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).
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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.
Remember that each data has its own trade-offs. And you need to pay attention more to why you're choosing a certain data structure than to how to implement it.
B - Beginner, A - Advanced
B Linked ListB Doubly Linked ListB QueueB StackB Deque - double-ended queueB Hash TableB Heap - max and min heap versionsB Priority QueueA TrieA Tree
A 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 SortB Bucket Sort
- Linked Lists
B Straight TraversalB Reverse Traversal
- 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 examplesB Valid Parentheses - check if a string has valid parentheses (using stack)A 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 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 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 the next solution, you test
if it satisfies all conditions and only then continue generating subsequent solutions. Otherwise, backtrack and go on a
different path to 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 the 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
- ▶ Data Structures and Algorithms on YouTube
- ✍🏻 Data Structure Sketches
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 the 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 |
Author
@trekhleb
A few more projects and articles about JavaScript and algorithms on trekhleb.dev:
- 🧠 yesbrainer.ai – council of AI models for the decisions that aren’t no-brainers (BYOK, private, no account)
- ✍🏻 okso.app – drawing app to express, grasp, and organize your thoughts and ideas
