The author introduces the problem of updating and performing range queries on a sequence of integers efficiently. They discuss the challenges of updating and querying efficiently, leading to the development of segment trees which allow both operations to run in logarithmic time. The author then introduces Fenwick trees as an alternative solution with a small memory footprint and fast implementation. They explore the implementation of Fenwick trees, highlighting the use of bit tricks. The paper delves into developing a functional DSL for bit manipulations to understand the imperative code of Fenwick trees better. Finally, the author discusses the relationship between segment trees and Fenwick trees, showcasing how inactivated nodes in a segment tree can lead to efficient range queries in Fenwick trees.
https://www.cambridge.org/core/journals/journal-of-functional-programming/article/you-could-have-invented-fenwick-trees/B4628279D4E54229CED97249E96F721D