Top-K Frequent Elements: From Brute Force to Clever

Concepts: pyTopK, pyBucketSort, pyHotKey

Top-K frequent elements is the most practically relevant frequency problem for data engineers. Top-K error codes in a production log. Top-K API endpoints by call volume. Top-K user IDs in a clickstream. This is business intelligence, not abstract algorithms. Interviewers know this, and they use it to see if you can connect coding to real systems. Start with the clean solution, then tease the O(n) approach, and watch the interviewer lean in. The O(n log n) Solution: Sort by Frequency most_common(k) is O(n log k) using heapq.nlargest. For small k (top 10 out of millions of elements), this is much faster than sorting all elements. Make sure you say this: 'most_common uses a heap internally, so it is O(n log k) not O(n log n). For small k and large n, that difference matters.' That one sentenc