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Two Sigma·Software Engineer·Onsite - Coding / Algorithms·Intermediate

IntermediatePrefer not to say
May 2026

Summary

Two Sigma coding round for a software engineer role. One question, but it had layers that I didn't fully appreciate until I was already halfway through a naive solution.

Questions Asked (1)

Q1

Implement a hash map from scratch supporting put and update, and get operations, using only arrays and your own linked list nodes. No built-in hash table types allowed. Must handle collisions via separate chaining and resize dynamically when the load factor exceeds 0.75.

Algorithms & Data StructuresTechnical Trade-offs
Author's notes

I got the basic structure down pretty fast, bucket array plus linked list nodes per bucket, and the put and get logic wasn't too bad.

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AI HintsAI Generated

Suggested Approach

Start by clarifying requirements and constraints, then outline the design: an array of buckets, each bucket a linked list of key-value nodes, with a hash function and dynamic resizing when load factor exceeds 0.75. Walk through the implementation of put, get, and resize, emphasizing collision handling via separate chaining and the rehashing process.

Pro tip: Mention that you'll use a good hash function (e.g., for strings, a polynomial rolling hash) and that resizing doubles the capacity to maintain amortized O(1) operations. Also, discuss how you handle null keys and the trade-offs of using separate chaining versus open addressing.

1. Clarify requirements and constraints

Ask about key/value types, expected operations, and any constraints (e.g., thread safety, memory). Confirm that only arrays and custom linked list nodes are allowed.

2. Design the data structure

Propose an array of buckets, each bucket being a linked list of nodes containing key, value, and next pointer. Define a hash function and initial capacity.

3. Implement core operations

Write put (insert or update), get, and resize methods. For put, compute hash, find bucket, traverse list to update or append. For get, traverse list to find key.

4. Handle resizing and load factor

Track size and capacity; when load factor > 0.75, double capacity and rehash all existing entries into the new bucket array.

5. Analyze complexity and trade-offs

Discuss time complexity: average O(1) for put/get, worst-case O(n) with many collisions. Mention space complexity and trade-offs of separate chaining vs open addressing.

Key Points to Mention

  • Hash function design: use a good hash (e.g., polynomial rolling hash for strings) and ensure uniform distribution.
  • Collision resolution: separate chaining with linked lists; explain how to traverse and update nodes.
  • Dynamic resizing: double capacity when load factor > 0.75, rehash all entries to maintain performance.
  • Load factor: define as size/capacity; explain why 0.75 is a good threshold (trade-off between time and space).
  • Time complexity: average O(1) for put/get, worst-case O(n) due to collisions; amortized O(1) with resizing.
  • Edge cases: null keys, duplicate keys (update), and handling resizing during iteration.

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