avl-tree-typed
What
Brief
This is a standalone AVL Tree data structure from the data-structure-typed collection. If you wish to access more data structures or advanced features, you can transition to directly installing the complete data-structure-typed package
How
install
npm
npm i avl-tree-typed --save
yarn
yarn add avl-tree-typed
methods
snippet
TS
import {AVLTree, AVLTreeNode} from 'data-structure-typed';
// /* or if you prefer */ import {AVLTree} from 'avl-tree-typed';
const avlTree = new AVLTree<AVLTreeNode<number>>();
const idsOrVals = [11, 3, 15, 1, 8, 13, 16, 2, 6, 9, 12, 14, 4, 7, 10, 5];
avlTree.addMany(idsOrVals, idsOrVals);
const node6 = avlTree.get(6);
node6 && avlTree.getHeight(node6) // 3
node6 && avlTree.getDepth(node6) // 1
const getNodeById = avlTree.get(10, 'id');
getNodeById?.id // 10
const getMinNodeByRoot = avlTree.getLeftMost();
getMinNodeByRoot?.id // 1
const node15 = avlTree.get(15);
const getMinNodeBySpecificNode = node15 && avlTree.getLeftMost(node15);
getMinNodeBySpecificNode?.id // 12
const subTreeSum = node15 && avlTree.subTreeSum(node15);
subTreeSum // 70
const lesserSum = avlTree.lesserSum(10);
lesserSum // 45
const node11 = avlTree.get(11);
node11?.id // 11
const dfs = avlTree.DFS('in', 'node');
dfs[0].id // 1
avlTree.perfectlyBalance();
const bfs = avlTree.BFS('node');
avlTree.isPerfectlyBalanced() && bfs[0].id // 8
avlTree.remove(11, true)[0].deleted?.id // 11
avlTree.isAVLBalanced(); // true
node15 && avlTree.getHeight(node15) // 2
avlTree.remove(1, true)[0].deleted?.id // 1
avlTree.isAVLBalanced(); // true
avlTree.getHeight() // 4
avlTree.remove(4, true)[0].deleted?.id // 4
avlTree.isAVLBalanced(); // true
avlTree.getHeight() // 4
avlTree.remove(10, true)[0].deleted?.id // 10
avlTree.isAVLBalanced(); // true
avlTree.getHeight() // 3
avlTree.remove(15, true)[0].deleted?.id // 15
avlTree.isAVLBalanced(); // true
avlTree.getHeight() // 3
avlTree.remove(5, true)[0].deleted?.id // 5
avlTree.isAVLBalanced(); // true
avlTree.getHeight() // 3
avlTree.remove(13, true)[0].deleted?.id // 13
avlTree.isAVLBalanced(); // true
avlTree.getHeight() // 3
avlTree.remove(3, true)[0].deleted?.id // 3
avlTree.isAVLBalanced(); // true
avlTree.getHeight() // 3
avlTree.remove(8, true)[0].deleted?.id // 8
avlTree.isAVLBalanced(); // true
avlTree.getHeight() // 3
avlTree.remove(6, true)[0].deleted?.id // 6
avlTree.remove(6, true).length // 0
avlTree.isAVLBalanced(); // true
avlTree.getHeight() // 2
avlTree.remove(7, true)[0].deleted?.id // 7
avlTree.isAVLBalanced(); // true
avlTree.getHeight() // 2
avlTree.remove(9, true)[0].deleted?.id // 9
avlTree.isAVLBalanced(); // true
avlTree.getHeight() // 2
avlTree.remove(14, true)[0].deleted?.id // 14
avlTree.isAVLBalanced(); // true
avlTree.getHeight() // 1
avlTree.isAVLBalanced(); // true
const lastBFSIds = avlTree.BFS();
lastBFSIds[0] // 12
const lastBFSNodes = avlTree.BFS('node');
lastBFSNodes[0].id // 12
JS
const {AVLTree} = require('data-structure-typed');
// /* or if you prefer */ const {AVLTree} = require('avl-tree-typed');
const avlTree = new AVLTree();
const idsOrVals = [11, 3, 15, 1, 8, 13, 16, 2, 6, 9, 12, 14, 4, 7, 10, 5];
avlTree.addMany(idsOrVals, idsOrVals);
const node6 = avlTree.get(6);
node6 && avlTree.getHeight(node6) // 3
node6 && avlTree.getDepth(node6) // 1
const getNodeById = avlTree.get(10, 'id');
getNodeById?.id // 10
const getMinNodeByRoot = avlTree.getLeftMost();
getMinNodeByRoot?.id // 1
const node15 = avlTree.get(15);
const getMinNodeBySpecificNode = node15 && avlTree.getLeftMost(node15);
getMinNodeBySpecificNode?.id // 12
const subTreeSum = node15 && avlTree.subTreeSum(node15);
subTreeSum // 70
const lesserSum = avlTree.lesserSum(10);
lesserSum // 45
const node11 = avlTree.get(11);
node11?.id // 11
const dfs = avlTree.DFS('in', 'node');
dfs[0].id // 1
avlTree.perfectlyBalance();
const bfs = avlTree.BFS('node');
avlTree.isPerfectlyBalanced() && bfs[0].id // 8
avlTree.remove(11, true)[0].deleted?.id // 11
avlTree.isAVLBalanced(); // true
node15 && avlTree.getHeight(node15) // 2
avlTree.remove(1, true)[0].deleted?.id // 1
avlTree.isAVLBalanced(); // true
avlTree.getHeight() // 4
avlTree.remove(4, true)[0].deleted?.id // 4
avlTree.isAVLBalanced(); // true
avlTree.getHeight() // 4
avlTree.remove(10, true)[0].deleted?.id // 10
avlTree.isAVLBalanced(); // true
avlTree.getHeight() // 3
avlTree.remove(15, true)[0].deleted?.id // 15
avlTree.isAVLBalanced(); // true
avlTree.getHeight() // 3
avlTree.remove(5, true)[0].deleted?.id // 5
avlTree.isAVLBalanced(); // true
avlTree.getHeight() // 3
avlTree.remove(13, true)[0].deleted?.id // 13
avlTree.isAVLBalanced(); // true
avlTree.getHeight() // 3
avlTree.remove(3, true)[0].deleted?.id // 3
avlTree.isAVLBalanced(); // true
avlTree.getHeight() // 3
avlTree.remove(8, true)[0].deleted?.id // 8
avlTree.isAVLBalanced(); // true
avlTree.getHeight() // 3
avlTree.remove(6, true)[0].deleted?.id // 6
avlTree.remove(6, true).length // 0
avlTree.isAVLBalanced(); // true
avlTree.getHeight() // 2
avlTree.remove(7, true)[0].deleted?.id // 7
avlTree.isAVLBalanced(); // true
avlTree.getHeight() // 2
avlTree.remove(9, true)[0].deleted?.id // 9
avlTree.isAVLBalanced(); // true
avlTree.getHeight() // 2
avlTree.remove(14, true)[0].deleted?.id // 14
avlTree.isAVLBalanced(); // true
avlTree.getHeight() // 1
avlTree.isAVLBalanced(); // true
const lastBFSIds = avlTree.BFS();
lastBFSIds[0] // 12
const lastBFSNodes = avlTree.BFS('node');
lastBFSNodes[0].id // 12
API docs & Examples
Data Structures
| Data Structure | Unit Test | Performance Test | API Documentation | Implemented |
|---|---|---|---|---|
| Binary Tree | 
|
|
Binary Tree | |
| Binary Search Tree (BST) | |
|
BST | |
| AVL Tree | |
|
AVLTree | |
| Tree Multiset | |
|
TreeMultiset | |
| Segment Tree | SegmentTree | |
||
| Binary Indexed Tree | |
BinaryIndexedTree | |
|
| Graph | |
|
AbstractGraph | |
| Directed Graph | |
|
DirectedGraph | |
| Undirected Graph | |
|
UndirectedGraph | |
| Linked List | |
|
SinglyLinkedList | |
| Singly Linked List | |
|
SinglyLinkedList | |
| Doubly Linked List | |
|
DoublyLinkedList | |
| Queue | |
|
Queue | |
| Object Deque | |
|
ObjectDeque | |
| Array Deque | |
|
ArrayDeque | |
| Stack | |
Stack | |
|
| Coordinate Set | CoordinateSet | |
||
| Coordinate Map | CoordinateMap | |
||
| Heap | |
|
Heap | |
| Priority Queue | |
|
PriorityQueue | |
| Max Priority Queue | |
|
MaxPriorityQueue | |
| Min Priority Queue | |
|
MinPriorityQueue | |
| Trie | |
Trie | |
Why
Complexities
performance of Big O
| Big O Notation | Type | Computations for 10 elements | Computations for 100 elements | Computations for 1000 elements |
|---|---|---|---|---|
| O(1) | Constant | 1 | 1 | 1 |
| O(log N) | Logarithmic | 3 | 6 | 9 |
| O(N) | Linear | 10 | 100 | 1000 |
| O(N log N) | n log(n) | 30 | 600 | 9000 |
| O(N^2) | Quadratic | 100 | 10000 | 1000000 |
| O(2^N) | Exponential | 1024 | 1.26e+29 | 1.07e+301 |
| O(N!) | Factorial | 3628800 | 9.3e+157 | 4.02e+2567 |
Data Structure Complexity
| Data Structure | Access | Search | Insertion | Deletion | Comments |
|---|---|---|---|---|---|
| Array | 1 | n | n | n | |
| Stack | n | n | 1 | 1 | |
| Queue | n | n | 1 | 1 | |
| Linked List | n | n | 1 | n | |
| Hash Table | - | n | n | n | In case of perfect hash function costs would be O(1) |
| Binary Search Tree | n | n | n | n | In case of balanced tree costs would be O(log(n)) |
| B-Tree | log(n) | log(n) | log(n) | log(n) | |
| Red-Black Tree | log(n) | log(n) | log(n) | log(n) | |
| AVL Tree | log(n) | log(n) | log(n) | log(n) | |
| Bloom Filter | - | 1 | 1 | - | False positives are possible while searching |
Sorting Complexity
| Name | Best | Average | Worst | Memory | Stable | Comments |
|---|---|---|---|---|---|---|
| Bubble sort | n | n2 | n2 | 1 | Yes | |
| Insertion sort | n | n2 | n2 | 1 | Yes | |
| Selection sort | n2 | n2 | n2 | 1 | No | |
| Heap sort | n log(n) | n log(n) | n log(n) | 1 | No | |
| Merge sort | n log(n) | n log(n) | n log(n) | n | Yes | |
| Quick sort | n log(n) | n log(n) | n2 | log(n) | No | Quicksort is usually done in-place with O(log(n)) stack space |
| Shell sort | n log(n) | depends on gap sequence | n (log(n))2 | 1 | No | |
| Counting sort | n + r | n + r | n + r | n + r | Yes | r - biggest number in array |
| Radix sort | n * k | n * k | n * k | n + k | Yes | k - length of longest key |
