data-structure-typed/README.md

# data-structure-typed

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<p><a href="https://github.com/zrwusa/data-structure-typed/blob/main/README.md">English</a> | <a href="https://github.com/zrwusa/data-structure-typed/blob/main/README_zh-CN.md">简体中文</a></p>

## Why

Do you envy C++ with [STL]() (std::), Python with [collections](), and Java with [java.util]() ? Well, no need to envy
anymore! JavaScript and TypeScript now have [data-structure-typed]().**`Benchmark`** compared with C++ STL. **`API standards`** aligned with ES6 and Java. **`Usability`** is comparable to Python


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### We provide data structures that are not available in JS/TS

Heap, Binary Tree, RedBlack Tree, Linked List, Deque, Trie, Directed Graph, Undirected Graph, BST, AVL Tree, Priority Queue, Queue, Tree Multiset.


### Performance surpasses that of native JS/TS


<table style="display: table; width:100%; table-layout: fixed;">
  <thead>
  <tr>
    <th>Method</th>
    <th>Time Taken (ms)</th>
    <th>Scale</th>
    <th>Belongs To</th>
  </tr>
  </thead>
  <tbody>
  <tr>
    <td>Queue.push &amp; shift</td>
    <td>5.83</td>
    <td>100,000</td>
    <td>data-structure-typed</td>
  </tr>
  <tr>
    <td>Array.push &amp; shift</td>
    <td>2829.59</td>
    <td>100,000</td>
    <td>Native JS</td>
  </tr>
  <tr>
    <td>Deque.unshift &amp; shift</td>
    <td>2.44</td>
    <td>100,000</td>
    <td>data-structure-typed</td>
  </tr>
  <tr>
    <td>Array.unshift &amp; shift</td>
    <td>4750.37</td>
    <td>100,000</td>
    <td>Native JS</td>
  </tr>
  <tr>
    <td>HashMap.set</td>
    <td>122.51</td>
    <td>1,000,000</td>
    <td>data-structure-typed</td>
  </tr>
  <tr>
    <td>Map.set</td>
    <td>223.80</td>
    <td>1,000,000</td>
    <td>Native JS</td>
  </tr>
  <tr>
    <td>Set.add</td>
    <td>185.06</td>
    <td>1,000,000</td>
    <td>Native JS</td>
  </tr>
  </tbody>
</table>

## Installation and Usage

Now you can use it in Node.js and browser environments

CommonJS:**`require export.modules =`**

ESModule:&nbsp;&nbsp;&nbsp;**`import export`**

Typescript:&nbsp;&nbsp;&nbsp;**`import export`**

UMD:&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;**`var Deque = dataStructureTyped.Deque`**


### npm

```bash
npm i data-structure-typed --save
```

### yarn

```bash
yarn add data-structure-typed
```

```js
import {
  BinaryTree, Graph, Queue, Stack, PriorityQueue, BST, Trie, DoublyLinkedList,
  AVLTree, MinHeap, SinglyLinkedList, DirectedGraph, TreeMultimap,
  DirectedVertex, AVLTreeNode
} from 'data-structure-typed';
```

### CDN

Copy the line below into the head tag in an HTML document.

#### development

```html
<script src='https://cdn.jsdelivr.net/npm/data-structure-typed/dist/umd/data-structure-typed.js'></script>
```

#### production

```html
<script src='https://cdn.jsdelivr.net/npm/data-structure-typed/dist/umd/data-structure-typed.min.js'></script>
```

Copy the code below into the script tag of your HTML, and you're good to go with your development.

```js
const {Heap} = dataStructureTyped;
const {
  BinaryTree, Graph, Queue, Stack, PriorityQueue, BST, Trie, DoublyLinkedList,
  AVLTree, MinHeap, SinglyLinkedList, DirectedGraph, TreeMultimap,
  DirectedVertex, AVLTreeNode
} = dataStructureTyped;
```

## Vivid Examples

### Binary Tree

[Try it out](https://vivid-algorithm.vercel.app/), or you can run your own code using
our [visual tool](https://github.com/zrwusa/vivid-algorithm)

![](https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/examples/videos/webp_output/binary-tree-array-to-binary-tree.webp)

### Binary Tree DFS

[Try it out](https://vivid-algorithm.vercel.app/)

![](https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/examples/videos/webp_output/binary-tree-dfs-in-order.webp)

### AVL Tree

[Try it out](https://vivid-algorithm.vercel.app/)

![](https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/examples/videos/webp_output/avl-tree-test.webp)

### Tree Multi Map

[Try it out](https://vivid-algorithm.vercel.app/)

![](https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/examples/videos/webp_output/tree-multiset-test.webp)

### Matrix

[Try it out](https://vivid-algorithm.vercel.app/algorithm/graph/)

![](https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/examples/videos/webp_output/matrix-cut-off-tree-for-golf.webp)

### Directed Graph

[Try it out](https://vivid-algorithm.vercel.app/algorithm/graph/)

![](https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/examples/videos/webp_output/directed-graph-test.webp)

### Map Graph

[Try it out](https://vivid-algorithm.vercel.app/algorithm/graph/)

![](https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/examples/videos/webp_output/map-graph-test.webp)

## Code Snippets

### RedBlackTree snippet

#### TS

```ts
import {RedBlackTree} from 'data-structure-typed';

const rbTree = new RedBlackTree<number>();
rbTree.addMany([11, 3, 15, 1, 8, 13, 16, 2, 6, 9, 12, 14, 4, 7, 10, 5])
rbTree.isAVLBalanced();    // true
rbTree.delete(10);
rbTree.isAVLBalanced();    // true
rbTree.print()
//         ___6________
//        /            \
//      ___4_       ___11________
//     /     \     /             \
//    _2_    5    _8_       ____14__
//   /   \       /   \     /        \
//   1   3       7   9    12__     15__
//                            \        \
//                           13       16
```

#### JS

```js
import {RedBlackTree} from 'data-structure-typed';

const rbTree = new RedBlackTree();
rbTree.addMany([11, 3, 15, 1, 8, 13, 16, 2, 6, 9, 12, 14, 4, 7, 10, 5])
rbTree.isAVLBalanced();    // true
rbTree.delete(10);
rbTree.isAVLBalanced();    // true
rbTree.print()
//         ___6________
//        /            \
//      ___4_       ___11________
//     /     \     /             \
//    _2_    5    _8_       ____14__
//   /   \       /   \     /        \
//   1   3       7   9    12__     15__
//                            \        \
//                           13       16
```

### Binary Search Tree (BST) snippet

```ts
import {BST, BSTNode} from 'data-structure-typed';

const bst = new BST<number>();
bst.add(11);
bst.add(3);
bst.addMany([15, 1, 8, 13, 16, 2, 6, 9, 12, 14, 4, 7, 10, 5]);
bst.size === 16;                // true
bst.has(6);                     // true
const node6 = bst.getNode(6);   // BSTNode
bst.getHeight(6) === 2;         // true
bst.getHeight() === 5;          // true
bst.getDepth(6) === 3;          // true

bst.getLeftMost()?.key === 1;   // true

bst.delete(6);
bst.get(6);                     // undefined
bst.isAVLBalanced();            // true
bst.bfs()[0] === 11;            // true
bst.print()
//       ______________11_____           
//      /                     \          
//   ___3_______            _13_____
//  /           \          /        \    
//  1_     _____8____     12      _15__
//    \   /          \           /     \ 
//    2   4_       _10          14    16
//          \     /                      
//          5_    9
//            \                          
//            7

const objBST = new BST<number, {height: number, age: number}>();

objBST.add(11, { "name": "Pablo", "age": 15 });
objBST.add(3, { "name": "Kirk", "age": 1 });

objBST.addMany([15, 1, 8, 13, 16, 2, 6, 9, 12, 14, 4, 7, 10, 5], [
    { "name": "Alice", "age": 15 },
    { "name": "Bob", "age": 1 },
    { "name": "Charlie", "age": 8 },
    { "name": "David", "age": 13 },
    { "name": "Emma", "age": 16 },
    { "name": "Frank", "age": 2 },
    { "name": "Grace", "age": 6 },
    { "name": "Hannah", "age": 9 },
    { "name": "Isaac", "age": 12 },
    { "name": "Jack", "age": 14 },
    { "name": "Katie", "age": 4 },
    { "name": "Liam", "age": 7 },
    { "name": "Mia", "age": 10 },
    { "name": "Noah", "age": 5 }
  ]
);

objBST.delete(11);
```

### AVLTree snippet

```ts
import {AVLTree} from 'data-structure-typed';

const avlTree = new AVLTree<number>();
avlTree.addMany([11, 3, 15, 1, 8, 13, 16, 2, 6, 9, 12, 14, 4, 7, 10, 5])
avlTree.isAVLBalanced();    // true
avlTree.delete(10);
avlTree.isAVLBalanced();    // true
```

### Directed Graph simple snippet

```ts
import {DirectedGraph} from 'data-structure-typed';

const graph = new DirectedGraph<string>();

graph.addVertex('A');
graph.addVertex('B');

graph.hasVertex('A');       // true
graph.hasVertex('B');       // true
graph.hasVertex('C');       // false

graph.addEdge('A', 'B');
graph.hasEdge('A', 'B');    // true
graph.hasEdge('B', 'A');    // false

graph.deleteEdgeSrcToDest('A', 'B');
graph.hasEdge('A', 'B');    // false

graph.addVertex('C');

graph.addEdge('A', 'B');
graph.addEdge('B', 'C');

const topologicalOrderKeys = graph.topologicalSort(); // ['A', 'B', 'C']
```

### Undirected Graph snippet

```ts
import {UndirectedGraph} from 'data-structure-typed';

const graph = new UndirectedGraph<string>();
graph.addVertex('A');
graph.addVertex('B');
graph.addVertex('C');
graph.addVertex('D');
graph.deleteVertex('C');
graph.addEdge('A', 'B');
graph.addEdge('B', 'D');

const dijkstraResult = graph.dijkstra('A');
Array.from(dijkstraResult?.seen ?? []).map(vertex => vertex.key) // ['A', 'B', 'D']


```

### Free conversion between data structures.

```js
const orgArr = [6, 1, 2, 7, 5, 3, 4, 9, 8];
const orgStrArr = ["trie", "trial", "trick", "trip", "tree", "trend", "triangle", "track", "trace", "transmit"];
const entries = [[6, 6], [1, 1], [2, 2], [7, 7], [5, 5], [3, 3], [4, 4], [9, 9], [8, 8]];

const queue = new Queue(orgArr);
queue.print();      
// [6, 1, 2, 7, 5, 3, 4, 9, 8]

const deque = new Deque(orgArr);
deque.print();      
// [6, 1, 2, 7, 5, 3, 4, 9, 8]

const sList = new SinglyLinkedList(orgArr);
sList.print();      
// [6, 1, 2, 7, 5, 3, 4, 9, 8]

const dList = new DoublyLinkedList(orgArr);
dList.print();      
// [6, 1, 2, 7, 5, 3, 4, 9, 8]

const stack = new Stack(orgArr);
stack.print();      
// [6, 1, 2, 7, 5, 3, 4, 9, 8]

const minHeap = new MinHeap(orgArr);
minHeap.print();    
// [1, 5, 2, 7, 6, 3, 4, 9, 8]

const maxPQ = new MaxPriorityQueue(orgArr);
maxPQ.print();      
// [9, 8, 4, 7, 5, 2, 3, 1, 6]

const biTree = new BinaryTree(entries);
biTree.print();
//         ___6___
//        /       \
//     ___1_     _2_
//    /     \   /   \
//   _7_    5   3   4
//  /   \
//  9   8

const bst = new BST(entries);
bst.print();
//     _____5___
//    /         \
//   _2_       _7_
//  /   \     /   \
//  1   3_    6   8_
//        \         \
//        4         9


const rbTree = new RedBlackTree(entries);
rbTree.print();
//     ___4___
//    /       \
//   _2_     _6___
//  /   \   /     \
//  1   3   5    _8_
//              /   \
//              7   9


const avl = new AVLTree(entries);
avl.print();
//     ___4___
//    /       \
//   _2_     _6___
//  /   \   /     \
//  1   3   5    _8_
//              /   \
//              7   9

const treeMulti = new TreeMultimap(entries);
treeMulti.print();
//     ___4___
//    /       \
//   _2_     _6___
//  /   \   /     \
//  1   3   5    _8_
//              /   \
//              7   9

const hm = new HashMap(entries);
hm.print()    
// [[6, 6], [1, 1], [2, 2], [7, 7], [5, 5], [3, 3], [4, 4], [9, 9], [8, 8]]

const rbTreeH = new RedBlackTree(hm);
rbTreeH.print();
//     ___4___
//    /       \
//   _2_     _6___
//  /   \   /     \
//  1   3   5    _8_
//              /   \
//              7   9

const pq = new MinPriorityQueue(orgArr);
pq.print();   
// [1, 5, 2, 7, 6, 3, 4, 9, 8]

const bst1 = new BST(pq);
bst1.print();
//     _____5___
//    /         \
//   _2_       _7_
//  /   \     /   \
//  1   3_    6   8_
//        \         \
//        4         9

const dq1 = new Deque(orgArr);
dq1.print();    
// [6, 1, 2, 7, 5, 3, 4, 9, 8]
const rbTree1 = new RedBlackTree(dq1);
rbTree1.print();
//    _____5___
//   /         \
//  _2___     _7___
// /     \   /     \
// 1    _4   6    _9
//      /         /
//      3         8


const trie2 = new Trie(orgStrArr);
trie2.print();    
// ['trie', 'trial', 'triangle', 'trick', 'trip', 'tree', 'trend', 'track', 'trace', 'transmit']
const heap2 = new Heap(trie2, { comparator: (a, b) => Number(a) - Number(b) });
heap2.print();    
// ['transmit', 'trace', 'tree', 'trend', 'track', 'trial', 'trip', 'trie', 'trick', 'triangle']
const dq2 = new Deque(heap2);
dq2.print();      
// ['transmit', 'trace', 'tree', 'trend', 'track', 'trial', 'trip', 'trie', 'trick', 'triangle']
const entries2 = dq2.map((el, i) => [i, el]);
const avl2 = new AVLTree(entries2);
avl2.print();
//     ___3_______
//    /           \
//   _1_       ___7_
//  /   \     /     \
//  0   2    _5_    8_
//          /   \     \
//          4   6     9
```

## API docs & Examples

[API Docs](https://data-structure-typed-docs.vercel.app)

[Live Examples](https://vivid-algorithm.vercel.app)

<a href="https://github.com/zrwusa/vivid-algorithm" target="_blank">Examples Repository</a>

## Data Structures

<table style="display: table; width:100%; table-layout: fixed;">
<thead>
<tr>
<th>Data Structure</th>
<th>Unit Test</th>
<th>Performance Test</th>
<th>API Docs</th>
</tr>
</thead>
<tbody>
<tr>
<td>Binary Tree</td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td><a href="https://data-structure-typed-docs.vercel.app/classes/BinaryTree.html"><span>View</span></a></td>
</tr>
<tr>
<td>Binary Search Tree (BST)</td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td><a href="https://data-structure-typed-docs.vercel.app/classes/BST.html"><span>View</span></a></td>
</tr>
<tr>
<td>AVL Tree</td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td><a href="https://data-structure-typed-docs.vercel.app/classes/AVLTree.html"><span>View</span></a></td>
</tr>
<tr>
<td>Red Black Tree</td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td><a href="https://data-structure-typed-docs.vercel.app/classes/RedBlackTree.html"><span>View</span></a></td>
</tr>
<tr>
<td>Tree Multimap</td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td><a href="https://data-structure-typed-docs.vercel.app/classes/TreeMultimap.html"><span>View</span></a></td>
</tr>
<tr>
<td>Heap</td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td><a href="https://data-structure-typed-docs.vercel.app/classes/Heap.html"><span>View</span></a></td>
</tr>
<tr>
<td>Priority Queue</td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td><a href="https://data-structure-typed-docs.vercel.app/classes/PriorityQueue.html"><span>View</span></a></td>
</tr>
<tr>
<td>Max Priority Queue</td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td><a href="https://data-structure-typed-docs.vercel.app/classes/MaxPriorityQueue.html"><span>View</span></a></td>
</tr>
<tr>
<td>Min Priority Queue</td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td><a href="https://data-structure-typed-docs.vercel.app/classes/MinPriorityQueue.html"><span>View</span></a></td>
</tr>
<tr>
<td>Trie</td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td><a href="https://data-structure-typed-docs.vercel.app/classes/Trie.html"><span>View</span></a></td>
</tr>
<tr>
<td>Graph</td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td><a href="https://data-structure-typed-docs.vercel.app/classes/AbstractGraph.html"><span>View</span></a></td>
</tr>
<tr>
<td>Directed Graph</td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td><a href="https://data-structure-typed-docs.vercel.app/classes/DirectedGraph.html"><span>View</span></a></td>
</tr>
<tr>
<td>Undirected Graph</td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td><a href="https://data-structure-typed-docs.vercel.app/classes/UndirectedGraph.html"><span>View</span></a></td>
</tr>
<tr>
<td>Queue</td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td><a href="https://data-structure-typed-docs.vercel.app/classes/Queue.html"><span>View</span></a></td>
</tr>
<tr>
<td>Deque</td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td><a href="https://data-structure-typed-docs.vercel.app/classes/Deque.html"><span>View</span></a></td>
</tr>
<tr>
<td>Hash Map</td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td><a href="https://data-structure-typed-docs.vercel.app/classes/HashMap.html"><span>View</span></a></td>
</tr>
<tr>
<td>Linked List</td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td><a href="https://data-structure-typed-docs.vercel.app/classes/SinglyLinkedList.html"><span>View</span></a></td>
</tr>
<tr>
<td>Singly Linked List</td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td><a href="https://data-structure-typed-docs.vercel.app/classes/SinglyLinkedList.html"><span>View</span></a></td>
</tr>
<tr>
<td>Doubly Linked List</td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td><a href="https://data-structure-typed-docs.vercel.app/classes/DoublyLinkedList.html"><span>View</span></a></td>
</tr>
<tr>
<td>Stack</td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td><a href="https://data-structure-typed-docs.vercel.app/classes/Stack.html"><span>View</span></a></td>
</tr>
<tr>
<td>Segment Tree</td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td></td>
<td><a href="https://data-structure-typed-docs.vercel.app/classes/SegmentTree.html"><span>View</span></a></td>
</tr>
<tr>
<td>Binary Indexed Tree</td>
<td><img src="https://raw.githubusercontent.com/zrwusa/assets/master/images/data-structure-typed/assets/tick.svg" alt=""></td>
<td></td>
<td><a href="https://data-structure-typed-docs.vercel.app/classes/BinaryIndexedTree.html"><span>View</span></a></td>
</tr>
</tbody>
</table>

## The corresponding relationships between data structures in different language standard libraries.

<table style="display: table; width:100%; table-layout: fixed;">
  <thead>
  <tr>
    <th>Data Structure Typed</th>
    <th>C++ STL</th>
    <th>java.util</th>
    <th>Python collections</th>
  </tr>
  </thead>
  <tbody>
  <tr>
    <td>Heap&lt;E&gt;</td>
    <td>-</td>
    <td>-</td>
    <td>heapq</td>
  </tr>
  <tr>
    <td>PriorityQueue&lt;E&gt;</td>
    <td>priority_queue&lt;T&gt;</td>
    <td>PriorityQueue&lt;E&gt;</td>
    <td>-</td>
  </tr>
  <tr>
    <td>Deque&lt;E&gt;</td>
    <td>deque&lt;T&gt;</td>
    <td>ArrayDeque&lt;E&gt;</td>
    <td>deque</td>
  </tr>
  <tr>
    <td>Queue&lt;E&gt;</td>
    <td>queue&lt;T&gt;</td>
    <td>Queue&lt;E&gt;</td>
    <td>-</td>
  </tr>
  <tr>
    <td>HashMap&lt;K, V&gt;</td>
    <td>unordered_map&lt;K, V&gt;</td>
    <td>HashMap&lt;K, V&gt;</td>
    <td>defaultdict</td>
  </tr>
  <tr>
    <td>DoublyLinkedList&lt;E&gt;</td>
    <td>list&lt;T&gt;</td>
    <td>LinkedList&lt;E&gt;</td>
    <td>-</td>
  </tr>
  <tr>
    <td>SinglyLinkedList&lt;E&gt;</td>
    <td>-</td>
    <td>-</td>
    <td>-</td>
  </tr>
  <tr>
    <td>BinaryTree&lt;K, V&gt;</td>
    <td>-</td>
    <td>-</td>
    <td>-</td>
  </tr>
  <tr>
    <td>BST&lt;K, V&gt;</td>
    <td>-</td>
    <td>-</td>
    <td>-</td>
  </tr>
  <tr>
    <td>RedBlackTree&lt;E&gt;</td>
    <td>set&lt;T&gt;</td>
    <td>TreeSet&lt;E&gt;</td>
    <td>-</td>
  </tr>
  <tr>
    <td>RedBlackTree&lt;K, V&gt;</td>
    <td>map&lt;K, V&gt;</td>
    <td>TreeMap&lt;K, V&gt;</td>
    <td>-</td>
  </tr>
  <tr>
    <td>TreeMultimap&lt;K, V&gt;</td>
    <td>multimap&lt;K, V&gt;</td>
    <td>-</td>
    <td>-</td>
  </tr>
  <tr>
    <td>TreeMultimap&lt;E&gt;</td>
    <td>multiset&lt;T&gt;</td>
    <td>-</td>
    <td>-</td>
  </tr>
  <tr>
    <td>Trie</td>
    <td>-</td>
    <td>-</td>
    <td>-</td>
  </tr>
  <tr>
    <td>DirectedGraph&lt;V, E&gt;</td>
    <td>-</td>
    <td>-</td>
    <td>-</td>
  </tr>
  <tr>
    <td>UndirectedGraph&lt;V, E&gt;</td>
    <td>-</td>
    <td>-</td>
    <td>-</td>
  </tr>
  <tr>
    <td>PriorityQueue&lt;E&gt;</td>
    <td>priority_queue&lt;T&gt;</td>
    <td>PriorityQueue&lt;E&gt;</td>
    <td>-</td>
  </tr>
  <tr>
    <td>Array&lt;E&gt;</td>
    <td>vector&lt;T&gt;</td>
    <td>ArrayList&lt;E&gt;</td>
    <td>list</td>
  </tr>
  <tr>
    <td>Stack&lt;E&gt;</td>
    <td>stack&lt;T&gt;</td>
    <td>Stack&lt;E&gt;</td>
    <td>-</td>
  </tr>
  <tr>
    <td>HashMap&lt;E&gt;</td>
    <td>unordered_set&lt;T&gt;</td>
    <td>HashSet&lt;E&gt;</td>
    <td>set</td>
  </tr>
  <tr>
    <td>-</td>
    <td>unordered_multiset</td>
    <td>-</td>
    <td>Counter</td>
  </tr>
  <tr>
    <td>LinkedHashMap&lt;K, V&gt;</td>
    <td>-</td>
    <td>LinkedHashMap&lt;K, V&gt;</td>
    <td>OrderedDict</td>
  </tr>
  <tr>
    <td>-</td>
    <td>unordered_multimap&lt;K, V&gt;</td>
    <td>-</td>
    <td>-</td>
  </tr>
  <tr>
    <td>-</td>
    <td>bitset&lt;N&gt;</td>
    <td>-</td>
    <td>-</td>
  </tr>
  </tbody>
</table>

## Built-in classic algorithms

<table style="display: table; width:100%; table-layout: fixed;">
  <thead>
  <tr>
    <th>Algorithm</th>
    <th>Function Description</th>
    <th>Iteration Type</th>
  </tr>
  </thead>
  <tbody>
  <tr>
    <td>Binary Tree DFS</td>
    <td>Traverse a binary tree in a depth-first manner, starting from the root node, first visiting the left subtree,
      and then the right subtree, using recursion.
    </td>
    <td>Recursion + Iteration</td>
  </tr>
  <tr>
    <td>Binary Tree BFS</td>
    <td>Traverse a binary tree in a breadth-first manner, starting from the root node, visiting nodes level by level
      from left to right.
    </td>
    <td>Iteration</td>
  </tr>
  <tr>
    <td>Graph DFS</td>
    <td>Traverse a graph in a depth-first manner, starting from a given node, exploring along one path as deeply as
      possible, and backtracking to explore other paths. Used for finding connected components, paths, etc.
    </td>
    <td>Recursion + Iteration</td>
  </tr>
  <tr>
    <td>Binary Tree Morris</td>
    <td>Morris traversal is an in-order traversal algorithm for binary trees with O(1) space complexity. It allows tree
      traversal without additional stack or recursion.
    </td>
    <td>Iteration</td>
  </tr>
  <tr>
    <td>Graph BFS</td>
    <td>Traverse a graph in a breadth-first manner, starting from a given node, first visiting nodes directly connected
      to the starting node, and then expanding level by level. Used for finding shortest paths, etc.
    </td>
    <td>Recursion + Iteration</td>
  </tr>
  <tr>
    <td>Graph Tarjan's Algorithm</td>
    <td>Find strongly connected components in a graph, typically implemented using depth-first search.</td>
    <td>Recursion</td>
  </tr>
  <tr>
    <td>Graph Bellman-Ford Algorithm</td>
    <td>Finding the shortest paths from a single source, can handle negative weight edges</td>
    <td>Iteration</td>
  </tr>
  <tr>
    <td>Graph Dijkstra's Algorithm</td>
    <td>Finding the shortest paths from a single source, cannot handle negative weight edges</td>
    <td>Iteration</td>
  </tr>
  <tr>
    <td>Graph Floyd-Warshall Algorithm</td>
    <td>Finding the shortest paths between all pairs of nodes</td>
    <td>Iteration</td>
  </tr>
  <tr>
    <td>Graph getCycles</td>
    <td>Find all cycles in a graph or detect the presence of cycles.</td>
    <td>Recursion</td>
  </tr>
  <tr>
    <td>Graph getCutVertexes</td>
    <td>Find cut vertices in a graph, which are nodes that, when removed, increase the number of connected components in
      the graph.
    </td>
    <td>Recursion</td>
  </tr>
  <tr>
    <td>Graph getSCCs</td>
    <td>Find strongly connected components in a graph, which are subgraphs where any two nodes can reach each other.
    </td>
    <td>Recursion</td>
  </tr>
  <tr>
    <td>Graph getBridges</td>
    <td>Find bridges in a graph, which are edges that, when removed, increase the number of connected components in the
      graph.
    </td>
    <td>Recursion</td>
  </tr>
  <tr>
    <td>Graph topologicalSort</td>
    <td>Perform topological sorting on a directed acyclic graph (DAG) to find a linear order of nodes such that all
      directed edges go from earlier nodes to later nodes.
    </td>
    <td>Recursion</td>
  </tr>
  </tbody>
</table>

## Software Engineering Design Standards

<table style="display: table; width:100%; table-layout: fixed;">
    <tr>
        <th>Principle</th>
        <th>Description</th>
    </tr>
    <tr>
        <td>Practicality</td>
        <td>Follows ES6 and ESNext standards, offering unified and considerate optional parameters, and simplifies method names.</td>
    </tr>
    <tr>
        <td>Extensibility</td>
        <td>Adheres to OOP (Object-Oriented Programming) principles, allowing inheritance for all data structures.</td>
    </tr>
    <tr>
        <td>Modularization</td>
        <td>Includes data structure modularization and independent NPM packages.</td>
    </tr>
    <tr>
        <td>Efficiency</td>
        <td>All methods provide time and space complexity, comparable to native JS performance.</td>
    </tr>
    <tr>
        <td>Maintainability</td>
        <td>Follows open-source community development standards, complete documentation, continuous integration, and adheres to TDD (Test-Driven Development) patterns.</td>
    </tr>
    <tr>
        <td>Testability</td>
        <td>Automated and customized unit testing, performance testing, and integration testing.</td>
    </tr>
    <tr>
        <td>Portability</td>
        <td>Plans for porting to Java, Python, and C++, currently achieved to 80%.</td>
    </tr>
    <tr>
        <td>Reusability</td>
        <td>Fully decoupled, minimized side effects, and adheres to OOP.</td>
    </tr>
    <tr>
        <td>Security</td>
        <td>Carefully designed security for member variables and methods. Read-write separation. Data structure software does not need to consider other security aspects.</td>
    </tr>
    <tr>
        <td>Scalability</td>
        <td>Data structure software does not involve load issues.</td>
    </tr>
</table>


## Benchmark

[//]: # (No deletion!!! Start of Replace Section)
<div class="json-to-html-collapse clearfix 0">
      <div class='collapsible level0' ><span class='json-to-html-label'>avl-tree</span></div>
      <div class="content"><table style="display: table; width:100%; table-layout: fixed;"><tr><th>test name</th><th>time taken (ms)</th><th>executions per sec</th><th>sample deviation</th></tr><tr><td>10,000 add randomly</td><td>118.62</td><td>8.43</td><td>0.00</td></tr><tr><td>10,000 add & delete randomly</td><td>179.74</td><td>5.56</td><td>0.00</td></tr><tr><td>10,000 addMany</td><td>154.34</td><td>6.48</td><td>0.04</td></tr><tr><td>10,000 get</td><td>50.53</td><td>19.79</td><td>0.00</td></tr></table></div>
    </div><div class="json-to-html-collapse clearfix 0">
      <div class='collapsible level0' ><span class='json-to-html-label'>rb-tree</span></div>
      <div class="content"><table style="display: table; width:100%; table-layout: fixed;"><tr><th>test name</th><th>time taken (ms)</th><th>executions per sec</th><th>sample deviation</th></tr><tr><td>100,000 add</td><td>90.63</td><td>11.03</td><td>0.01</td></tr><tr><td>100,000 add & delete randomly</td><td>225.64</td><td>4.43</td><td>0.01</td></tr><tr><td>100,000 getNode</td><td>174.39</td><td>5.73</td><td>0.00</td></tr><tr><td>100,000 add & iterator</td><td>120.94</td><td>8.27</td><td>0.02</td></tr></table></div>
    </div><div class="json-to-html-collapse clearfix 0">
      <div class='collapsible level0' ><span class='json-to-html-label'>directed-graph</span></div>
      <div class="content"><table style="display: table; width:100%; table-layout: fixed;"><tr><th>test name</th><th>time taken (ms)</th><th>executions per sec</th><th>sample deviation</th></tr><tr><td>1,000 addVertex</td><td>0.10</td><td>9850.83</td><td>1.41e-6</td></tr><tr><td>1,000 addEdge</td><td>6.21</td><td>160.97</td><td>2.65e-4</td></tr><tr><td>1,000 getVertex</td><td>0.05</td><td>1.91e+4</td><td>2.18e-5</td></tr><tr><td>1,000 getEdge</td><td>26.38</td><td>37.90</td><td>0.00</td></tr><tr><td>tarjan</td><td>233.90</td><td>4.28</td><td>0.02</td></tr><tr><td>tarjan all</td><td>7008.22</td><td>0.14</td><td>0.34</td></tr><tr><td>topologicalSort</td><td>206.12</td><td>4.85</td><td>0.02</td></tr></table></div>
    </div><div class="json-to-html-collapse clearfix 0">
      <div class='collapsible level0' ><span class='json-to-html-label'>hash-map</span></div>
      <div class="content"><table style="display: table; width:100%; table-layout: fixed;"><tr><th>test name</th><th>time taken (ms)</th><th>executions per sec</th><th>sample deviation</th></tr><tr><td>1,000,000 set</td><td>129.16</td><td>7.74</td><td>0.05</td></tr><tr><td>Native Map 1,000,000 set</td><td>230.98</td><td>4.33</td><td>0.05</td></tr><tr><td>Native Set 1,000,000 add</td><td>201.94</td><td>4.95</td><td>0.05</td></tr><tr><td>1,000,000 set & get</td><td>132.13</td><td>7.57</td><td>0.03</td></tr><tr><td>Native Map 1,000,000 set & get</td><td>317.16</td><td>3.15</td><td>0.06</td></tr><tr><td>Native Set 1,000,000 add & has</td><td>229.56</td><td>4.36</td><td>0.06</td></tr><tr><td>1,000,000 ObjKey set & get</td><td>323.02</td><td>3.10</td><td>0.04</td></tr><tr><td>Native Map 1,000,000 ObjKey set & get</td><td>301.07</td><td>3.32</td><td>0.04</td></tr><tr><td>Native Set 1,000,000 ObjKey add & has</td><td>282.01</td><td>3.55</td><td>0.04</td></tr></table></div>
    </div><div class="json-to-html-collapse clearfix 0">
      <div class='collapsible level0' ><span class='json-to-html-label'>heap</span></div>
      <div class="content"><table style="display: table; width:100%; table-layout: fixed;"><tr><th>test name</th><th>time taken (ms)</th><th>executions per sec</th><th>sample deviation</th></tr><tr><td>100,000 add & poll</td><td>27.32</td><td>36.61</td><td>9.27e-4</td></tr><tr><td>100,000 add & dfs</td><td>33.83</td><td>29.56</td><td>3.94e-4</td></tr><tr><td>10,000 fib add & pop</td><td>353.37</td><td>2.83</td><td>0.00</td></tr></table></div>
    </div><div class="json-to-html-collapse clearfix 0">
      <div class='collapsible level0' ><span class='json-to-html-label'>doubly-linked-list</span></div>
      <div class="content"><table style="display: table; width:100%; table-layout: fixed;"><tr><th>test name</th><th>time taken (ms)</th><th>executions per sec</th><th>sample deviation</th></tr><tr><td>1,000,000 push</td><td>220.80</td><td>4.53</td><td>0.02</td></tr><tr><td>1,000,000 unshift</td><td>235.94</td><td>4.24</td><td>0.06</td></tr><tr><td>1,000,000 unshift & shift</td><td>180.11</td><td>5.55</td><td>0.04</td></tr><tr><td>1,000,000 addBefore</td><td>335.72</td><td>2.98</td><td>0.11</td></tr></table></div>
    </div><div class="json-to-html-collapse clearfix 0">
      <div class='collapsible level0' ><span class='json-to-html-label'>singly-linked-list</span></div>
      <div class="content"><table style="display: table; width:100%; table-layout: fixed;"><tr><th>test name</th><th>time taken (ms)</th><th>executions per sec</th><th>sample deviation</th></tr><tr><td>1,000,000 push & shift</td><td>217.29</td><td>4.60</td><td>0.06</td></tr><tr><td>10,000 push & pop</td><td>223.41</td><td>4.48</td><td>0.02</td></tr><tr><td>10,000 addBefore</td><td>253.79</td><td>3.94</td><td>0.01</td></tr></table></div>
    </div><div class="json-to-html-collapse clearfix 0">
      <div class='collapsible level0' ><span class='json-to-html-label'>priority-queue</span></div>
      <div class="content"><table style="display: table; width:100%; table-layout: fixed;"><tr><th>test name</th><th>time taken (ms)</th><th>executions per sec</th><th>sample deviation</th></tr><tr><td>100,000 add & poll</td><td>81.55</td><td>12.26</td><td>0.01</td></tr></table></div>
    </div><div class="json-to-html-collapse clearfix 0">
      <div class='collapsible level0' ><span class='json-to-html-label'>deque</span></div>
      <div class="content"><table style="display: table; width:100%; table-layout: fixed;"><tr><th>test name</th><th>time taken (ms)</th><th>executions per sec</th><th>sample deviation</th></tr><tr><td>1,000,000 push</td><td>14.14</td><td>70.71</td><td>4.71e-4</td></tr><tr><td>1,000,000 push & pop</td><td>29.75</td><td>33.61</td><td>0.01</td></tr><tr><td>100,000 push & shift</td><td>3.06</td><td>326.93</td><td>0.00</td></tr><tr><td>Native Array 100,000 push & shift</td><td>2211.02</td><td>0.45</td><td>0.05</td></tr><tr><td>100,000 unshift & shift</td><td>2.23</td><td>447.63</td><td>3.63e-4</td></tr><tr><td>Native Array 100,000 unshift & shift</td><td>4586.53</td><td>0.22</td><td>0.86</td></tr></table></div>
    </div><div class="json-to-html-collapse clearfix 0">
      <div class='collapsible level0' ><span class='json-to-html-label'>queue</span></div>
      <div class="content"><table style="display: table; width:100%; table-layout: fixed;"><tr><th>test name</th><th>time taken (ms)</th><th>executions per sec</th><th>sample deviation</th></tr><tr><td>1,000,000 push</td><td>48.44</td><td>20.65</td><td>0.01</td></tr><tr><td>100,000 push & shift</td><td>5.28</td><td>189.27</td><td>6.59e-4</td></tr><tr><td>Native Array 100,000 push & shift</td><td>2335.96</td><td>0.43</td><td>0.14</td></tr><tr><td>Native Array 100,000 push & pop</td><td>4.48</td><td>223.08</td><td>5.56e-4</td></tr></table></div>
    </div><div class="json-to-html-collapse clearfix 0">
      <div class='collapsible level0' ><span class='json-to-html-label'>stack</span></div>
      <div class="content"><table style="display: table; width:100%; table-layout: fixed;"><tr><th>test name</th><th>time taken (ms)</th><th>executions per sec</th><th>sample deviation</th></tr><tr><td>1,000,000 push</td><td>45.61</td><td>21.93</td><td>0.01</td></tr><tr><td>1,000,000 push & pop</td><td>50.96</td><td>19.62</td><td>0.01</td></tr></table></div>
    </div><div class="json-to-html-collapse clearfix 0">
      <div class='collapsible level0' ><span class='json-to-html-label'>trie</span></div>
      <div class="content"><table style="display: table; width:100%; table-layout: fixed;"><tr><th>test name</th><th>time taken (ms)</th><th>executions per sec</th><th>sample deviation</th></tr><tr><td>100,000 push</td><td>58.40</td><td>17.12</td><td>0.02</td></tr><tr><td>100,000 getWords</td><td>99.70</td><td>10.03</td><td>0.01</td></tr></table></div>
    </div>

[//]: # (No deletion!!! End of Replace Section)