javascript-algorithms/README.md
Oleksii Trekhleb 77e897b3b9 Add factorial.
2018-04-18 13:04:05 +03:00

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# JavaScript Algorithms and Data Structures
[![Build Status](https://travis-ci.org/trekhleb/javascript-algorithms.svg?branch=master)](https://travis-ci.org/trekhleb/javascript-algorithms)
[![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
## Code Examples
### Data Structures
1. [Linked List](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/linked-list)
2. [Queue](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/queue)
3. [Stack](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/stack)
4. [Hash Table](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/hash-table)
5. [Heap](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/heap)
6. [Priority Queue](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/priority-queue)
7. [Trie](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/trie)
8. [Tree](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/tree)
* [Binary Search Tree](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/tree/binary-search-tree)
* [AVL Tree](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/tree/avl-tree)
* B-Tree
* 2-3 Tree
* Red-Black Tree
* Suffix Tree
* Segment Tree or Interval Tree
* Binary Indexed Tree or Fenwick Tree
9. [Graph](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/graph)
### Algorithms
* **Math**
* [Factorial](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/factorial)
* [Fibonacci Number](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/fibonacci)
* [Cartesian Product](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/cartesian-product)
* [Power Set](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/power-set)
* [Primality Test](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/primality-test) (trial division)
* [Euclidean Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/euclidean-algorithm) - calculate the greatest common divisor (GCD)
* [Least Common Multiple (LCM)](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/least-common-multiple)
* [FisherYates Shuffle](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/fisher-yates) - random permutation of a finite sequence
* **String**
* [Permutations](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/permutations) (with and without repetitions)
* [Combinations](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/combinations) (with and without repetitions)
* Minimum Edit distance (Levenshtein Distance)
* Hamming
* Huffman
* Knuth Morris Pratt
* Longest common subsequence
* longest common substring
* Rabin Karp
* **Search**
* [Binary Search](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/search/binary-search)
* **Sorting**
* [Bubble Sort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/bubble-sort)
* [Selection Sort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/selection-sort)
* [Insertion Sort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/insertion-sort)
* [Heap Sort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/heap-sort)
* [Merge Sort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/merge-sort)
* [Quicksort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/quick-sort)
* [Shellsort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/shell-sort)
* **Graph**
* [Depth-First Search (DFS)](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/depth-first-search)
* [Breadth-First Search (BFS)](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/breadth-first-search)
* Detect Cycle
* Topological Sorting
* Dijkstra Algorithm to Find Shortest Path
* Eulerian path, Eulerian circuit
* Bellman Ford
* Strongly Connected Component algorithm
* Shortest Path Faster Algorithm (SPFA)
* **Tree**
* Depth-First Search (DFS)
* Breadth-First Search (BFS)
* **Minimum Spanning Tree**
* Prims algorithm
* Kruskals algorithm
* **Dynamic Programming**
* Increasing subsequence
* Knapsack problem
* Maximum subarray
* Maximum sum path
* Integer Partition
* Longest common Subsequence
* Longest Increasing subsequence
* Shortest common supersequence
* **Uncategorized**
* Union-Find
* Maze
## Running Tests
**Run all tests**
```
npm test
```
**Run tests by name**
```
npm test -- -t 'LinkedList'
```
## Playground
You may play with data-structures and algorithms in `./src/playground/playground.js` file and write
tests for it in `./src/playground/__test__/playground.test.js`.
Then just simply run the following command to test if your playground code works as expected:
```
npm test -- -t 'playground'
```
## Useful links
* [Data Structures and Algorithms on YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
* Algorithms
* Dynamic Programming
* [Introduction to Dynamic Programming 1](https://www.hackerearth.com/practice/algorithms/dynamic-programming/introduction-to-dynamic-programming-1/tutorial/)
## Useful Information
### Big O Notation
Order of growth of algorithms specified in Big O notation.
![Big O graphs](https://github.com/trekhleb/javascript-algorithms/blob/master/assets/big-o-graph.png)
Source: [Big O Cheat Sheet](http://bigocheatsheet.com/).
Below is the list of some of the most used Big O notations and their performance comparisons against different sizes of the input data.
| Big O Notation | Computations for 10 elements | Computations for 100 elements | Computations for 1000 elements |
| -------------- | ---------------------------- | ----------------------------- | ------------------------------- |
| **O(1)** | 1 | 1 | 1 |
| **O(log N)** | 3 | 6 | 9 |
| **O(N)** | 10 | 100 | 1000 |
| **O(N log N)** | 30 | 60 | 9000 |
| **O(N^2)** | 100 | 10000 | 1000000 |
| **O(2^N)** | 1024 | 1.26e+29 | 1.07e+301 |
| **O(N!)** | 3628800 | 9.3e+157 | 4.02e+2567 |
### Data Structure Operations Complexity
| Data Structure | Access | Search | Insertion | Deletion |
| ----------------------- | :-------: | :-------: | :-------: | :-------: |
| **Array** | 1 | n | n | n |
| **Stack** | n | n | 1 | 1 |
| **Queue** | n | n | 1 | 1 |
| **Linked List** | n | n | 1 | 1 |
| **Hash Table** | - | n | n | n |
| **Binary Search Tree** | n | n | n | 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) |
### Array Sorting Algorithms Complexity
| Name | Best | Average | Worst | Memory | Stable |
| --------------------- | :-------: | :-------: | :-----------: | :-------: | :-------: |
| **Bubble sort** | n | n^2 | n^2 | 1 | Yes |
| **Insertion sort** | n | n^2 | n^2 | 1 | Yes |
| **Selection sort** | n^2 | n^2 | n^2 | 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) | n^2 | log(n) | No |
| **Shell sort** | n log(n) | depends on gap sequence | n (log(n))^2 | 1 | No |