DE Applications: Prefix Sums in Spark and pandas

Concepts: pyPandasCumsum, pySparkWindow, pyRollingOptimization

Here is the part that turns a good algorithm answer into an exceptional data engineering answer. Prefix sums are not academic constructs -- they are the engine under several production pipeline patterns. When you call cumsum() in pandas, Spark's window functions compute running totals, or you write a rolling aggregation over a sorted dataset, you are using prefix sums. Understanding this connection lets you reason about performance, explain trade-offs, and design better pipelines. It also gives you material to bridge back to in the interview. pandas cumsum and Rolling Windows The pandas rolling() with a fixed window is literally implementing the prefix-sum difference trick: rolling_sum[i] = prefix[i+1] - prefix[i-K+1]. This is why rolling() on a large DataFrame is O(n) not O(n*K): it uses