Binary Indexed Tree
A Binary Indexed Tree (BIT), also known as a Fenwick Tree, is a data structure that efficiently supports dynamic cumulative frequency tables. It allows for quick updates and prefix sum queries, making it useful in scenarios where data changes frequently. The structure uses an array to represent the tree, where each index stores cumulative information.
The main advantage of a Binary Indexed Tree is its ability to perform both updates and queries in logarithmic time, O(log n). This efficiency makes it suitable for applications in competitive programming and algorithms that require frequent calculations of sums over ranges of data.