š Algorithms and data structures implemented in JavaScript with explanations and links to further readings
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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: ē®ä½äøę, ē¹é«äøę, ķźµģ“, ę„ę¬čŖ, Polski, FranĆ§ais, EspaĆ±ol, PortuguĆŖs, Š ŃŃŃŠŗŠøŠ¹, TĆ¼rkĆ§e, Italiana, Bahasa Indonesia, Š£ŠŗŃŠ°ŃŠ½ŃŃŠŗŠ°, Arabic, Tiįŗæng Viį»t, Deutsch
ā 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.
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 versionsB
Priority Queue
A
Trie
A
Tree
A
Binary Search Tree
A
AVL Tree
A
Red-Black Tree
A
Segment Tree - with min/max/sum range queries examplesA
Fenwick Tree (Binary Indexed Tree)A
Graph (both directed and undirected)A
Disjoint Set - a unionāfind data structure or mergeāfind setA
Bloom Filter
A
LRU Cache - Least Recently Used (LRU) cacheAn 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
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
Factorial
B
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 Triangle
B
Complex Number - complex numbers and basic operations with themB
Radian & Degree - radians to degree and backwards conversionB
Fast Powering
B
Horner's method - polynomial evaluationB
Matrices - matrices and basic matrix operations (multiplication, transposition, etc.)B
Euclidean Distance - distance between two points/vectors/matricesA
Integer Partition
A
Square Root - Newton's methodA
Liu Hui Ļ Algorithm - approximate Ļ calculations based on N-gonsA
Discrete Fourier Transform - decompose a function of time (a signal) into the frequencies that make it upB
Cartesian Product - product of multiple setsB
FisherāYates 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 Subsequence
A
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 sumB
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
KnuthāMorrisāPratt Algorithm (KMP Algorithm) - substring search (pattern matching)A
Z Algorithm - substring search (pattern matching)A
Rabin Karp Algorithm - substring searchA
Longest Common Substring
A
Regular Expression Matching
B
Linear Search
B
Jump Search (or Block Search) - search in sorted arrayB
Binary Search - search in sorted arrayB
Interpolation Search - search in uniformly distributed sorted arrayB
Bubble Sort
B
Selection Sort
B
Insertion Sort
B
Heap Sort
B
Merge Sort
B
Quicksort - in-place and non-in-place implementationsB
Shellsort
B
Counting Sort
B
Radix Sort
B
Bucket Sort
B
Depth-First Search (DFS)B
Breadth-First Search (BFS)B
Depth-First Search (DFS)B
Breadth-First Search (BFS)B
Kruskalās 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
Primās 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 cityB
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 algebraB
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 algorithmB
Seam Carving - content-aware image resizing algorithmB
Weighted Random - select the random item from the list based on items' weightsA
Genetic algorithm - example of how the genetic algorithm may be applied for training the self-parking carsB
Tower of Hanoi
B
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 Problem
A
Knight's Tour
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.
B
Linear Search
B
Rain Terraces - trapping rain water problemB
Recursive Staircase - count the number of ways to reach to the topA
Maximum Subarray
A
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 upB
Jump Game
A
Unbound Knapsack Problem
A
Dijkstra Algorithm - finding the shortest path to all graph verticesA
Primās Algorithm - finding Minimum Spanning Tree (MST) for weighted undirected graphA
Kruskalās Algorithm - finding Minimum Spanning Tree (MST) for weighted undirected graphB
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 Depth-First Search (DFS)B
Graph Depth-First Search (DFS)B
Matrices - generating and traversing the matrices of different shapesB
Jump Game
B
Fast Powering
B
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
B
Fibonacci Number
B
Jump Game
B
Unique Paths
B
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 Substring
A
Longest Increasing Subsequence
A
Shortest Common Supersequence
A
0/1 Knapsack Problem
A
Integer Partition
A
Maximum Subarray
A
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
B
Jump Game
B
Unique Paths
B
Power Set - all subsets of a setA
Hamiltonian Cycle - Visit every vertex exactly onceA
N-Queens Problem
A
Knight's Tour
A
Combination Sum - find all combinations that form specific sumInstall 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'
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 | 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 |
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 | nĀ log(n) | nĀ log(n) | nĀ log(n) | 1 | No | |
Merge sort | nĀ log(n) | nĀ log(n) | nĀ log(n) | n | Yes | |
Quick sort | nĀ log(n) | nĀ log(n) | n^{2} | log(n) | No | Quicksort is usually done in-place with O(log(n)) stack space |
Shell sort | nĀ log(n) | depends on gap sequence | nĀ (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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A few more projects and articles about JavaScript and algorithms on trekhleb.dev