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

* added fenwick tree implementation * added fenwick tree implementation

Author: malfple

src/data-structures/tree/fenwick-tree/FenwickTree.js

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+exportdefaultclassFenwickTree{
+/**
+ * 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(leti=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(leti=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)returnthis.query(this.n);
+letret=0;
+for(leti=x;i>0;i-=(i&-i)){
+ret+=this.arr[i];
+}
+returnret;
+}
+
+/**
+ * query sum from index l to r
+ * @param{number} [l]
+ * @param{number} [r]
+ * @return{number}
+ */
+queryRange(l,r){
+if(l>r)return0;
+returnthis.query(r)-this.query(l-1);
+}
+}

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/)

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

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+importFenwickTreefrom'../FenwickTree';
+
+describe('FenwickTree',()=>{
+it('should create empty fenwick tree of correct size',()=>{
+consttree1=newFenwickTree(5);
+expect(tree1.arr.length).toBe(5+1);
+
+for(leti=0;i<5;i+=1){
+expect(tree1.arr[i]).toBe(0);
+}
+
+consttree2=newFenwickTree(50);
+expect(tree2.arr.length).toBe(50+1);
+});
+
+it('should correctly execute queries',()=>{
+consttree=newFenwickTree(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
+});
+});