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).

    Read this in other languages: , 繁體中文, , 日本語, , Français, , Português, , Türk, , Bahasa Indonesia, , Arabic

    ☝ 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.

    - Beginner, A - Advanced

    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.

    • Math
      • B Bit Manipulation - set/get/update/clear bits, multiplication/division by two, make negative etc.
      • B
      • B Fibonacci Number - classic and closed-form versions
      • B - finding prime factors and counting them using Hardy-Ramanujan’s theorem
      • B Primality Test (trial division method)
      • B - calculate the Greatest Common Divisor (GCD)
      • B Least Common Multiple (LCM)
      • B - 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
      • B Complex Number - complex numbers and basic operations with them
      • B - radians to degree and backwards conversion
      • B Fast Powering
      • B - polynomial evaluation
      • B Matrices - matrices and basic matrix operations (multiplication, transposition, etc.)
      • B - distance between two points/vectors/matrices
      • A Integer Partition
      • A - Newton’s method
      • A Liu Hui π Algorithm - approximate π calculations based on N-gons
      • A - decompose a function of time (a signal) into the frequencies that make it up
    • Sets
    • Strings
    • Searches
    • Sorting
    • Linked Lists
    • Trees
    • Graphs
      • B Depth-First Search (DFS)
      • B (BFS)
      • B Kruskal’s Algorithm - finding Minimum Spanning Tree (MST) for weighted undirected graph
      • A - finding the shortest paths to all graph vertices from single vertex
      • A Bellman-Ford Algorithm - finding the shortest paths to all graph vertices from single vertex
      • A - 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 - finding Minimum Spanning Tree (MST) for weighted undirected graph
      • A Topological Sorting - DFS method
      • A - Tarjan’s algorithm (DFS based)
      • A Bridges - DFS based algorithm
      • A - Fleury’s algorithm - Visit every edge exactly once
      • A Hamiltonian Cycle - Visit every vertex exactly once
      • A - Kosaraju’s algorithm
      • A Travelling Salesman Problem - shortest possible route that visits each city and returns to the origin city
    • Cryptography
      • B - rolling hash function based on polynomial
      • B Rail Fence Cipher - a transposition cipher algorithm for encoding messages
      • B - simple substitution cipher
      • B Hill Cipher - substitution cipher based on linear algebra
    • Machine Learning
      • B - 7 simple JS functions that illustrate how machines can actually learn (forward/backward propagation)
      • B k-NN - k-nearest neighbors classification algorithm
      • B - k-Means clustering algorithm
    • Uncategorized
      • B Tower of Hanoi
      • B - in-place algorithm
      • B Jump Game - backtracking, dynamic programming (top-down + bottom-up) and greedy examples
      • B - 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)
      • - divide and conquer and one-pass examples
      • A N-Queens Problem
      • A

    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 - trapping rain water problem
      • B Recursive Staircase - count the number of ways to reach to the top
      • A
      • A Travelling Salesman Problem - shortest possible route that visits each city and returns to the origin city
      • A - 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
      • A Dijkstra Algorithm - finding the shortest path to all graph vertices
      • A - 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
    • Dynamic Programming - build up a solution using previously found sub-solutions
    • 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.
    • 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.

    Install all dependencies

    Run ESLint

    You may want to run it to check code quality.

    Run all tests

    Run tests by name

    Playground

    Then just simply run the following command to test if your playground code works as expected:

    ▶ 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.

    Array Sorting Algorithms Complexity