Microsoft·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Jul 2026

Summary

Microsoft SWE interview with a classic k-way merge problem. Pretty standard algorithmic round but the constraints pushed you toward actually knowing your heap usage rather than brute-forcing it.

Questions Asked (1)

Given k sorted arrays with a total of N elements, merge them into a single sorted array using an asymptotically optimal algorithm. Describe your approach including data structures, time and space complexity, then implement it.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

The naive approach of scanning all k heads at each step is O(N*k) and they basically told you upfront that wasn't acceptable.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the problem constraints and edge cases, then propose using a min-heap to efficiently merge the arrays. Explain the algorithm step-by-step, analyze its time and space complexity, and finally implement it in code.

Pro tip: Mention that if k is very large compared to N, a divide-and-conquer approach (merging pairs of arrays) can be more cache-friendly and avoid heap overhead, but the heap solution is generally optimal for arbitrary k.

1. Clarify and Confirm

Ask about constraints: Are the arrays sorted ascending? What is the range of k and N? Can we assume non-null arrays? This shows attention to detail.

2. Propose Heap-Based Approach

Explain that a min-heap of size k, storing the current element from each array, allows us to repeatedly extract the minimum and insert the next element from the same array.

3. Analyze Complexity

State that each of the N elements is inserted and extracted once, each operation O(log k), giving O(N log k) time. Space is O(k) for the heap plus O(N) for the output.

4. Implement the Algorithm

Write clean code, handling edge cases like empty arrays. Use a priority queue (min-heap) and track the array index and element index for each entry.

5. Test and Discuss Trade-offs

Walk through a small example, then mention alternative approaches (e.g., divide-and-conquer) and when they might be preferable.

Key Points to Mention

Min-heap (priority queue) to efficiently get the smallest current element among k arrays.
Time complexity O(N log k) and space complexity O(k) for the heap (plus O(N) for output).
Handling edge cases: empty arrays, k=0, N=0, duplicate elements.
Comparison with alternative approaches: divide-and-conquer merging (O(N log k) time, O(N) space) and its cache performance.
Implementation details: storing tuples (value, array_index, element_index) in the heap.
Stability and whether the merge should be stable (if equal elements, preserve original order).

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