JavaScript Algorithms and Data Structures
🇺🇦 UKRAINE IS BEING ATTACKED BY RUSSIAN ARMY. CIVILIANS ARE GETTING KILLED. RESIDENTIAL AREAS ARE GETTING BOMBED.
![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)
This repository contains JavaScript based examples of many
popular algorithms and data structures.
Each algorithm and data structure has its own separate README
with related explanations and links for further reading (including ones
to YouTube videos).
Read this in other languages:
简体中文,
繁體中文,
한국어,
日本語,
Polski,
Français,
Español,
Português,
Русский,
Türk,
Italiana,
Bahasa Indonesia,
Українська,
Arabic,
Tiếng Việt,
Deutsch
☝ Note that this project is meant to be used for learning and researching purposes
only, and it is not meant to be used for production.
Data Structures
A data structure is a particular way of organizing and storing data in a computer so that it can
be accessed and modified efficiently. More precisely, a data structure is a collection of data
values, the relationships among them, and the functions or operations that can be applied to
the data.
B
- Beginner, A
- Advanced
Algorithms
An algorithm is an unambiguous specification of how to solve a class of problems. It is
a set of rules that precisely define a sequence of operations.
B
- Beginner, A
- Advanced
Algorithms by Topic
- Math
- Sets
- Strings
- Searches
- Sorting
- Linked Lists
- Trees
- Graphs
- Cryptography
- Machine Learning
B
NanoNeuron - 7 simple JS functions that illustrate how machines can actually learn (forward/backward propagation)B
k-NN - k-nearest neighbors classification algorithmB
k-Means - k-Means clustering algorithm
- Image Processing
- Statistics
B
Weighted Random - select the random item from the list based on items' weights
- Evolutionary algorithms
A
Genetic algorithm - example of how the genetic algorithm may be applied for training the self-parking cars
- Uncategorized
Algorithms by Paradigm
An algorithmic paradigm is a generic method or approach which underlies the design of a class
of algorithms. It is an abstraction higher than the notion of an algorithm, just as an
algorithm is an abstraction higher than a computer program.
- Brute Force - look at all the possibilities and selects the best solution
- Greedy - choose the best option at the current time, without any consideration for the future
- Divide and Conquer - divide the problem into smaller parts and then solve those parts
- Dynamic Programming - build up a solution using previously found sub-solutions
- Backtracking - similarly to brute force, try to generate all possible solutions, but each time you generate next solution you test
if it satisfies all conditions, and only then continue generating subsequent solutions. Otherwise, backtrack, and go on a
different path of finding a solution. Normally the DFS traversal of state-space is being used.
- Branch & Bound - remember the lowest-cost solution found at each stage of the backtracking
search, and use the cost of the lowest-cost solution found so far as a lower bound on the cost of
a least-cost solution to the problem, in order to discard partial solutions with costs larger than the
lowest-cost solution found so far. Normally BFS traversal in combination with DFS traversal of state-space
tree is being used.
How to use this repository
Install all dependencies
npm install
Run ESLint
You may want to run it to check code quality.
npm run lint
Run all tests
npm test
Run tests by name
npm test -- 'LinkedList'
Troubleshooting
In case if linting or testing is failing try to delete the node_modules
folder and re-install npm packages:
rm -rf ./node_modules
npm i
Also make sure that you're using a correct Node version (>=14.16.0
). If you're using nvm for Node version management you may run nvm use
from the root folder of the project and the correct version will be picked up.
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 -- 'playground'
Useful Information
References
▶ Data Structures and Algorithms on YouTube
Big O Notation
Big O notation is used to classify algorithms according to how their running time or space requirements grow as the input size grows.
On the chart below you may find most common orders of growth of algorithms specified in Big O notation.
![Big O graphs](https://gitlab.com/feng3d/data-structures-and-algorithms/raw/HEAD/./assets/big-o-graph.png)
Source: Big O Cheat Sheet.
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 | 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 Operations 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 |
Array Sorting Algorithms 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 |
Project Backers
You may support this project via ❤️️ GitHub or ❤️️ Patreon.
Folks who are backing this project ∑ = 0
ℹ️ A few more projects and articles about JavaScript and algorithms on trekhleb.dev