What is a Binary Indexed Tree (BIT)?

A Binary Indexed Tree, also known as a Fenwick Tree, is a data structure that can efficiently update elements and calculate prefix sums in a table of numbers.

What are the time complexities of BIT operations?

Both updating a value and querying a prefix sum in a Binary Indexed Tree take O(log n) time, where n is the number of elements. Building the tree takes O(n log n) time.

Advanced Data Structures

Binary Indexed Tree (Fenwick Tree) Guide

Unlock efficient solutions for range sum queries and updates with the Binary Indexed Tree. This guide provides a clear implementation, common problems, and AI-powered hints.

Fenwick Tree Implementation

A Binary Indexed Tree is a powerful data structure for problems involving prefix sums. It's more space-efficient than a segment tree and often simpler to implement.

                            class FenwickTree {
                            constructor(size) {
                            this.tree = new Array(size + 1).fill(0);
                            }
                            
                            update(index, delta) {
                            index++;
                            while (index < this.tree.length) {
                            this.tree[index] += delta;
                            index += index & -index;
                            }
                            }
                            
                            query(index) {
                            index++;
                            let sum = 0;
                            while (index > 0) {
                            sum += this.tree[index];
                            index -= index & -index;
                            }
                            return sum;
                            }
                            
                            rangeSum(left, right) {
                            return this.query(right) - this.query(left - 1);
                            }
                            }
                        

AI Coach Hint: The magic of the Fenwick Tree is in the bitwise operation `index & -index`, which gets the least significant bit. This allows you to jump to the next relevant index in the tree for both updates and queries, achieving the O(log n) complexity.