Amazon·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Jun 2026

Summary

Amazon SWE interview with a data structure design question that seemed straightforward at first but had a few wrinkles worth thinking through carefully. One question, focused on system design and complexity analysis.

Questions Asked (1)

Design a data structure that accepts login events (user_id, timestamp) and can return the user with the earliest login among users who have logged in exactly once. Walk through insert and query complexity, and explain how the structure needs to handle a user logging in a second time.

Algorithms & Data StructuresSystem DesignTechnical Trade-offs

Author's notes

The 'exactly once' constraint is what makes this interesting.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the requirements: we need to support insertions of login events and queries for the user with the earliest login among those who have logged in exactly once. Propose a data structure that maintains a set of unique users and a min-heap of their first login times, and explain how to handle a second login by removing the user from the set and marking them as ineligible. Then analyze the time and space complexity of each operation.

Pro tip: Mention that you would use a hash map to track login counts and a min-heap for efficient retrieval, but also discuss the trade-off of lazy deletion versus eager removal to handle duplicates, showing awareness of real-world performance considerations.

1. Clarify requirements and constraints

Ask about expected volume, whether timestamps are unique, and if queries are frequent. Confirm that we need to handle multiple logins per user and that only users with exactly one login are considered.

2. Design the data structure

Propose using a hash map to store each user's login count and first timestamp, and a min-heap (priority queue) keyed by timestamp to retrieve the earliest login. Alternatively, consider a balanced BST or a combination of hash map and sorted set.

3. Handle insertions and duplicate logins

On insert, if the user is new, add them to the map with count 1 and push their timestamp to the heap. If the user already exists, increment their count and mark them as ineligible (e.g., set count > 1), and optionally remove them from the heap lazily.

4. Implement the query operation

To find the user with the earliest login among those with exactly one login, pop from the min-heap until the top element corresponds to a user with count 1. Return that user, or null if none.

5. Analyze complexity and trade-offs

Insert: O(log n) for heap push, O(1) for map update. Query: amortized O(log n) due to lazy deletions. Space: O(n). Discuss alternatives like using a balanced BST for O(log n) insert and O(1) query, or a doubly linked list for O(1) operations if timestamps are monotonic.

Key Points to Mention

Use a hash map to track user login counts and first timestamps.
Use a min-heap to efficiently retrieve the earliest login timestamp.
Handle duplicate logins by marking users as ineligible and using lazy deletion from the heap.
Analyze time complexity: O(log n) for insert (heap push), O(log n) amortized for query (due to lazy deletions).
Discuss space complexity: O(n) for storing user data.
Mention alternative data structures like balanced BST or sorted set and their trade-offs.

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