The Binary Indexed Tree (BIT), also known as a Fenwick Tree, is a data structure that efficiently supports dynamic cumulative frequency tables.
It allows you to compute prefix sums and update elements in O(log n) time. It is particularly useful for problems that require frequent range sum queries and updates.
Steps:
The tree is implemented using an array, where each node represents a cumulative sum of elements.
Update Operation: Updates an element in the array, and its impact propagates upward.
Query Operation: Computes the sum of elements from the start to a given index by summing the values of the relevant nodes.