JavaScript Algorithms and Data Structures
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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, Türkçe, 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
B
Linked ListB
Doubly Linked ListB
QueueB
StackB
Hash TableB
Heap - max and min heap versionsB
Priority QueueA
TrieA
TreeA
Binary Search TreeA
AVL TreeA
Red-Black TreeA
Segment Tree - with min/max/sum range queries examplesA
Fenwick Tree (Binary Indexed Tree)
A
Graph (both directed and undirected)A
Disjoint Set - a union–find data structure or merge–find setA
Bloom FilterA
LRU Cache - Least Recently Used (LRU) cache
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 floating-point numbers.B
FactorialB
Fibonacci Number - classic and closed-form versionsB
Prime Factors - finding prime factors and counting them using Hardy-Ramanujan's theoremB
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 limitB
Is Power of Two - check if the number is power of two (naive and bitwise algorithms)B
Pascal's TriangleB
Complex Number - complex numbers and basic operations with themB
Radian & Degree - radians to degree and backwards conversionB
Fast PoweringB
Horner's method - polynomial evaluationB
Matrices - matrices and basic matrix operations (multiplication, transposition, etc.)B
Euclidean Distance - distance between two points/vectors/matricesA
Integer PartitionA
Square Root - Newton's methodA
Liu Hui π Algorithm - approximate π calculations based on N-gonsA
Discrete Fourier Transform - decompose a function of time (a signal) into the frequencies that make it up
- Sets
B
Cartesian Product - product of multiple setsB
Fisher–Yates Shuffle - random permutation of a finite sequenceA
Power Set - all subsets of a set (bitwise, backtracking, and cascading solutions)A
Permutations (with and without repetitions)A
Combinations (with and without repetitions)A
Longest Common Subsequence (LCS)A
Longest Increasing SubsequenceA
Shortest Common Supersequence (SCS)A
Knapsack Problem - "0/1" and "Unbound" onesA
Maximum Subarray - "Brute Force" and "Dynamic Programming" (Kadane's) versionsA
Combination Sum - find all combinations that form specific sum
- Strings
B
Hamming Distance - number of positions at which the symbols are differentB
Palindrome - check if the string is the same in reverseA
Levenshtein Distance - minimum edit distance between two sequencesA
Knuth–Morris–Pratt Algorithm (KMP Algorithm) - substring search (pattern matching)A
Z Algorithm - substring search (pattern matching)A
Rabin Karp Algorithm - substring searchA
Longest Common SubstringA
Regular Expression Matching
- Searches
B
Linear SearchB
Jump Search (or Block Search) - search in sorted arrayB
Binary Search - search in sorted arrayB
Interpolation Search - search in uniformly distributed sorted array
- Sorting
B
Bubble SortB
Selection SortB
Insertion SortB
Heap SortB
Merge SortB
Quicksort - in-place and non-in-place implementationsB
ShellsortB
Counting SortB
Radix Sort
- Linked Lists
- Trees
B
Depth-First Search (DFS)B
Breadth-First Search (BFS)
- Graphs
B
Depth-First Search (DFS)B
Breadth-First Search (BFS)B
Kruskal’s Algorithm - finding Minimum Spanning Tree (MST) for weighted undirected graphA
Dijkstra Algorithm - finding the shortest paths to all graph vertices from single vertexA
Bellman-Ford Algorithm - finding the shortest paths to all graph vertices from single vertexA
Floyd-Warshall Algorithm - find the shortest paths between all pairs of verticesA
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 graphA
Topological Sorting - DFS methodA
Articulation Points - Tarjan's algorithm (DFS based)A
Bridges - DFS based algorithmA
Eulerian Path and Eulerian Circuit - Fleury's algorithm - Visit every edge exactly onceA
Hamiltonian Cycle - Visit every vertex exactly onceA
Strongly Connected Components - Kosaraju's algorithmA
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 polynomialB
Rail Fence Cipher - a transposition cipher algorithm for encoding messagesB
Caesar Cipher - simple substitution cipherB
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
k-NN - k-nearest neighbors classification algorithmB
k-Means - k-Means clustering algorithm
- Image Processing
B
Seam Carving - content-aware image resizing algorithm
- 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
B
Tower of HanoiB
Square Matrix Rotation - in-place algorithmB
Jump Game - backtracking, dynamic programming (top-down + bottom-up) and greedy examplesB
Unique Paths - backtracking, dynamic programming and Pascal's Triangle based examplesB
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 one-pass examplesA
N-Queens ProblemA
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 SearchB
Rain Terraces - trapping rain water problemB
Recursive Staircase - count the number of ways to reach to the topA
Maximum SubarrayA
Travelling Salesman Problem - shortest possible route that visits each city and returns to the origin cityA
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 GameA
Unbound Knapsack ProblemA
Dijkstra Algorithm - finding the shortest path to all graph verticesA
Prim’s Algorithm - finding Minimum Spanning Tree (MST) for weighted undirected graphA
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 SearchB
Tower of HanoiB
Pascal's TriangleB
Euclidean Algorithm - calculate the Greatest Common Divisor (GCD)B
Merge SortB
QuicksortB
Tree Depth-First Search (DFS)B
Graph Depth-First Search (DFS)B
Matrices - generating and traversing the matrices of different shapesB
Jump GameB
Fast PoweringB
Best Time To Buy Sell Stocks - divide and conquer and one-pass examplesA
Permutations (with and without repetitions)A
Combinations (with and without repetitions)A
Maximum Subarray
- Dynamic Programming - build up a solution using previously found sub-solutions
B
Fibonacci NumberB
Jump GameB
Unique PathsB
Rain Terraces - trapping rain water problemB
Recursive Staircase - count the number of ways to reach to the topB
Seam Carving - content-aware image resizing algorithmA
Levenshtein Distance - minimum edit distance between two sequencesA
Longest Common Subsequence (LCS)A
Longest Common SubstringA
Longest Increasing SubsequenceA
Shortest Common SupersequenceA
0/1 Knapsack ProblemA
Integer PartitionA
Maximum SubarrayA
Bellman-Ford Algorithm - finding the shortest path to all graph verticesA
Floyd-Warshall Algorithm - find the shortest paths between all pairs of verticesA
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 state-space is being used.
B
Jump GameB
Unique PathsB
Power Set - all subsets of a setA
Hamiltonian Cycle - Visit every vertex exactly onceA
N-Queens ProblemA
Knight's TourA
Combination Sum - find all combinations that form specific sum
- 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
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 (>=16
). 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
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 | 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 |
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Author
A few more projects and articles about JavaScript and algorithms on trekhleb.dev