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This repository contains JavaScript based examples of manypopular algorithms and data structures.

Each algorithm and data structure has its own separate READMEwith related explanations and links for further reading (including onesto 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 purposesonly, and it isnot meant to be used for production.

A data structure is a particular way of organizing and storing data in a computer so that it canbe accessed and modified efficiently. More precisely, a data structure is a collection of datavalues, the relationships among them, and the functions or operations that can be applied tothe data.

B - Beginner,A - Advanced

• BLinked List
• BDoubly Linked List
• BQueue
• BStack
• BHash Table
• BHeap - max and min heap versions
• BPriority Queue
• ATrie
• ATree
  • ABinary Search Tree
  • AAVL Tree
  • ARed-Black Tree
  • ASegment Tree - with min/max/sum range queries examples
  • AFenwick Tree (Binary Indexed Tree)
• AGraph (both directed and undirected)
• ADisjoint Set
• ABloom Filter

An algorithm is an unambiguous specification of how to solve a class of problems. It isa set of rules that precisely define a sequence of operations.

B - Beginner,A - Advanced

• Math
  • BBit Manipulation - set/get/update/clear bits, multiplication/division by two, make negative etc.
  • BBinary Floating Point - binary representation of the floating-point numbers.
  • BFactorial
  • BFibonacci Number - classic and closed-form versions
  • BPrime Factors - finding prime factors and counting them using Hardy-Ramanujan's theorem
  • BPrimality Test (trial division method)
  • BEuclidean Algorithm - calculate the Greatest Common Divisor (GCD)
  • BLeast Common Multiple (LCM)
  • BSieve of Eratosthenes - finding all prime numbers up to any given limit
  • BIs Power of Two - check if the number is power of two (naive and bitwise algorithms)
  • BPascal's Triangle
  • BComplex Number - complex numbers and basic operations with them
  • BRadian & Degree - radians to degree and backwards conversion
  • BFast Powering
  • BHorner's method - polynomial evaluation
  • BMatrices - matrices and basic matrix operations (multiplication, transposition, etc.)
  • BEuclidean Distance - distance between two points/vectors/matrices
  • AInteger Partition
  • ASquare Root - Newton's method
  • ALiu Hui π Algorithm - approximate π calculations based on N-gons
  • ADiscrete Fourier Transform - decompose a function of time (a signal) into the frequencies that make it up
• Sets
  • BCartesian Product - product of multiple sets
  • BFisher–Yates Shuffle - random permutation of a finite sequence
  • APower Set - all subsets of a set (bitwise and backtracking solutions)
  • APermutations (with and without repetitions)
  • ACombinations (with and without repetitions)
  • ALongest Common Subsequence (LCS)
  • ALongest Increasing Subsequence
  • AShortest Common Supersequence (SCS)
  • AKnapsack Problem - "0/1" and "Unbound" ones
  • AMaximum Subarray - "Brute Force" and "Dynamic Programming" (Kadane's) versions
  • ACombination Sum - find all combinations that form specific sum
• Strings
  • BHamming Distance - number of positions at which the symbols are different
  • BPalindrome - check if the string is the same in reverse
  • ALevenshtein Distance - minimum edit distance between two sequences
  • AKnuth–Morris–Pratt Algorithm (KMP Algorithm) - substring search (pattern matching)
  • AZ Algorithm - substring search (pattern matching)
  • ARabin Karp Algorithm - substring search
  • ALongest Common Substring
  • ARegular Expression Matching
• Searches
  • BLinear Search
  • BJump Search (or Block Search) - search in sorted array
  • BBinary Search - search in sorted array
  • BInterpolation Search - search in uniformly distributed sorted array
• Sorting
  • BBubble Sort
  • BSelection Sort
  • BInsertion Sort
  • BHeap Sort
  • BMerge Sort
  • BQuicksort - in-place and non-in-place implementations
  • BShellsort
  • BCounting Sort
  • BRadix Sort
• Linked Lists
  • BStraight Traversal
  • BReverse Traversal
• Trees
  • BDepth-First Search (DFS)
  • BBreadth-First Search (BFS)
• Graphs
  • BDepth-First Search (DFS)
  • BBreadth-First Search (BFS)
  • BKruskal’s Algorithm - finding Minimum Spanning Tree (MST) for weighted undirected graph
  • ADijkstra Algorithm - finding the shortest paths to all graph vertices from single vertex
  • ABellman-Ford Algorithm - finding the shortest paths to all graph vertices from single vertex
  • AFloyd-Warshall Algorithm - find the shortest paths between all pairs of vertices
  • ADetect Cycle - for both directed and undirected graphs (DFS and Disjoint Set based versions)
  • APrim’s Algorithm - finding Minimum Spanning Tree (MST) for weighted undirected graph
  • ATopological Sorting - DFS method
  • AArticulation Points - Tarjan's algorithm (DFS based)
  • ABridges - DFS based algorithm
  • AEulerian Path and Eulerian Circuit - Fleury's algorithm - Visit every edge exactly once
  • AHamiltonian Cycle - Visit every vertex exactly once
  • AStrongly Connected Components - Kosaraju's algorithm
  • ATravelling Salesman Problem - shortest possible route that visits each city and returns to the origin city
• Cryptography
  • BPolynomial Hash - rolling hash function based on polynomial
  • BRail Fence Cipher - a transposition cipher algorithm for encoding messages
  • BCaesar Cipher - simple substitution cipher
  • BHill Cipher - substitution cipher based on linear algebra
• Machine Learning
  • BNanoNeuron - 7 simple JS functions that illustrate how machines can actually learn (forward/backward propagation)
  • Bk-NN - k-nearest neighbors classification algorithm
  • Bk-Means - k-Means clustering algorithm
• Image Processing
  • BSeam Carving - content-aware image resizing algorithm
• Statistics
  • BWeighted Random - select the random item from the list based on items' weights
• Evolutionary algorithms
  • AGenetic algorithm - example of how the genetic algorithm may be applied for training the self-parking cars
• Uncategorized
  • BTower of Hanoi
  • BSquare Matrix Rotation - in-place algorithm
  • BJump Game - backtracking, dynamic programming (top-down + bottom-up) and greedy examples
  • BUnique Paths - backtracking, dynamic programming and Pascal's Triangle based examples
  • BRain Terraces - trapping rain water problem (dynamic programming and brute force versions)
  • BRecursive Staircase - count the number of ways to reach to the top (4 solutions)
  • BBest Time To Buy Sell Stocks - divide and conquer and one-pass examples
  • AN-Queens Problem
  • AKnight's Tour

An algorithmic paradigm is a generic method or approach which underlies the design of a classof algorithms. It is an abstraction higher than the notion of an algorithm, just as analgorithm is an abstraction higher than a computer program.

• Brute Force - look at all the possibilities and selects the best solution
  • BLinear Search
  • BRain Terraces - trapping rain water problem
  • BRecursive Staircase - count the number of ways to reach to the top
  • AMaximum Subarray
  • ATravelling Salesman Problem - shortest possible route that visits each city and returns to the origin city
  • ADiscrete 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
  • BJump Game
  • AUnbound Knapsack Problem
  • ADijkstra Algorithm - finding the shortest path to all graph vertices
  • APrim’s Algorithm - finding Minimum Spanning Tree (MST) for weighted undirected graph
  • AKruskal’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
  • BBinary Search
  • BTower of Hanoi
  • BPascal's Triangle
  • BEuclidean Algorithm - calculate the Greatest Common Divisor (GCD)
  • BMerge Sort
  • BQuicksort
  • BTree Depth-First Search (DFS)
  • BGraph Depth-First Search (DFS)
  • BMatrices - generating and traversing the matrices of different shapes
  • BJump Game
  • BFast Powering
  • BBest Time To Buy Sell Stocks - divide and conquer and one-pass examples
  • APermutations (with and without repetitions)
  • ACombinations (with and without repetitions)
  • AMaximum Subarray
• Dynamic Programming - build up a solution using previously found sub-solutions
  • BFibonacci Number
  • BJump Game
  • BUnique Paths
  • BRain Terraces - trapping rain water problem
  • BRecursive Staircase - count the number of ways to reach to the top
  • BSeam Carving - content-aware image resizing algorithm
  • ALevenshtein Distance - minimum edit distance between two sequences
  • ALongest Common Subsequence (LCS)
  • ALongest Common Substring
  • ALongest Increasing Subsequence
  • AShortest Common Supersequence
  • A0/1 Knapsack Problem
  • AInteger Partition
  • AMaximum Subarray
  • ABellman-Ford Algorithm - finding the shortest path to all graph vertices
  • AFloyd-Warshall Algorithm - find the shortest paths between all pairs of vertices
  • ARegular Expression Matching
• Backtracking - similarly to brute force, try to generate all possible solutions, but each time you generate next solution you testif it satisfies all conditions, and only then continue generating subsequent solutions. Otherwise, backtrack, and go on adifferent path of finding a solution. Normally the DFS traversal of state-space is being used.
  • BJump Game
  • BUnique Paths
  • BPower Set - all subsets of a set
  • AHamiltonian Cycle - Visit every vertex exactly once
  • AN-Queens Problem
  • AKnight's Tour
  • ACombination Sum - find all combinations that form specific sum
• Branch & Bound - remember the lowest-cost solution found at each stage of the backtrackingsearch, and use the cost of the lowest-cost solution found so far as a lower bound on the cost ofa least-cost solution to the problem, in order to discard partial solutions with costs larger than thelowest-cost solution found so far. Normally BFS traversal in combination with DFS traversal of state-spacetree is being used.

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 thenode_modules folder and re-install npm packages:

rm -rf ./node_modulesnpm i

Also make sure that you're using a correct Node version (>=14.16.0). If you're usingnvm for Node version management you may runnvm 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 writetests 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'

• ▶ Data Structures and Algorithms on YouTube
• ✍🏻 Data Structure Sketches

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.

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ℹ️ A few moreprojects andarticles about JavaScript and algorithms ontrekhleb.dev