mirror of
https://github.moeyy.xyz/https://github.com/trekhleb/javascript-algorithms.git
synced 2024-12-26 23:21:18 +08:00
229 lines
19 KiB
Markdown
229 lines
19 KiB
Markdown
# JavaScript Algorithms and Data Structures
|
||
|
||
[](https://travis-ci.org/trekhleb/javascript-algorithms)
|
||
[](https://codecov.io/gh/trekhleb/javascript-algorithms)
|
||
|
||
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](https://github.com/trekhleb/javascript-algorithms/blob/master/README.zh-CN.md),
|
||
[繁體中文](https://github.com/trekhleb/javascript-algorithms/blob/master/README.zh-TW.md)
|
||
|
||
## 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.
|
||
|
||
* [Linked List](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/linked-list)
|
||
* [Queue](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/queue)
|
||
* [Stack](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/stack)
|
||
* [Hash Table](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/hash-table)
|
||
* [Heap](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/heap)
|
||
* [Priority Queue](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/priority-queue)
|
||
* [Trie](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/trie)
|
||
* [Tree](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/tree)
|
||
* [Binary Search Tree](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/tree/binary-search-tree)
|
||
* [AVL Tree](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/tree/avl-tree)
|
||
* [Red-Black Tree](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/tree/red-black-tree)
|
||
* [Graph](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/graph) (both directed and undirected)
|
||
* [Disjoint Set](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/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.
|
||
|
||
### Algorithms by Topic
|
||
|
||
* **Math**
|
||
* [Factorial](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/factorial)
|
||
* [Fibonacci Number](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/fibonacci)
|
||
* [Primality Test](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/primality-test) (trial division method)
|
||
* [Euclidean Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/euclidean-algorithm) - calculate the Greatest Common Divisor (GCD)
|
||
* [Least Common Multiple](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/least-common-multiple) (LCM)
|
||
* [Integer Partition](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/integer-partition)
|
||
* **Sets**
|
||
* [Cartesian Product](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/cartesian-product) - product of multiple sets
|
||
* [Power Set](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/power-set) - all subsets of a set
|
||
* [Permutations](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/permutations) (with and without repetitions)
|
||
* [Combinations](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/combinations) (with and without repetitions)
|
||
* [Fisher–Yates Shuffle](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/fisher-yates) - random permutation of a finite sequence
|
||
* [Longest Common Subsequence](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/longest-common-subsequnce) (LCS)
|
||
* [Longest Increasing subsequence](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/longest-increasing-subsequence)
|
||
* [Shortest Common Supersequence](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/shortest-common-supersequence) (SCS)
|
||
* [Knapsack Problem](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/knapsack-problem) - "0/1" and "Unbound" ones
|
||
* [Maximum Subarray](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/maximum-subarray) - "Brute Force" and "Dynamic Programming" (Kadane's) versions
|
||
* **Strings**
|
||
* [Levenshtein Distance](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/levenshtein-distance) - minimum edit distance between two sequences
|
||
* [Hamming Distance](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/hamming-distance) - number of positions at which the symbols are different
|
||
* [Knuth–Morris–Pratt Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/knuth-morris-pratt) - substring search
|
||
* [Rabin Karp Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/rabin-karp) - substring search
|
||
* [Longest Common Substring](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/longest-common-substring)
|
||
* **Searches**
|
||
* [Linear Search](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/search/linear-search)
|
||
* [Binary Search](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/search/binary-search)
|
||
* **Sorting**
|
||
* [Bubble Sort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/bubble-sort)
|
||
* [Selection Sort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/selection-sort)
|
||
* [Insertion Sort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/insertion-sort)
|
||
* [Heap Sort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/heap-sort)
|
||
* [Merge Sort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/merge-sort)
|
||
* [Quicksort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/quick-sort) - in-place and non-in-place implementations
|
||
* [Shellsort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/shell-sort)
|
||
* [Counting Sort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/counting-sort)
|
||
* [Radix Sort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/radix-sort)
|
||
* **Trees**
|
||
* [Depth-First Search](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/tree/depth-first-search) (DFS)
|
||
* [Breadth-First Search](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/tree/breadth-first-search) (BFS)
|
||
* **Graphs**
|
||
* [Depth-First Search](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/depth-first-search) (DFS)
|
||
* [Breadth-First Search](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/breadth-first-search) (BFS)
|
||
* [Dijkstra Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/dijkstra) - finding shortest path to all graph vertices
|
||
* [Bellman-Ford Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/bellman-ford) - finding shortest path to all graph vertices
|
||
* [Detect Cycle](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/detect-cycle) - for both directed and undirected graphs (DFS and Disjoint Set based versions)
|
||
* [Prim’s Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/prim) - finding Minimum Spanning Tree (MST) for weighted undirected graph
|
||
* [Kruskal’s Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/kruskal) - finding Minimum Spanning Tree (MST) for weighted undirected graph
|
||
* [Topological Sorting](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/topological-sorting) - DFS method
|
||
* [Articulation Points](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/articulation-points) - Tarjan's algorithm (DFS based)
|
||
* [Bridges](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/bridges) - DFS based algorithm
|
||
* [Eulerian Path and Eulerian Circuit](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/eulerian-path) - Fleury's algorithm - Visit every edge exactly once
|
||
* [Hamiltonian Cycle](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/hamiltonian-cycle) - Visit every vertex exactly once
|
||
* [Strongly Connected Components](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/strongly-connected-components) - Kosaraju's algorithm
|
||
* [Travelling Salesman Problem](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/travelling-salesman) - shortest possible route that visits each city and returns to the origin city
|
||
* **Uncategorized**
|
||
* [Tower of Hanoi](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/uncategorized/hanoi-tower)
|
||
* [N-Queens Problem](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/uncategorized/n-queens)
|
||
* [Knight's Tour](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/uncategorized/knight-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
|
||
* [Maximum Subarray](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/maximum-subarray)
|
||
* [Travelling Salesman Problem](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/travelling-salesman) - 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
|
||
* [Unbound Knapsack Problem](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/knapsack-problem)
|
||
* [Dijkstra Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/dijkstra) - finding shortest path to all graph vertices
|
||
* [Prim’s Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/prim) - finding Minimum Spanning Tree (MST) for weighted undirected graph
|
||
* [Kruskal’s Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/kruskal) - finding Minimum Spanning Tree (MST) for weighted undirected graph
|
||
* **Divide and Conquer** - divide the problem into smaller parts and then solve those parts
|
||
* [Binary Search](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/search/binary-search)
|
||
* [Tower of Hanoi](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/uncategorized/hanoi-tower)
|
||
* [Euclidean Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/euclidean-algorithm) - calculate the Greatest Common Divisor (GCD)
|
||
* [Permutations](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/permutations) (with and without repetitions)
|
||
* [Combinations](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/combinations) (with and without repetitions)
|
||
* [Merge Sort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/merge-sort)
|
||
* [Quicksort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/quick-sort)
|
||
* [Tree Depth-First Search](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/tree/depth-first-search) (DFS)
|
||
* [Graph Depth-First Search](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/depth-first-search) (DFS)
|
||
* **Dynamic Programming** - build up a solution using previously found sub-solutions
|
||
* [Fibonacci Number](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/fibonacci)
|
||
* [Levenshtein Distance](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/levenshtein-distance) - minimum edit distance between two sequences
|
||
* [Longest Common Subsequence](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/longest-common-subsequnce) (LCS)
|
||
* [Longest Common Substring](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/longest-common-substring)
|
||
* [Longest Increasing subsequence](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/longest-increasing-subsequence)
|
||
* [Shortest Common Supersequence](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/shortest-common-supersequence)
|
||
* [0/1 Knapsack Problem](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/knapsack-problem)
|
||
* [Integer Partition](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/integer-partition)
|
||
* [Maximum Subarray](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/maximum-subarray)
|
||
* [Bellman-Ford Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/bellman-ford) - finding shortest path to all graph vertices
|
||
* **Backtracking** - similarly to brute force, try to generate all possible solutions, but each time you generate a solution 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
|
||
* [Hamiltonian Cycle](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/hamiltonian-cycle) - Visit every vertex exactly once
|
||
* [N-Queens Problem](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/uncategorized/n-queens)
|
||
* [Knight's Tour](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/uncategorized/knight-tour)
|
||
* **Branch & Bound**
|
||
|
||
## 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
|
||
|
||
[▶ Data Structures and Algorithms on YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
|
||
|
||
### Big O Notation
|
||
|
||
Order of growth of algorithms specified in Big O notation.
|
||
|
||
|
||
|
||
Source: [Big O Cheat Sheet](http://bigocheatsheet.com/).
|
||
|
||
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 | 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 | |
|
||
| **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 |
|