I knew this one going in but still fumbled the eviction logic at first.
Start by clarifying requirements and constraints, then propose a hash map combined with a doubly linked list to achieve O(1) get and put. Explain the design, walk through an example, and discuss trade-offs and edge cases.
Pro tip: Mention that you would use a sentinel head and tail to simplify edge cases, and discuss how the design can be extended for thread safety or persistence if needed.
Ask about cache capacity, eviction policy (LRU), and whether operations need to be thread-safe. Confirm that get and put must be O(1).
Suggest using a hash map for O(1) access to nodes and a doubly linked list to maintain recency order. Explain how they work together.
Describe get: if key exists, move node to front and return value; else return -1. Describe put: if key exists, update value and move to front; else add new node and evict least recently used if capacity exceeded.
Trace through a sequence of operations to demonstrate correctness and O(1) time complexity.
Mention alternative implementations (e.g., OrderedDict in Python), handling of null values, and potential concurrency issues.
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Went with Union-Find because I'd just reviewed it.
Start by clarifying the problem constraints (e.g., n up to 10^5, edges list format) and then present two standard solutions: Union-Find (Disjoint Set Union) and DFS/BFS. Compare their trade-offs in terms of time/space complexity, implementation simplicity, and suitability for dynamic graphs, then code the most appropriate one.
Pro tip: Mention that Union-Find with path compression and union by rank achieves near O(1) amortized time per operation, making it ideal for large graphs, and that it can handle dynamic edge additions, unlike DFS. Also, note that the number of components starts at n and decreases by 1 for each successful union.
Ask about constraints: size of n, number of edges, whether edges can be repeated or self-loops, and if the graph is guaranteed to be connected initially. Confirm the expected output (just the count).
Present two main approaches: Union-Find (DSU) and graph traversal (DFS/BFS). Explain how each works and their time/space complexities.
Highlight that Union-Find is better for dynamic graphs and has near-constant time per operation, while DFS/BFS is simpler to implement and may be preferred for static graphs. Mention that both are O(n + e) time.
Write clean code for the selected approach, handling edge cases like empty graph or no edges. For Union-Find, include path compression and union by rank.
Walk through a small example (e.g., n=5, edges=[[0,1],[1,2],[3,4]]) to show the component count. Discuss potential pitfalls like 0-indexed vs 1-indexed nodes.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Mentioned a global read-write lock and the interviewer immediately pushed on contention.
Start by explaining the need for thread safety in an LRU cache, then describe how to protect the shared data structures (hash map and doubly linked list) using locks. Discuss the trade-offs between coarse-grained and fine-grained locking, and identify where contention arises under high concurrency.
Pro tip: Mention that Amazon often deals with high-throughput systems, so you should emphasize minimizing lock contention and consider lock-free or read-optimized approaches like read-write locks or sharding.
Point out that the hash map and doubly linked list are shared mutable state that must be protected from concurrent access.
Discuss options: a single global lock (simple but high contention), fine-grained locks per bucket or node, or read-write locks to allow concurrent reads.
Explain that the head and tail of the linked list are frequently accessed during get and put operations, causing contention, especially with a global lock.
Suggest sharding the cache into multiple independent segments, each with its own lock, or using lock-free data structures with atomic operations.
Compare complexity, scalability, and correctness; note that sharding reduces contention but complicates eviction and may lead to uneven load.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying that LRU evicts based on recency while LFU evicts based on access frequency, and that maintaining O(1) for LFU requires careful data structure design. Then propose a solution using a combination of a frequency map, a doubly linked list per frequency, and a min-frequency pointer, explaining how get and put operations update frequencies in constant time.
Pro tip: Mention that LFU can suffer from cache pollution where historically frequent items block new items; briefly discuss aging or frequency decay as a practical enhancement, showing you think beyond textbook algorithms.
Confirm that the cache has a fixed capacity, operations are get(key) and put(key, value), and both must be O(1). Note that ties in frequency can be broken by LRU order for determinism.
Use a hash map for key-to-node lookup, a frequency map mapping frequency to a doubly linked list of nodes with that frequency, and a min_freq variable to track the lowest frequency for O(1) eviction.
On get, retrieve the node, increment its frequency, move it from its current frequency list to the next frequency list, and update min_freq if the old list becomes empty.
On put, if key exists, update value and increment frequency like get. If new, insert with frequency 1; if at capacity, evict the least frequently used node (from min_freq list, LRU order for ties) before inserting.
Explain that all operations are O(1) due to hash map lookups and constant-time list manipulations. Discuss edge cases like capacity 1, updating existing keys, and tie-breaking.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Union-Find is the obvious answer here and I said so.
Compare DFS and Union-Find for streaming graph edges, focusing on dynamic connectivity and scalability. Highlight that Union-Find is better suited for incremental edge additions due to near-constant time per operation, while DFS requires reprocessing. Discuss trade-offs and mention Amazon's leadership principles like customer obsession and deliver results.
Pro tip: Mention that Union-Find with path compression and union by rank achieves amortized O(α(n)) per operation, making it ideal for large-scale streaming scenarios, and relate it to real-world systems like network monitoring or social network analysis.
Restate the question to ensure understanding: we need to determine which algorithm scales better when edges arrive as a stream, requiring dynamic connectivity queries.
Explain that DFS is typically used for static graphs; for each new edge, it would require re-running DFS from scratch, leading to O(V+E) per edge, which is inefficient for large streams.
Describe Union-Find's ability to incrementally add edges and answer connectivity queries in nearly constant amortized time, making it highly scalable for streaming scenarios.
Summarize that Union-Find scales better due to its incremental nature and efficient operations, while DFS is impractical for dynamic updates.
Tie the answer to Amazon's leadership principles, such as customer obsession (efficient systems) and deliver results (scalable solutions), and mention potential use cases like real-time network analysis.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.