Feature Request: Implement Fenwick Tree (Binary Indexed Tree)

[arvinder004]

As mentioned, the Fenwick Tree is a data structure that efficiently calculates prefix sums and performs single element updates on an array. The core idea is that each element in the Fenwick Tree array stores the sum of a specific range of elements from the original array. The size of this range is determined by the position of the element and its binary representation, specifically the least significant bit.

Use Cases:

Fenwick Trees are particularly useful in scenarios where you need to perform frequent prefix sum queries and single element updates on an array. Some common use cases include:

Range Sum Queries (with single point updates): While segment trees can handle general range sum queries, Fenwick Trees are often simpler and have lower constant factors for the specific case of prefix sums and single point updates.

Calculating Cumulative Frequencies: Useful in statistical applications to efficiently track the cumulative count of events.

Solving Competitive Programming Problems: Many competitive programming problems involve these types of operations, making the Fenwick Tree a valuable tool. Examples include problems related to:
>>Counting inversions in an array.
>>Range updates and point queries (with a slight modification using two Fenwick Trees).
>>Problems involving dynamic arrays where you need to query sums of ranges.

Data Stream Analysis: Can be used to maintain running totals and perform updates in real-time data streams.

I am willing to contribute to the implementation of this data structure if the project maintainers are interested. I would appreciate feedback on this proposal and any specific implementation guidelines.