You could have invented Fenwick trees

Abstract

Fenwick trees, also known as binary indexed trees are a clever solution to the problem of maintaining a sequence of values while allowing both updates and range queries in sublinear time. Their implementation is concise and efficient - but also somewhat baffling, consisting largely of nonobvious bitwise operations on indices. We begin with segment trees, a much more straightforward, easy-to-verify, purely functional solution to the problem, and use equational reasoning to explain the implementation of Fenwick trees as an optimized variant, making use of a Haskell EDSL for operations on infinite two's complement binary numbers.