Design a least-recently-used cache

Design and implement a least-recently-used (LRU) cache with a fixed capacity. Support get(key) -> value and put(key, value) in average O(1) time. When the cache is full, evict the least recently used entry. Explain your choice of data structures, detail how you update recency on reads and writes, and describe how you handle updates to existing keys, missing keys, and capacity edge cases (e.g., capacity = 0). Analyze time and space complexity.

What a Strong Answer Covers

• A clear algorithm with the right data structures and enough pseudocode or code-level detail to implement it.
• A correctness argument that explains why the algorithm covers all required cases.
• Time and space complexity, plus at least one alternative approach when relevant.
• Focused tests for normal cases, edge cases, and failure modes.

Follow-up Questions

• How would the approach change if the input were streaming or too large for memory?
• What invariants would you assert in production code?
• Which tests would catch off-by-one, duplicate, or tie-breaking bugs?

Solution

Solution Alignment

The prompt asks for an implementation-level answer. The safest way to present it is to define the state, maintain clear invariants, then walk through complexity and tests.

Problem Restatement

Design and implement a least-recently-used (LRU) cache with a fixed capacity. Support get(key) -> value and put(key, value) in average O(1) time. When the cache is full, evict the least recently used entry. Explain your choice of data structures, detail how you update recency on reads and writes, and describe how you handle updates to existing keys, missing keys, and capacity edge cases (e.g., capacity = 0). Analyze time and space complexity.

Recommended Approach

Use a hash map from key to doubly linked-list node plus a doubly linked list ordered by recency. get moves the node to the front. put updates and moves an existing node, or inserts a new node at the front and evicts the tail when capacity is exceeded.

Correctness

The implementation should maintain an invariant after each loop or operation that directly matches the problem statement. At termination, that invariant implies the returned value has considered every valid candidate exactly once, or has preserved the required data-structure state after every API call.

Complexity

get and put are O(1) average time. Space is O(capacity).

Edge Cases and Tests

Capacity 0 or 1, updating an existing key, eviction order after get, repeated puts, and missing-key gets.