Amazon·Data Scientist·Onsite - Coding / Algorithms·Intermediate

Intermediate

May 2026

Summary

Final round for a Data Scientist role at Amazon, and they threw a classic hard algorithm problem at me. Not what I was expecting given the role, but apparently they do this.

Questions Asked (1)

Implement a function to merge k sorted linked lists into one sorted list, and walk through the time and space complexity of your approach.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

I went straight for the min-heap solution because it felt cleaner to explain.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the problem constraints (e.g., k and list sizes) and then present a solution using a min-heap to efficiently merge the lists. Walk through the algorithm step-by-step, analyze time and space complexity, and discuss trade-offs compared to alternatives like divide-and-conquer.

Pro tip: Emphasize that the heap approach is optimal for large k and discuss how it can be adapted for streaming data, which is relevant for Amazon's scalable systems. Also, mention that you would test edge cases like empty lists and duplicate values.

1. Clarify the problem

Ask about constraints: number of lists (k), average length, whether lists are sorted, and if we can modify input. This shows attention to detail and ensures the solution fits the context.

2. Propose a heap-based approach

Explain that you will use a min-heap to store the head nodes of each list. Repeatedly extract the smallest node and add its next node to the heap until all lists are exhausted.

3. Walk through the algorithm

Describe initialization: push the head of each non-empty list into the heap. Then loop: pop the smallest node, append it to the result, and if it has a next node, push that next node into the heap.

4. Analyze complexity

Time complexity: O(N log k) where N is total number of nodes and k is number of lists, because each node is pushed/popped from the heap (log k). Space complexity: O(k) for the heap (plus O(N) for the output list if not counted as extra).

5. Discuss trade-offs and alternatives

Mention that a divide-and-conquer approach (merging pairs of lists) can also achieve O(N log k) time but with O(1) extra space if done iteratively. Compare with naive sequential merging which is O(N k).

Key Points to Mention

Min-heap (priority queue) to efficiently select the smallest current node among k lists.
Time complexity O(N log k) and why it's better than O(N k) for large k.
Space complexity O(k) for the heap, and note that output list takes O(N) space.
Handling edge cases: empty lists, k=0, lists with different lengths.
Comparison with divide-and-conquer approach: similar time complexity but different space trade-offs.
Potential optimization: if k is small, a simple sequential merge might be sufficient; discuss when to choose which.

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