I knew immediately this was a sliding window problem but the tricky part is maintaining the running max and min efficiently as the window moves.
Use a sliding window with two monotonic deques to maintain the max and min of the current window in O(1) amortized time. Expand the right pointer, and while the difference between max and min exceeds the limit, shrink from the left. Track the maximum window length throughout.
Pro tip: Emphasize that the monotonic deques store indices, not values, so you can efficiently remove elements that fall out of the window. Also, mention that this approach handles negative numbers and duplicates seamlessly.
Restate the problem to ensure understanding: find the longest contiguous subarray where max - min <= limit. Ask about edge cases like empty array, negative numbers, and whether the limit can be negative.
Explain that you'll maintain a window [left, right] and expand right. Use two deques to track the maximum and minimum values in the current window.
For the max deque, before adding a new element, remove indices from the back while the corresponding value is <= the new value. For the min deque, remove while the value is >= the new value. Also, remove indices from the front if they fall out of the window.
While max - min > limit, increment left. If the front indices of the deques are less than left, pop them. Update the maximum length after each valid window.
State that each element is added and removed from each deque at most once, giving O(n) time and O(n) space. Walk through a small example to verify correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Classic union-find setup but with the extra twist of tracking max component size.
Use Union-Find (Disjoint Set Union) to dynamically track connected components as cells flip to land. For each flip, union the new land cell with adjacent land cells, updating the island count and maintaining the size of the largest island. This approach efficiently handles the incremental nature of the problem with near-constant time per operation.
Pro tip: Mention that Union-Find with union by rank and path compression gives amortized O(α(N)) per operation, and that you can maintain the maximum island size by updating it only when unions occur, avoiding a full scan each time.
Confirm grid dimensions, whether flips are given as a list of coordinates, and if multiple flips can occur at the same cell. Ask about expected input size to choose the right algorithm.
Explain that Union-Find is ideal for dynamic connectivity. Each land cell is a node; initially all water cells are inactive. When a cell becomes land, it becomes an active node.
For each flipped cell, mark it as land, increment island count, and initialize its size to 1. Then check its four neighbors: if a neighbor is land, union the two sets, decrement island count, and update the size of the merged set.
Keep a variable for the maximum island size seen so far. After each union, compare the new merged size with the current maximum and update if larger. Also handle the case when a new island of size 1 is created.
After processing each flip, record the current island count and the maximum island size. Return these as a list of pairs or update a result array.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying requirements (exact vs. rolling window, precision, scale, per-user vs. global) and then propose a simple solution like a circular buffer or timestamp queue for the 5-minute hit counter. For the rate limiter, extend the design to per-user tracking with configurable limits, discussing trade-offs between memory, accuracy, and performance, and consider distributed scenarios if needed.
Pro tip: Mention that a sliding window log can be memory-heavy at scale, so you might use a sliding window counter with approximation or a token bucket for smoother rate limiting, and always discuss how you'd handle distributed rate limiting with Redis or a similar store.
Ask about the definition of 'last 5 minutes' (rolling vs. fixed), expected scale (hits per second, number of users), precision requirements, and whether the solution needs to be distributed.
Propose a data structure like a circular buffer of timestamps or a queue with timestamps, and explain how to evict old entries and count hits in O(1) or O(k) time.
Adapt the design to track per-user request timestamps, with configurable limits and window size, and discuss how to enforce the limit (e.g., reject or queue requests).
Compare approaches (e.g., sliding window log vs. sliding window counter vs. token bucket) in terms of memory, accuracy, and complexity, and suggest optimizations like sharding or approximate counting.
If relevant, discuss how to scale the solution across multiple servers using a centralized store (e.g., Redis) or a distributed algorithm, and mention concurrency, cleanup, and monitoring.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.