Solve Throughput, Rate Limiting, and LFU

The interview included the following coding tasks: 1. **Minimum processing speed**: You are given an array `piles`, where `piles[i]` is the size of the `i`th pile, and an integer `h`. In one hour, you may choose exactly one pile and process up to `k` items from it. If a pile has fewer than `k` items remaining, you finish it and the rest of that hour is unused. Return the minimum integer `k` such that all piles can be finished within `h` hours. 2. **Implement a rate limiter**: Design and implement a rate limiter that enforces a rule such as allowing at most `limit` requests per user within any rolling `windowSeconds` interval. Provide an API like `allow(userId, timestamp) -> bool`. Explain how you store request history, how expired requests are removed efficiently, and what the time and space complexity is. 3. **Implement an LFU eviction structure**: Design a key-value cache with a fixed capacity. Support `get(key)` and `put(key, value)` in O(1) average time. When the cache is full, evict the key with the lowest access frequency. If multiple keys have the same frequency, evict the least recently used among them.