Microsoft·Data Scientist·Technical Phone Screen·Senior

Senior

Jun 2026

Summary

Microsoft Data Scientist interview with a pretty involved coding question that blended algorithm design with correctness proofs and test case generation. Single question but they really dug into every layer of it.

Questions Asked (1)

Given a non-decreasing integer array that has been rotated an unknown number of times (with possible duplicates), write a function returning both the rotation point index and the leftmost index of a target value. Walk through your algorithm idea, correctness argument, complexity analysis, and write thorough unit tests covering edge cases like all-equal arrays, target spanning the rotation boundary, single element, and empty input.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

This one took me a while to untangle.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the problem and constraints, then propose a modified binary search that handles duplicates and finds both the rotation point and the leftmost target index. Walk through the algorithm, prove correctness, analyze time/space complexity, and discuss edge cases with thorough unit tests.

Pro tip: Emphasize that duplicates can degrade performance to O(n) in the worst case, and mention that you would confirm with the interviewer whether the array is guaranteed to be rotated at least once or could be unrotated.

1. Clarify requirements and constraints

Ask about input size, whether the array can be empty, if rotation is guaranteed, and if duplicates affect the definition of rotation point. Confirm the expected return format for both indices.

2. Outline the algorithm

Describe a two-phase binary search: first find the rotation point (smallest element) using a modified binary search that handles duplicates, then find the leftmost occurrence of the target in the appropriate sorted subarray.

3. Prove correctness and analyze complexity

Argue that the rotation point is the only index where the previous element is greater, and that binary search on the correct subarray finds the leftmost target. State time complexity: O(log n) average, O(n) worst-case with duplicates; space O(1).

4. Design thorough unit tests

List test cases: empty array, single element, all equal, no rotation, rotation at various points, target at rotation point, target spanning boundary, target absent, duplicates causing worst-case.

5. Discuss trade-offs and optimizations

Mention alternative approaches (e.g., linear scan for small arrays), handling of duplicates by shrinking search space, and potential to combine both searches into one pass if needed.

Key Points to Mention

Modified binary search to find rotation point (minimum element) in O(log n) time, with O(n) worst-case due to duplicates.
Binary search for leftmost target in the correct sorted subarray (either left or right of rotation point).
Correctness proof: rotation point is the only index where arr[i] > arr[i+1]; leftmost target found by continuing search on left when equal.
Complexity analysis: average O(log n), worst-case O(n) when duplicates force linear scan; space O(1).
Edge cases: empty array, single element, all equal, target at rotation point, target spanning boundary, no rotation.
Unit tests should cover normal, boundary, and worst-case scenarios, including duplicates and missing target.

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