions and return the index. Test with examples: [4,5,6,7,0,1,2] returns 4, [1,2,3,4] returns 0, [2,1] returns 1.

5. Analyze complexity and discuss duplicates

State time complexity O(log n) and space O(1). If duplicates are allowed, explain that binary search may degrade to O(n) and outline a modified approach.

Key Points to Mention

  • The number of rotations equals the index of the minimum element in the rotated sorted array.
  • Binary search can find the minimum in O(log n) time by comparing mid with the rightmost element.
  • Edge cases: empty array, single element, and already sorted array (0 rotations).
  • Handling duplicates requires a modified binary search that may run in O(n) worst-case time.
  • Time and space complexity: O(log n) time, O(1) space for distinct elements.
  • Alternative approach: linear scan O(n) is trivial but not optimal; binary search is preferred.

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