Advanced DE Patterns: Sparse, Floating Point, and Event Log Prefix Sums

Concepts: pySparsePrefixSum, pyKahanSummation, pyFinancialPrecision

Three advanced scenarios that trip up even strong candidates: sparse time-series (most time buckets are empty and a dense prefix array wastes memory), prefix sums over sorted event logs (you do not have random access, you need binary search), and floating point accumulation errors in financial data (your prefix sum is silently wrong after millions of additions). These are the production gotchas that separate engineers who have actually built these systems from those who have only solved LeetCode problems. Sparse Prefix Sums If you have 86,400 seconds per day but only 500 events, a dense prefix array of 86,400 entries is wasteful and slow to rebuild. Instead, store only the active buckets in a sorted list and use binary search for queries. The prefix sum is built over the sorted active buck