Two-Heap Running Median: Full Implementation

Concepts: pyStreamingMedian, pyLazyDeletion, pyTwoHeapFull

You saw the basic two-heap MedianFinder in the intermediate lesson. The advanced version adds two things: a proof of why this is O(n log n) and why it cannot be beaten for streaming, and the full sliding window implementation with lazy deletion. This is the complete picture. If you can implement this correctly from scratch in an interview, you are demonstrating algorithm design skill that puts you firmly in the staff-level candidate pool. Why O(n log n) is the Lower Bound for Streaming Median For a static dataset, finding the median is O(n) with QuickSelect. But for a streaming dataset where you must output the running median after each insertion, you cannot do better than O(log n) per insertion. Why? Because the median position in the sorted order changes with every insertion, and maintai