Xai·Machine Learning Engineer·Technical Phone Screen·Senior

Senior

Jun 2026

Summary

Interviewed for an MLE role at xAI and got a data structures problem that looks deceptively simple until you actually try to make all three operations O(1). Classic design question but the constraints are tight enough that you can't just wing it.

Questions Asked (1)

Design a data structure that supports inserting, removing, and sampling a uniformly random element, all in average O(1) time, with no duplicate values allowed.

Algorithms & Data StructuresSystem DesignTechnical Trade-offs

Author's notes

The insert and remove feel easy until you realize getRandom is the hard part.

Create a free account to read the full note

AI HintsAI Generated

Suggested Approach

Combine a dynamic array (for O(1) random access) with a hash map (for O(1) value-to-index lookup). Insert by appending to the array and adding to the map; remove by swapping the target with the last element, updating the map, and popping; sample by picking a random index in the array. This yields average O(1) for all operations.

Pro tip: Mention that the swap-with-last trick is the key to O(1) removal, and discuss how this design scales for ML applications like experience replay in reinforcement learning, where uniform sampling of transitions is crucial.

1. Clarify requirements and constraints

Confirm that all operations must be average O(1), no duplicates allowed, and that sampling must be uniformly random. Ask about expected data size and whether thread-safety is needed.

2. Choose the right data structures

Select a dynamic array (e.g., Python list, C++ vector) for O(1) random access and a hash map (e.g., dict, unordered_map) for O(1) value-to-index lookup.

3. Design insert and sample operations

For insert: append value to array, store its index in map. For sample: generate a random index in [0, size-1] and return the array element at that index.

4. Design remove operation with swap-with-last

To remove a value: look up its index, swap it with the last element in the array, update the map for the swapped element, then pop the last element and remove the value from the map.

5. Analyze complexity and edge cases

Argue that each operation is average O(1) due to hash map operations and array indexing. Discuss edge cases: removing the last element, removing the only element, and handling duplicates (reject or ignore).

Key Points to Mention

Hash map provides O(1) average lookup for value-to-index mapping.
Dynamic array provides O(1) random access for uniform sampling.
Swap-with-last trick enables O(1) removal by avoiding shifting elements.
Uniformity is guaranteed by picking a random index uniformly from the array.
No duplicates: check map before insertion; if present, handle appropriately (e.g., return false or ignore).
Average O(1) assumes good hash function and low collision rate; worst-case O(n) for hash map operations.

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