By https://github.com/trekhleb/javascriptalgorithms
JavaScript Algorithms and Data Structures
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).
☝ 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

B
Linked List 
B
Doubly Linked List 
B
Queue 
B
Stack 
B
Hash Table 
B
Heap  max and min heap versions 
B
Priority Queue 
A
Trie 
A
Tree
A
Binary Search Tree 
A
AVL Tree 
A
RedBlack Tree 
A
Segment Tree  with min/max/sum range queries examples 
A
Fenwick Tree (Binary Indexed Tree)


A
Graph (both directed and undirected) 
A
Disjoint Set 
A
Bloom Filter
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

B
Bit Manipulation  set/get/update/clear bits, multiplication/division by two, make negative etc. 
B
Binary Floating Point  binary representation of the floatingpoint numbers. 
B
Factorial 
B
Fibonacci Number  classic and closedform versions 
B
Prime Factors  finding prime factors and counting them using HardyRamanujan's theorem 
B
Primality Test (trial division method) 
B
Euclidean Algorithm  calculate the Greatest Common Divisor (GCD) 
B
Least Common Multiple (LCM) 
B
Sieve of Eratosthenes  finding all prime numbers up to any given limit 
B
Is Power of Two  check if the number is power of two (naive and bitwise algorithms) 
B
Pascal's Triangle 
B
Complex Number  complex numbers and basic operations with them 
B
Radian & Degree  radians to degree and backwards conversion 
B
Fast Powering 
B
Horner's method  polynomial evaluation 
B
Matrices  matrices and basic matrix operations (multiplication, transposition, etc.) 
B
Euclidean Distance  distance between two points/vectors/matrices 
A
Integer Partition 
A
Square Root  Newton's method 
A
Liu Hui π Algorithm  approximate π calculations based on Ngons 
A
Discrete Fourier Transform  decompose a function of time (a signal) into the frequencies that make it up


Sets

B
Cartesian Product  product of multiple sets 
B
Fisher–Yates Shuffle  random permutation of a finite sequence 
A
Power Set  all subsets of a set (bitwise and backtracking solutions) 
A
Permutations (with and without repetitions) 
A
Combinations (with and without repetitions) 
A
Longest Common Subsequence (LCS) 
A
Longest Increasing Subsequence 
A
Shortest Common Supersequence (SCS) 
A
Knapsack Problem  "0/1" and "Unbound" ones 
A
Maximum Subarray  "Brute Force" and "Dynamic Programming" (Kadane's) versions 
A
Combination Sum  find all combinations that form specific sum


Strings

B
Hamming Distance  number of positions at which the symbols are different 
A
Levenshtein Distance  minimum edit distance between two sequences 
A
Knuth–Morris–Pratt Algorithm (KMP Algorithm)  substring search (pattern matching) 
A
Z Algorithm  substring search (pattern matching) 
A
Rabin Karp Algorithm  substring search 
A
Longest Common Substring 
A
Regular Expression Matching


Searches

B
Linear Search 
B
Jump Search (or Block Search)  search in sorted array 
B
Binary Search  search in sorted array 
B
Interpolation Search  search in uniformly distributed sorted array


Sorting

B
Bubble Sort 
B
Selection Sort 
B
Insertion Sort 
B
Heap Sort 
B
Merge Sort 
B
Quicksort  inplace and noninplace implementations 
B
Shellsort 
B
Counting Sort 
B
Radix Sort

 Linked Lists

Trees

B
DepthFirst Search (DFS) 
B
BreadthFirst Search (BFS)


Graphs

B
DepthFirst Search (DFS) 
B
BreadthFirst Search (BFS) 
B
Kruskal’s Algorithm  finding Minimum Spanning Tree (MST) for weighted undirected graph 
A
Dijkstra Algorithm  finding the shortest paths to all graph vertices from single vertex 
A
BellmanFord Algorithm  finding the shortest paths to all graph vertices from single vertex 
A
FloydWarshall Algorithm  find the shortest paths between all pairs of vertices 
A
Detect Cycle  for both directed and undirected graphs (DFS and Disjoint Set based versions) 
A
Prim’s Algorithm  finding Minimum Spanning Tree (MST) for weighted undirected graph 
A
Topological Sorting  DFS method 
A
Articulation Points  Tarjan's algorithm (DFS based) 
A
Bridges  DFS based algorithm 
A
Eulerian Path and Eulerian Circuit  Fleury's algorithm  Visit every edge exactly once 
A
Hamiltonian Cycle  Visit every vertex exactly once 
A
Strongly Connected Components  Kosaraju's algorithm 
A
Travelling Salesman Problem  shortest possible route that visits each city and returns to the origin city


Cryptography

B
Polynomial Hash  rolling hash function based on polynomial 
B
Rail Fence Cipher  a transposition cipher algorithm for encoding messages 
B
Caesar Cipher  simple substitution cipher 
B
Hill Cipher  substitution cipher based on linear algebra


Machine Learning

B
NanoNeuron  7 simple JS functions that illustrate how machines can actually learn (forward/backward propagation) 
B
kNN  knearest neighbors classification algorithm 
B
kMeans  kMeans clustering algorithm


Image Processing

B
Seam Carving  contentaware image resizing algorithm


Uncategorized

B
Tower of Hanoi 
B
Square Matrix Rotation  inplace algorithm 
B
Jump Game  backtracking, dynamic programming (topdown + bottomup) and greedy examples 
B
Unique Paths  backtracking, dynamic programming and Pascal's Triangle based examples 
B
Rain Terraces  trapping rain water problem (dynamic programming and brute force versions) 
B
Recursive Staircase  count the number of ways to reach to the top (4 solutions) 
B
Best Time To Buy Sell Stocks  divide and conquer and onepass examples 
A
NQueens Problem 
A
Knight's Tour

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

B
Linear Search 
B
Rain Terraces  trapping rain water problem 
B
Recursive Staircase  count the number of ways to reach to the top 
A
Maximum Subarray 
A
Travelling Salesman Problem  shortest possible route that visits each city and returns to the origin city 
A
Discrete Fourier Transform  decompose a function of time (a signal) into the frequencies that make it up


Greedy  choose the best option at the current time, without any consideration for the future

B
Jump Game 
A
Unbound Knapsack Problem 
A
Dijkstra Algorithm  finding the shortest path to all graph vertices 
A
Prim’s Algorithm  finding Minimum Spanning Tree (MST) for weighted undirected graph 
A
Kruskal’s Algorithm  finding Minimum Spanning Tree (MST) for weighted undirected graph


Divide and Conquer  divide the problem into smaller parts and then solve those parts

B
Binary Search 
B
Tower of Hanoi 
B
Pascal's Triangle 
B
Euclidean Algorithm  calculate the Greatest Common Divisor (GCD) 
B
Merge Sort 
B
Quicksort 
B
Tree DepthFirst Search (DFS) 
B
Graph DepthFirst Search (DFS) 
B
Matrices  generating and traversing the matrices of different shapes 
B
Jump Game 
B
Fast Powering 
B
Best Time To Buy Sell Stocks  divide and conquer and onepass examples 
A
Permutations (with and without repetitions) 
A
Combinations (with and without repetitions)


Dynamic Programming  build up a solution using previously found subsolutions

B
Fibonacci Number 
B
Jump Game 
B
Unique Paths 
B
Rain Terraces  trapping rain water problem 
B
Recursive Staircase  count the number of ways to reach to the top 
B
Seam Carving  contentaware image resizing algorithm 
A
Levenshtein Distance  minimum edit distance between two sequences 
A
Longest Common Subsequence (LCS) 
A
Longest Common Substring 
A
Longest Increasing Subsequence 
A
Shortest Common Supersequence 
A
0/1 Knapsack Problem 
A
Integer Partition 
A
Maximum Subarray 
A
BellmanFord Algorithm  finding the shortest path to all graph vertices 
A
FloydWarshall Algorithm  find the shortest paths between all pairs of vertices 
A
Regular Expression Matching


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 statespace is being used.

B
Jump Game 
B
Unique Paths 
B
Power Set  all subsets of a set 
A
Hamiltonian Cycle  Visit every vertex exactly once 
A
NQueens Problem 
A
Knight's Tour 
A
Combination Sum  find all combinations that form specific sum

 Branch & Bound  remember the lowestcost solution found at each stage of the backtracking search, and use the cost of the lowestcost solution found so far as a lower bound on the cost of a leastcost solution to the problem, in order to discard partial solutions with costs larger than the lowestcost solution found so far. Normally BFS traversal in combination with DFS traversal of statespace 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 reinstall npm packages:
rm rf ./node_modules
npm i
Playground
You may play with datastructures 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.
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  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  600  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  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)) 
BTree  log(n)  log(n)  log(n)  log(n)  
RedBlack 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  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  Quicksort is usually done inplace 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 
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ℹ️ A few more projects and articles about JavaScript and algorithms on trekhleb.dev
Top comments (2)
None of the links are working.
links adjusted, thanks!