Added Binary Indexed Tree / Fenwick Tree Implementation (trekhleb#51)

* added fenwick tree implementation

* added fenwick tree implementation

Author: malfple

Diff for: src/data-structures/tree/fenwick-tree/FenwickTree.js

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+export default class FenwickTree {
+  /**
+   * Constructor creates empty fenwick tree of size 'size',
+   *    however, array size is size+1, because index is 1-based
+   * @param  {number} [size]
+   */
+  constructor(size) {
+    this.n = size;
+    this.arr = [];
+    for (let i = 0; i <= size; i += 1) this.arr.push(0);
+  }
+
+  /**
+   * Adds v to index x
+   * @param  {number} [x]
+   * @param  {number} [v]
+   */
+  update(x, v) {
+    if (x < 1 || x > this.n) return;
+    for (let i = x; i <= this.n; i += (i & -i)) {
+      this.arr[i] += v;
+    }
+  }
+
+  /**
+   * query sum from index 1 to x
+   * @param  {number} [x]
+   * @return {number} sum
+   */
+  query(x) {
+    if (x > this.n) return this.query(this.n);
+    let ret = 0;
+    for (let i = x; i > 0; i -= (i & -i)) {
+      ret += this.arr[i];
+    }
+    return ret;
+  }
+
+  /**
+   * query sum from index l to r
+   * @param  {number} [l]
+   * @param  {number} [r]
+   * @return {number}
+   */
+  queryRange(l, r) {
+    if (l > r) return 0;
+    return this.query(r) - this.query(l - 1);
+  }
+}

Diff for: src/data-structures/tree/fenwick-tree/README.md

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+# Binary Indexed Tree / Fenwick Tree
+
+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
+
+This implementation uses the basic range sum query and point update. All the indexes are 1-based
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Fenwick_tree)
+- [Geeksforgeeks](https://www.geeksforgeeks.org/binary-indexed-tree-or-fenwick-tree-2/)

Diff for: src/data-structures/tree/fenwick-tree/__test__/FenwickTree.test.js

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+import FenwickTree from '../FenwickTree';
+
+describe('FenwickTree', () => {
+  it('should create empty fenwick tree of correct size', () => {
+    const tree1 = new FenwickTree(5);
+    expect(tree1.arr.length).toBe(5 + 1);
+
+    for (let i = 0; i < 5; i += 1) {
+      expect(tree1.arr[i]).toBe(0);
+    }
+
+    const tree2 = new FenwickTree(50);
+    expect(tree2.arr.length).toBe(50 + 1);
+  });
+
+  it('should correctly execute queries', () => {
+    const tree = new FenwickTree(5);
+
+    tree.update(1, 4);
+    tree.update(3, 7);
+
+    expect(tree.query(1)).toBe(4);
+    expect(tree.query(3)).toBe(11);
+    expect(tree.query(5)).toBe(11);
+    expect(tree.queryRange(2, 3)).toBe(7);
+
+    tree.update(2, 5);
+    expect(tree.query(5)).toBe(16);
+
+    tree.update(1, 3);
+    expect(tree.queryRange(1, 1)).toBe(7);
+    expect(tree.query(5)).toBe(19);
+    expect(tree.queryRange(1, 5)).toBe(19);
+
+    expect(tree.queryRange(5, 1)).toBe(0); // invalid test
+  });
+});