I went with a map from user pairs to a sorted list of timestamps.
Clarify requirements first: updates are append-only, queries are point-in-time, and the system must handle high write throughput and low-latency reads. Then propose a hybrid design: store each follow edge as a time-stamped record in a write-optimized store (e.g., LSM-tree or log), and maintain a per-user interval index (e.g., sorted list of (start, end) intervals) for fast point queries. Discuss trade-offs between memory, latency, and consistency, and mention how to handle deletions (unfollows) as interval closures.
Pro tip: Emphasize that this is a temporal graph problem and that you would use a persistent data structure (like a persistent balanced BST or versioned key-value store) to answer historical queries efficiently, showing you understand the difference between current-state and time-travel queries.
Ask about query patterns (point-in-time vs. range), update frequency, read/write ratio, latency requirements, and whether deletions (unfollows) are supported. This shows you think about real-world usage before jumping to a solution.
Represent each follow relationship as an interval [start_time, end_time) where end_time is infinity if still active. Store these intervals in a structure that allows efficient point queries, such as a sorted list per (follower, followee) pair or a global interval tree.
Use a write-optimized store (e.g., LSM-tree, append-only log) for updates, and build an in-memory index (e.g., hash map from (A,B) to a sorted list of intervals) for fast reads. Discuss how to shard by follower or followee to scale horizontally.
Update: append a new interval with start=t and end=infinity, and if there was a previous open interval, close it at t. Query: look up the interval list for (A,B) and binary search for the interval containing t. Explain time complexity: O(log n) for query, O(1) amortized for update.
Compare memory vs. latency: keeping all intervals in memory is fast but costly; using a persistent database (e.g., RocksDB with timestamps) is more scalable but slower. Mention compression of intervals, caching recent queries, and handling out-of-order updates.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Pretty straightforward extension once the base structure is there.
First, clarify the existing design and scale requirements, then propose a bidirectional index that stores edges in both directions and supports efficient intersection. Discuss how to leverage sorted adjacency lists or hash sets to find mutual followers in O(min(|A|, |B|)) time, and consider trade-offs for large-scale systems.
Pro tip: Mention that mutual-follower queries are essentially set intersections, and that using a hash-based approach can be faster for small sets while sorted arrays enable merge-based intersection with better cache locality. Also, note that caching frequent mutual-follower pairs can significantly reduce latency.
Ask about scale (number of users, average followers), read/write ratio, latency requirements, and whether the graph is directed. Confirm that 'mutual-follower' means users who follow each other.
Explain how the current design handles follower queries (e.g., adjacency lists) and why it may not efficiently support bidirectional queries. Highlight the need for an index that allows fast lookup in both directions.
Suggest storing both outgoing and incoming edges (followers and following) for each user. For mutual followers, compute the intersection of a user's followers and the set of users they follow.
Choose an efficient intersection method: if sets are sorted, use a merge-based approach; if unsorted, use hash sets. Discuss complexity and trade-offs (e.g., O(min(|A|, |B|)) with hashing).
Discuss partitioning, sharding, and caching strategies (e.g., Redis) for hot mutual-follower pairs. Mention precomputation for frequently queried pairs and consistency trade-offs.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying the data model and constraints (e.g., graph size, directionality, update frequency). Then outline an algorithm that finds all second-degree connections of A and counts distinct intermediaries for each candidate, using efficient data structures like hash maps and sets. Finally, discuss ranking, scalability, and trade-offs between precomputation and on-the-fly computation.
Pro tip: Mention that you would deduplicate intermediaries per candidate to avoid double-counting, and discuss how to handle large graphs with distributed processing or approximate algorithms if needed.
Ask about graph size, directionality, whether connections are symmetric, and if recommendations should be real-time or batch. This shapes algorithm choice and scalability considerations.
For each intermediary B connected to A, iterate over B's connections C (excluding A and existing direct connections). Use a hash map to count distinct intermediaries per candidate C.
Sort candidates by the count of distinct intermediaries in descending order. Optionally filter out users already directly connected to A or apply other business rules.
Time complexity is O(sum of degrees of A's neighbors). Discuss optimizations like precomputing second-degree connections, using distributed graph processing (e.g., Pregel), or approximate counting for very large graphs.
Compare precomputation vs. on-the-fly, exact vs. approximate counts, and how to handle dynamic updates. Mention potential use of MapReduce or graph databases.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.