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Commit 1a4fe11

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malfpletrekhleb
authored andcommitted
Added Binary Indexed Tree / Fenwick Tree Implementation (trekhleb#51)
* added fenwick tree implementation * added fenwick tree implementation
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export default class FenwickTree {
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/**
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* Constructor creates empty fenwick tree of size 'size',
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* however, array size is size+1, because index is 1-based
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* @param {number} [size]
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*/
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constructor(size) {
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this.n = size;
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this.arr = [];
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for (let i = 0; i <= size; i += 1) this.arr.push(0);
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}
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/**
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* Adds v to index x
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* @param {number} [x]
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* @param {number} [v]
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*/
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update(x, v) {
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if (x < 1 || x > this.n) return;
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for (let i = x; i <= this.n; i += (i & -i)) {
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this.arr[i] += v;
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}
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}
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/**
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* query sum from index 1 to x
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* @param {number} [x]
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* @return {number} sum
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*/
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query(x) {
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if (x > this.n) return this.query(this.n);
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let ret = 0;
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for (let i = x; i > 0; i -= (i & -i)) {
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ret += this.arr[i];
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}
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return ret;
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}
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/**
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* query sum from index l to r
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* @param {number} [l]
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* @param {number} [r]
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* @return {number}
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*/
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queryRange(l, r) {
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if (l > r) return 0;
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return this.query(r) - this.query(l - 1);
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}
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}
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# Binary Indexed Tree / Fenwick Tree
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A simple data structure that supports fast range queries in an array. However, it is usually only valid for reversible operations, like addition and subtraction
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This implementation uses the basic range sum query and point update. All the indexes are 1-based
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- [Wikipedia](https://en.wikipedia.org/wiki/Fenwick_tree)
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- [Geeksforgeeks](https://www.geeksforgeeks.org/binary-indexed-tree-or-fenwick-tree-2/)
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import FenwickTree from '../FenwickTree';
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describe('FenwickTree', () => {
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it('should create empty fenwick tree of correct size', () => {
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const tree1 = new FenwickTree(5);
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expect(tree1.arr.length).toBe(5 + 1);
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for (let i = 0; i < 5; i += 1) {
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expect(tree1.arr[i]).toBe(0);
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}
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const tree2 = new FenwickTree(50);
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expect(tree2.arr.length).toBe(50 + 1);
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});
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it('should correctly execute queries', () => {
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const tree = new FenwickTree(5);
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tree.update(1, 4);
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tree.update(3, 7);
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expect(tree.query(1)).toBe(4);
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expect(tree.query(3)).toBe(11);
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expect(tree.query(5)).toBe(11);
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expect(tree.queryRange(2, 3)).toBe(7);
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tree.update(2, 5);
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expect(tree.query(5)).toBe(16);
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tree.update(1, 3);
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expect(tree.queryRange(1, 1)).toBe(7);
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expect(tree.query(5)).toBe(19);
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expect(tree.queryRange(1, 5)).toBe(19);
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expect(tree.queryRange(5, 1)).toBe(0); // invalid test
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});
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});

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