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: 简体中文, 繁體中文
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.
B
- Beginner, A
- Advanced
B
Linked ListB
QueueB
StackB
Hash TableB
HeapB
Priority QueueA
TrieA
TreeA
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
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
FactorialB
Fibonacci NumberB
Primality Test (trial division method)B
Euclidean Algorithm - calculate the Greatest Common Divisor (GCD)B
Least Common Multiple (LCM)A
Integer PartitionB
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)A
Liu Hui π Algorithm - approximate π calculations based on N-gons
- Sets
B
Cartesian Product - product of multiple setsA
Power Set - all subsets of a setA
Permutations (with and without repetitions)A
Combinations (with and without repetitions)B
Fisher–Yates Shuffle - random permutation of a finite sequenceA
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) versions
- Strings
A
Levenshtein Distance - minimum edit distance between two sequencesB
Hamming Distance - number of positions at which the symbols are differentA
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
- Sorting
B
Bubble SortB
Selection SortB
Insertion SortB
Heap SortB
Merge SortB
Quicksort - in-place and non-in-place implementationsB
ShellsortA
Counting SortA
Radix Sort
- Trees
B
Depth-First Search (DFS)B
Breadth-First Search (BFS)
- Graphs
B
Depth-First Search (DFS)B
Breadth-First Search (BFS)A
Dijkstra Algorithm - finding shortest path to all graph verticesA
Bellman-Ford Algorithm - finding shortest path to all graph 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 graphB
Kruskal’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
- Uncategorized
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
A
Maximum SubarrayA
Travelling Salesman Problem - shortest possible route that visits each city and returns to the origin city
- Greedy - choose the best option at the current time, without any consideration for the future
A
Unbound Knapsack ProblemA
Dijkstra Algorithm - finding 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
Euclidean Algorithm - calculate the Greatest Common Divisor (GCD)A
Permutations (with and without repetitions)A
Combinations (with and without repetitions)B
Merge SortB
QuicksortB
Tree Depth-First Search (DFS)B
Graph Depth-First Search (DFS)
- Dynamic Programming - build up a solution using previously found sub-solutions
B
Fibonacci NumberA
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 shortest path to all graph verticesA
Regular Expression Matching
- 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.
A
Hamiltonian Cycle - Visit every vertex exactly onceA
N-Queens ProblemA
Knight's Tour
- 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 all tests
npm test
Run tests by name
npm test -- -t 'LinkedList'
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 -- -t 'playground'
Useful Information
References
Big O Notation
Order 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 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 | 1 | |
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) |
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 | |
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 |