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Xai·Software Engineer·Technical Phone Screen·Senior

SeniorPrefer not to say
Jun 2026Remote

Summary

Interviewed for a software engineer role at xAI and got hit with an LFU cache design question. The problem itself is pretty classic but the O(1) constraint is what separates people who've seen it from people who haven't.

Questions Asked (1)

Q1

Design and implement an LFU (least frequently used) cache class supporting get and put operations, both in O(1) time. On eviction, remove the least frequently used key, breaking ties by recency.

Algorithms & Data StructuresSystem DesignTechnical Trade-offs
Author's notes

I knew LRU cold but LFU tripped me up for a minute because the tie-breaking rule means you need to track both frequency AND insertion/access order within each frequency bucket.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the requirements and edge cases, then propose a design using a combination of a hash map and a doubly linked list of frequency buckets. Explain how each operation achieves O(1) by maintaining pointers and updating frequency lists, and finally discuss trade-offs and potential optimizations.

Pro tip: Mention that LFU with tie-breaking by recency is equivalent to LRU within each frequency level, so you can reuse an LRU structure per frequency. This shows deep understanding and simplifies the implementation.

1. Clarify Requirements and Edge Cases

Ask about cache capacity, behavior when capacity is 0, handling of duplicate keys, and whether get updates frequency. Confirm that tie-breaking is by least recently used among least frequently used.

2. Design Data Structures

Propose using a hash map for O(1) key lookup, a doubly linked list for each frequency to maintain recency order, and a min-frequency pointer to track the lowest frequency for eviction.

3. Detail Operations

Explain get: if key exists, update its frequency (move to next frequency list) and return value. Explain put: if key exists, update value and frequency; if new, insert with frequency 1, and if capacity exceeded, evict from min-frequency list's tail (least recently used).

4. Analyze Complexity and Trade-offs

Argue that both operations are O(1) due to constant-time hash lookups and pointer manipulations. Discuss trade-offs: memory overhead vs. speed, and compare with other eviction policies like LRU.

5. Handle Edge Cases and Optimizations

Address edge cases: capacity 0, updating existing key, and frequency overflow. Mention possible optimizations like using a single linked list with frequency buckets or a heap (but heap would not be O(1)).

Key Points to Mention

  • Use a hash map for O(1) key access.
  • Maintain a doubly linked list for each frequency to preserve recency order.
  • Track the minimum frequency to quickly find the eviction candidate.
  • On get or put, increment the key's frequency and move it to the appropriate list.
  • Evict the least recently used key from the minimum frequency list.
  • Discuss trade-offs: memory overhead vs. O(1) performance, and compare with LRU.

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