đ Algorithms and data structures implemented in JavaScript with explanations and links to further readings
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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â 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
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 is a set of rules that precisely define a sequence of operations.
B- Beginner,
A- Advanced
BBit Manipulation - set/get/update/clear bits, multiplication/division by two, make negative etc.
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 Ď Algorithm - approximate Ď calculations based on N-gons
ADiscrete Fourier Transform - decompose a function of time (a signal) into the frequencies that make it up
BCartesian Product - product of multiple sets
BFisherâYates 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
BHamming Distance - number of positions at which the symbols are different
ALevenshtein Distance - minimum edit distance between two sequences
AKnuthâMorrisâPratt Algorithm (KMP Algorithm) - substring search (pattern matching)
AZ Algorithm - substring search (pattern matching)
ARabin Karp Algorithm - substring search
ALongest Common Substring
ARegular Expression Matching
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
BBubble Sort
BSelection Sort
BInsertion Sort
BHeap Sort
BMerge Sort
BQuicksort - in-place and non-in-place implementations
BShellsort
BCounting Sort
BRadix Sort
BDepth-First Search (DFS)
BBreadth-First Search (BFS)
BDepth-First Search (DFS)
BBreadth-First Search (BFS)
BKruskalâs 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)
APrimâs 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
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
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
BSeam Carving - content-aware image resizing algorithm
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 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.
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
BJump Game
AUnbound Knapsack Problem
ADijkstra Algorithm - finding the shortest path to all graph vertices
APrimâs Algorithm - finding Minimum Spanning Tree (MST) for weighted undirected graph
AKruskalâs Algorithm - finding Minimum Spanning Tree (MST) for weighted undirected graph
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)
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
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
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 the
node_modulesfolder and re-install npm packages:
rm -rf ./node_modules npm i
Playground
You may play with data-structures and algorithms in
./src/playground/playground.jsfile 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'
âś Data Structures and Algorithms on YouTube
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 | Computations for 10 elements | Computations for 100 elements | Computations for 1000 elements | | -------------- | ---------------------------- | ----------------------------- | ------------------------------- | | O(1) | 1 | 1 | 1 | | O(log N) | 3 | 6 | 9 | | O(N) | 10 | 100 | 1000 | | O(N log N) | 30 | 600 | 9000 | | O(N^2) | 100 | 10000 | 1000000 | | O(2^N) | 1024 | 1.26e+29 | 1.07e+301 | | O(N!) | 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 | 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) | n^{2} | 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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