Openai·Software Engineer·Onsite - System Design / Architecture·Senior

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May 2026

Summary

OpenAI system design round for a software engineer role, one meaty question about building a memory allocator from scratch. The kind of problem where you think you know what they want and then realize halfway through you're missing something fundamental.

Questions Asked (1)

Design and implement a memory allocator that supports allocate(size) and free(pointer) operations, both running in O(log N) time where N is the number of free intervals. The allocator manages a fixed memory region and must merge adjacent free intervals on free.

Algorithms & Data StructuresSystem DesignTechnical Trade-offs

Author's notes

I started with a sorted list of free intervals keyed by start address, which is the obvious move, but then they pushed on how you'd find a free block of a given size efficiently without scanning the whole thing.

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AI HintsAI Generated

Suggested Approach

Start by clarifying requirements and constraints, then propose a data structure like a balanced BST or skip list to store free intervals keyed by start address, enabling O(log N) operations. Explain how allocate finds a suitable interval, splits it, and updates the structure, while free inserts the interval and merges with adjacent free intervals.

Pro tip: Mention that using a balanced BST (e.g., red-black tree) or a skip list provides O(log N) for search, insert, and delete, and that merging adjacent intervals requires finding predecessor and successor, which is efficient in these structures. Also, discuss how to handle edge cases like allocation at the beginning or end of the memory region.

1. Clarify Requirements and Constraints

Ask about the memory region size, alignment requirements, allocation strategies (first-fit, best-fit), and whether the allocator needs to be thread-safe. Confirm that O(log N) is required for both allocate and free, where N is the number of free intervals.

2. Choose Data Structure

Select a balanced binary search tree (e.g., red-black tree) or a skip list to store free intervals, keyed by start address. This allows O(log N) search, insert, and delete, and supports finding predecessor and successor for merging.

3. Design Allocate Operation

Traverse the tree to find a free interval that fits the requested size (e.g., first-fit or best-fit). If found, split the interval: allocate the requested block and reinsert the remaining free portion (if any) into the tree. Return the pointer to the allocated block.

4. Design Free Operation

Insert the freed interval into the tree. Then check for adjacent free intervals (predecessor and successor) and merge them if they are contiguous. Update the tree accordingly to maintain O(log N) complexity.

5. Analyze Complexity and Trade-offs

Explain that each operation involves O(log N) tree operations, so overall O(log N). Discuss trade-offs: balanced BST vs. skip list (implementation complexity, memory overhead), and allocation strategies (first-fit vs. best-fit) affecting fragmentation.

Key Points to Mention

Use of a balanced BST (e.g., red-black tree) or skip list to maintain free intervals sorted by start address.
Allocate: find a suitable interval, split it, and update the tree; Free: insert and merge with adjacent intervals.
Merging requires finding predecessor and successor in the tree, which is O(log N).
Complexity analysis: each operation involves O(log N) tree operations, satisfying the requirement.
Trade-offs: first-fit vs. best-fit allocation strategies and their impact on fragmentation.
Edge cases: allocation at boundaries, zero-size allocation, and handling of coalescing multiple intervals.

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