Xai·Machine Learning Engineer·Onsite - System Design / Architecture·Senior

Senior

May 2026

Summary

System design question for an ML Engineer role at xAI. The whole thing revolved around one meaty data structure problem with a bunch of follow-ups layered on top. Pretty intense for what felt like a single question.

Questions Asked (1)

Design a data structure that supports insert, remove, and get_random operations, all in expected O(1) time. Walk through your algorithm choices, how you handle edge cases like deleting the last element or filling gaps, how you'd verify the randomness is actually uniform, and how you'd extend it to support duplicates or thread-safety.

Algorithms & Data StructuresSystem DesignTechnical Trade-offs

Author's notes

The core idea clicked pretty fast for me: combine a hashmap with a dynamic array.

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AI HintsAI Generated

Suggested Approach

Start by proposing a hybrid data structure: a dynamic array for O(1) random access and a hash map for O(1) insert/remove by mapping values to their indices. Explain how to handle deletions by swapping with the last element and updating the map, and then discuss extensions for duplicates and thread-safety with appropriate synchronization.

Pro tip: Mention that Python's set/dict or Java's HashSet/HashMap provide expected O(1) but worst-case O(n); for strict guarantees, consider a balanced BST or skip list, but that's overkill for most interviews. Also, emphasize that randomness uniformity depends on the random number generator, not the data structure itself.

1. Clarify requirements and constraints

Ask about expected time complexity (expected vs worst-case), whether duplicates are allowed, and if thread-safety is required. This shows you think about edge cases before diving in.

2. Propose core data structure

Suggest using a dynamic array (list) for O(1) random access and a hash map (dictionary) for O(1) insert/remove by storing value-to-index mappings. Explain that insert appends to the array and adds to the map.

3. Handle deletion and edge cases

For remove, swap the target element with the last element, update the map for the swapped element, then pop from the array and delete from the map. Handle edge cases: removing the last element (just pop), and ensuring the map is updated correctly when swapping.

4. Discuss randomness and verification

Explain that get_random picks a random index from the array using a uniform random number generator. To verify uniformity, you could run statistical tests (e.g., chi-squared) or reason about the RNG's uniformity.

5. Extend for duplicates and thread-safety

For duplicates, store a set of indices per value in the map, and for removal, pick any index from the set. For thread-safety, use locks (e.g., a mutex) around operations, or use concurrent data structures, noting trade-offs in performance.

Key Points to Mention

Use a dynamic array for O(1) random access and a hash map for O(1) insert/remove by mapping values to indices.
Deletion via swap-with-last and updating the map to maintain O(1) expected time.
Edge cases: removing the last element, handling empty structure, and updating indices correctly.
Randomness uniformity depends on the random number generator; can be tested statistically.
For duplicates, store a set of indices per value in the map; removal picks any index.
Thread-safety can be achieved with locks or concurrent data structures, but consider performance implications.

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