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Commit 183dade

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Update Fenwick Tree readme and do code style fixes.
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‎README.md‎

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Original file line numberDiff line numberDiff line change
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* [AVL Tree](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/tree/avl-tree)
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* [Red-Black Tree](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/tree/red-black-tree)
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* [Segment Tree](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/tree/segment-tree) - with min/max/sum range queries examples
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* [Fenwick Tree](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/tree/fenwick-tree) (Binary Indexed Tree)
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* [Graph](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/graph) (both directed and undirected)
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* [Disjoint Set](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/disjoint-set)
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@@ -1,49 +1,72 @@
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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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* Constructor creates empty fenwick tree of size 'arraySize',
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* however, array size is size+1, because index is 1-based.
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*
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* @param {number} arraySize
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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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constructor(arraySize) {
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this.arraySize = arraySize;
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// Fill tree array with zeros.
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this.treeArray = Array(this.arraySize + 1).fill(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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* Adds value to position.
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*
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* @param {number} position
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* @param {number} value
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* @return {FenwickTree}
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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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update(position, value) {
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if (position < 1 || position > this.arraySize) {
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throw new Error('Position is out of allowed range');
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}
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for (let i = position; i <= this.arraySize; i += (i & -i)) {
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this.treeArray[i] += value;
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}
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return this;
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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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* Query sum from index 1 to position.
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*
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* @param {number} position
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* @return {number}
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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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query(position) {
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if (position < 1 || position > this.arraySize) {
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throw new Error('Position is out of allowed range');
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}
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return ret;
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let sum = 0;
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for (let i = position; i > 0; i -= (i & -i)) {
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sum += this.treeArray[i];
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}
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return sum;
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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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* Query sum from index leftIndex to rightIndex.
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*
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* @param {number} leftIndex
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* @param {number} rightIndex
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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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queryRange(leftIndex, rightIndex) {
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if (leftIndex > rightIndex) {
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throw new Error('Left index can not be greater then right one');
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}
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if (leftIndex === 1) {
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return this.query(rightIndex);
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}
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return this.query(rightIndex) - this.query(leftIndex - 1);
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}
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}
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@@ -1,8 +1,18 @@
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# Binary Indexed Tree / Fenwick Tree
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# Fenwick Tree / Binary Indexed 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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A simple data structure that supports fast range queries
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in an array. However, it is usually only valid for reversible
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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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Binary Indexed Tree is represented as an array. Each node of Binary Indexed Tree
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stores sum of some elements of given array. Size of Binary Indexed Tree is equal
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to `n` where `n` is size of input array. In current implementation we have used
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size as `n+1` for ease of implementation. All the indexes are 1-based.
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![Binary Indexed Tree](https://www.geeksforgeeks.org/wp-content/uploads/BITSum.png)
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## References
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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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- [GeeksForGeeks](https://www.geeksforgeeks.org/binary-indexed-tree-or-fenwick-tree-2/)
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- [YouTube](https://www.youtube.com/watch?v=CWDQJGaN1gY&index=18&t=0s&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)

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

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@@ -3,14 +3,44 @@ 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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expect(tree1.treeArray.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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expect(tree1.treeArray[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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expect(tree2.treeArray.length).toBe(50 + 1);
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});
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it('should create correct fenwick tree', () => {
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const inputArray = [3, 2, -1, 6, 5, 4, -3, 3, 7, 2, 3];
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const tree = new FenwickTree(inputArray.length);
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expect(tree.treeArray.length).toBe(inputArray.length + 1);
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inputArray.forEach((value, index) => {
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tree.update(index + 1, value);
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});
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expect(tree.treeArray).toEqual([0, 3, 5, -1, 10, 5, 9, -3, 19, 7, 9, 3]);
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expect(tree.query(1)).toBe(3);
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expect(tree.query(2)).toBe(5);
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expect(tree.query(3)).toBe(4);
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expect(tree.query(4)).toBe(10);
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expect(tree.query(5)).toBe(15);
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expect(tree.query(6)).toBe(19);
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expect(tree.query(7)).toBe(16);
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expect(tree.query(8)).toBe(19);
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expect(tree.query(9)).toBe(26);
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expect(tree.query(10)).toBe(28);
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expect(tree.query(11)).toBe(31);
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expect(tree.queryRange(1, 1)).toBe(3);
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expect(tree.queryRange(1, 2)).toBe(5);
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expect(tree.queryRange(2, 4)).toBe(7);
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expect(tree.queryRange(6, 9)).toBe(11);
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});
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it('should correctly execute queries', () => {
@@ -31,7 +61,35 @@ describe('FenwickTree', () => {
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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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});
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it('should throw exceptions', () => {
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const tree = new FenwickTree(5);
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const updateAtInvalidLowIndex = () => {
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tree.update(0, 1);
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};
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const updateAtInvalidHighIndex = () => {
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tree.update(10, 1);
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};
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const queryInvalidLowIndex = () => {
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tree.query(0);
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};
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const queryInvalidHighIndex = () => {
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tree.query(10);
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};
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const rangeQueryInvalidIndex = () => {
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tree.queryRange(3, 2);
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};
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expect(tree.queryRange(5, 1)).toBe(0); // invalid test
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expect(updateAtInvalidLowIndex).toThrowError();
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expect(updateAtInvalidHighIndex).toThrowError();
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expect(queryInvalidLowIndex).toThrowError();
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expect(queryInvalidHighIndex).toThrowError();
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expect(rangeQueryInvalidIndex).toThrowError();
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});
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});

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