Microsoft·Machine Learning Engineer·Technical Phone Screen·Intermediate

IntermediatePrefer not to say

Jun 2026

Summary

Microsoft ML engineer interview with a classic array problem that sounds trivial until you actually think about the constraints.

Questions Asked (1)

Given an array of integers ranging from 1 to n, determine whether the array contains any duplicate values using constant time and constant space.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

The constant space part is what tripped me up.

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AI HintsAI Generated

Suggested Approach

Clarify the problem constraints and assumptions, then propose an in-place algorithm that uses the array itself as a hash table by marking visited indices. Explain that this achieves O(n) time and O(1) extra space, and discuss potential trade-offs such as modifying the input.

Pro tip: Always state your assumptions and edge cases upfront (e.g., whether the array can be modified, if n is the array length, and if values are guaranteed to be in 1..n). This shows thoroughness and prevents miscommunication.

1. Clarify constraints and assumptions

Confirm that the array length is n, values are in 1..n, and that constant space means O(1) auxiliary space. Ask if modifying the input is allowed.

2. Propose an in-place marking algorithm

For each element, use its value as an index; if the value at that index is already negative, a duplicate exists; otherwise, negate the value at that index to mark it as seen.

3. Analyze time and space complexity

Explain that the algorithm runs in O(n) time with a single pass and uses O(1) extra space, as it only modifies the input array.

4. Discuss trade-offs and alternatives

Mention that this approach modifies the input; if that's not allowed, consider other methods like sorting (O(n log n) time, O(1) space) or using a hash set (O(n) space).

5. Handle edge cases and conclude

Test with small arrays, arrays with no duplicates, and arrays with multiple duplicates. Summarize the solution and its suitability for the given constraints.

Key Points to Mention

In-place marking using negation to track visited indices
Time complexity O(n) and space complexity O(1) auxiliary
Modification of input array as a trade-off
Edge cases: empty array, single element, all duplicates
Alternative approaches: sorting, hash set, and their complexities
Assumption that values are in range 1 to n and n is array length

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