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Hudson River Trading·Software Engineer·Onsite - System Design / Architecture·Senior

Senior
Jul 2026

Summary

HRT system design round focused on a deque-backed data structure with stable logical indexing. Pretty niche problem, more CS fundamentals than typical system design fare.

Questions Asked (5)

Q1

Design a data structure backed by a deque that supports push/pop from both ends and O(1) access by logical index. How do you use an offset to maintain stable logical indexing as elements are removed from the front?

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

The offset trick clicked for me partway through but I fumbled explaining it cleanly.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the requirements: O(1) push/pop at both ends and O(1) access by logical index, where logical index is stable as elements are removed from the front. Then describe a circular buffer implementation with a head offset that tracks the logical start, and explain how the offset adjusts on front removals to keep indices stable. Finally, discuss trade-offs like resizing, memory overhead, and edge cases.

Pro tip: Emphasize that the offset must be updated modulo capacity to handle wrap-around, and mention that using a power-of-two capacity allows bitwise AND for fast modulo. Also, proactively discuss how to handle resizing while preserving logical indices.

1. Clarify Requirements and Constraints

Confirm that logical index 0 refers to the current front element, and that removing from the front should not change the logical index of remaining elements. Ask about expected sizes, concurrency, and whether resizing is needed.

2. Choose Underlying Data Structure

Propose a circular buffer (ring buffer) backed by a fixed-size array, with head and tail pointers and a size counter. Explain that this gives O(1) push/pop at both ends and O(1) random access.

3. Define Logical Indexing with Offset

Define logical index i as mapping to physical index (head + i) mod capacity. Explain that head is the offset, and that removing from the front increments head (mod capacity) and decrements size, so logical indices of remaining elements stay the same.

4. Handle Operations and Edge Cases

Detail push_front (decrement head mod capacity), push_back (increment tail mod capacity), pop_front (increment head), pop_back (decrement tail), and access (compute physical index). Discuss full/empty conditions and resizing when size equals capacity.

5. Discuss Trade-offs and Optimizations

Mention that resizing requires copying elements in logical order to a new buffer and resetting head to 0. Compare with alternatives like a balanced BST or skip list, and note that the circular buffer is optimal for O(1) operations.

Key Points to Mention

  • Circular buffer with head offset and modulo arithmetic for O(1) access.
  • Logical index stability: removing from front increments head, so logical index i always maps to (head + i) mod capacity.
  • Use of power-of-two capacity for fast modulo via bitwise AND.
  • Handling resizing: copy elements in logical order to a new array, reset head to 0.
  • Edge cases: empty deque, full deque, wrap-around when head or tail crosses the array boundary.
  • Trade-offs: memory overhead of fixed capacity vs. dynamic resizing, and comparison with other data structures.

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

Q2

How would you implement this without stable iterators?

Algorithms & Data StructuresTechnical Trade-offs
Author's notes

Short answer from me: use index arithmetic on a backing array or block-based structure instead of relying on iterator validity.

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AI HintsAI Generated

Suggested Approach

First, clarify what 'stable iterators' means in the context of the problem—likely iterators that remain valid after container modifications. Then, propose alternative designs such as index-based access, copying data, or using data structures that provide stable references (e.g., linked lists, node-based containers). Discuss trade-offs like performance, memory overhead, and complexity.

Pro tip: Acknowledge that the best solution depends on the specific operations and constraints; showing awareness of trade-offs (e.g., O(1) vs O(n) access, memory overhead) demonstrates engineering maturity.

1. Clarify the problem

Ask clarifying questions to understand what 'stable iterators' means here and what operations are required (e.g., insertions, deletions, lookups).

2. Identify constraints

Determine performance requirements, memory limits, and concurrency needs that influence the choice of alternative.

3. Propose alternatives

Suggest index-based access, copying the container, using node-based structures (e.g., linked list, tree), or reference-counted handles.

4. Analyze trade-offs

Compare alternatives on time complexity, memory overhead, and implementation complexity, and justify the best fit for the context.

5. Conclude with a recommendation

Summarize the chosen approach and explain why it meets the requirements, noting any remaining limitations.

Key Points to Mention

  • Definition of stable iterators and why they matter (e.g., avoiding invalidation on modification).
  • Index-based access: simple but may be O(n) for non-random-access containers and can break with insertions/deletions.
  • Copying data: safe but potentially expensive in time and memory.
  • Node-based containers (e.g., std::list, std::map): provide stable references/iterators but may have worse cache locality.
  • Reference-counted handles or smart pointers: allow stable references but add overhead and complexity.
  • Trade-offs between performance, memory, and code complexity; choose based on use case.

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

Q3

How would you handle memory reclamation as elements are popped?

System DesignTechnical Trade-offs
Author's notes

Blanked for a second.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the data structure and memory model, then discuss the trade-offs between eager reclamation (e.g., freeing memory immediately) and lazy reclamation (e.g., deferring until necessary). Emphasize the importance of avoiding memory leaks, fragmentation, and performance overhead, and propose a strategy that balances these factors based on the use case.

Pro tip: Mention that in high-frequency trading systems, predictable low-latency is critical, so you might prefer a custom allocator or object pool to avoid the overhead of frequent malloc/free calls. This shows awareness of domain-specific constraints.

1. Clarify the Data Structure and Memory Model

Ask whether the structure is a stack, queue, or something else, and whether memory is managed manually (e.g., C++) or automatically (e.g., Java). This determines the reclamation options.

2. Identify Reclamation Strategies

Discuss eager reclamation (freeing memory immediately on pop) vs. lazy reclamation (deferring until a threshold or explicit cleanup). Mention reference counting, garbage collection, or manual free.

3. Analyze Trade-offs

Compare strategies on latency, throughput, memory usage, and fragmentation. For example, eager reclamation reduces memory footprint but may cause frequent allocator calls; lazy reclamation improves performance but risks memory bloat.

4. Propose a Solution with Justification

Recommend a strategy based on the context (e.g., real-time system vs. batch processing). For HRT, emphasize low-latency and predictability, suggesting object pooling or custom allocators.

5. Discuss Implementation Details and Edge Cases

Cover how to handle concurrent access, memory fragmentation, and potential leaks. Mention tools like Valgrind or sanitizers for debugging.

Key Points to Mention

  • Eager vs. lazy reclamation and their impact on latency and memory usage
  • Object pooling or custom allocators to reduce allocation overhead
  • Memory fragmentation and its effect on performance
  • Concurrency considerations (e.g., thread safety, lock-free structures)
  • Garbage collection vs. manual memory management
  • Profiling and debugging tools for memory issues

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

Q4

How would concurrency affect the offset map and the deque together?

System DesignTechnical Trade-offs
Author's notes

This one I didn't prep for at all.

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AI HintsAI Generated

Suggested Approach

First, clarify the data structures: an offset map likely maps keys to positions, and a deque is a double-ended queue. Then, analyze how concurrent operations (e.g., insertions, deletions, lookups) on both structures could lead to race conditions, inconsistencies, or performance bottlenecks. Discuss synchronization strategies and trade-offs between lock-based and lock-free approaches.

Pro tip: Emphasize that the offset map and deque must be updated atomically to maintain consistency; consider using a single lock or a lock-free algorithm with atomic operations, but be aware of contention and scalability issues.

1. Clarify the Data Structures

Define the offset map (e.g., key to index mapping) and the deque (double-ended queue) and their typical operations. Explain how they might be used together, such as in a sliding window or task scheduling.

2. Identify Concurrency Challenges

List potential race conditions: e.g., a thread updating the deque while another reads the offset map, leading to stale or inconsistent views. Consider atomicity, visibility, and ordering issues.

3. Propose Synchronization Strategies

Discuss options: coarse-grained locking (simple but may bottleneck), fine-grained locking (complex but scalable), lock-free using atomic operations (e.g., CAS), or transactional memory. Mention how to maintain consistency between the two structures.

4. Analyze Trade-offs

Compare strategies in terms of performance, scalability, complexity, and correctness. For example, lock-free may offer better throughput but is harder to implement and debug; locking is simpler but may limit concurrency.

5. Conclude with a Recommendation

Based on the use case (e.g., high-frequency trading), suggest a suitable approach, such as using a lock-free deque with an atomic offset map, or a single mutex if contention is low.

Key Points to Mention

  • Atomicity: operations on the offset map and deque must appear as a single atomic unit to avoid inconsistencies.
  • Race conditions: concurrent updates can cause lost updates, stale reads, or corruption if not properly synchronized.
  • Lock granularity: coarse-grained locks simplify but reduce parallelism; fine-grained locks increase complexity but improve concurrency.
  • Lock-free data structures: use atomic operations like compare-and-swap (CAS) to avoid locks, but beware of ABA problem and memory reclamation.
  • Memory consistency: ensure proper memory ordering (e.g., acquire-release semantics) to prevent reordering issues.
  • Performance impact: concurrency control adds overhead; consider contention and scalability for high-throughput systems.

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

Q5

How would you support random deletion by logical index?

Algorithms & Data StructuresSystem Design
Author's notes

Worst answer of the session.

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AI HintsAI Generated

Suggested Approach

Clarify that 'logical index' refers to the position in the current sequence, then discuss data structures that support O(1) or O(log n) deletion by index while maintaining order. Compare trade-offs between array-based (O(n) deletion) and tree-based (O(log n) deletion) approaches, and mention hybrid solutions like order-statistic trees or Fenwick trees with a mapping.

Pro tip: Emphasize that in real systems, you often need to balance deletion speed with other operations like insertion and lookup; propose a solution that fits the overall access pattern rather than optimizing deletion in isolation.

1. Clarify requirements

Confirm what 'logical index' means (e.g., position in the current sequence after deletions) and the expected frequency of deletions versus other operations.

2. Evaluate naive approaches

Discuss using a dynamic array: deletion by index is O(n) due to shifting, which may be acceptable if deletions are rare.

3. Propose efficient data structures

Introduce order-statistic trees (e.g., balanced BST with subtree sizes) or Fenwick tree with binary lifting to achieve O(log n) deletion by index.

4. Address implementation details

Explain how to maintain the mapping between logical indices and physical storage, and handle updates after deletion.

5. Compare trade-offs

Summarize time/space complexity and suitability for different scenarios, such as high-frequency deletions or memory constraints.

Key Points to Mention

  • Order-statistic tree (e.g., augmented AVL or red-black tree) for O(log n) deletion by rank
  • Fenwick tree (Binary Indexed Tree) with binary lifting for O(log n) index lookup and deletion
  • Dynamic array with lazy deletion and compaction for amortized O(1) deletion if order doesn't need to be strictly maintained
  • Trade-offs: O(n) vs O(log n) deletion, memory overhead, and impact on other operations
  • Use cases: real-time systems where deletions are frequent and order matters
  • Potential for hybrid approaches: e.g., chunked arrays or skip lists

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