diff --git a/README.bs-BA.md b/README.bs-BA.md new file mode 100644 index 00000000..3bbcbb22 --- /dev/null +++ b/README.bs-BA.md @@ -0,0 +1,344 @@ +# JavaScript Algoritmi i Strukture podataka + +[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions?query=workflow%3ACI+branch%3Amaster) +[![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](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_](README.zh-CN.md), +[_繁體中文_](README.zh-TW.md), +[_한국어_](README.ko-KR.md), +[_日本語_](README.ja-JP.md), +[_Polski_](README.pl-PL.md), +[_Français_](README.fr-FR.md), +[_Español_](README.es-ES.md), +[_Português_](README.pt-BR.md), +[_Русский_](README.ru-RU.md), +[_Türk_](README.tr-TR.md), +[_Italiana_](README.it-IT.md), +[_Bahasa Indonesia_](README.id-ID.md), +[_Українська_](README.uk-UA.md), +[_Arabic_](README.ar-AR.md) + +*☝ 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.* + +## 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 List](src/data-structures/linked-list) +* `B` [Doubly Linked List](src/data-structures/doubly-linked-list) +* `B` [Queue](src/data-structures/queue) +* `B` [Stack](src/data-structures/stack) +* `B` [Hash Table](src/data-structures/hash-table) +* `B` [Heap](src/data-structures/heap) - max and min heap versions +* `B` [Priority Queue](src/data-structures/priority-queue) +* `A` [Trie](src/data-structures/trie) +* `A` [Tree](src/data-structures/tree) + * `A` [Binary Search Tree](src/data-structures/tree/binary-search-tree) + * `A` [AVL Tree](src/data-structures/tree/avl-tree) + * `A` [Red-Black Tree](src/data-structures/tree/red-black-tree) + * `A` [Segment Tree](src/data-structures/tree/segment-tree) - with min/max/sum range queries examples + * `A` [Fenwick Tree](src/data-structures/tree/fenwick-tree) (Binary Indexed Tree) +* `A` [Graph](src/data-structures/graph) (both directed and undirected) +* `A` [Disjoint Set](src/data-structures/disjoint-set) +* `A` [Bloom Filter](src/data-structures/bloom-filter) + +## 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` [Bit Manipulation](src/algorithms/math/bits) - set/get/update/clear bits, multiplication/division by two, make negative etc. + * `B` [Factorial](src/algorithms/math/factorial) + * `B` [Fibonacci Number](src/algorithms/math/fibonacci) - classic and closed-form versions + * `B` [Prime Factors](src/algorithms/math/prime-factors) - finding prime factors and counting them using Hardy-Ramanujan's theorem + * `B` [Primality Test](src/algorithms/math/primality-test) (trial division method) + * `B` [Euclidean Algorithm](src/algorithms/math/euclidean-algorithm) - calculate the Greatest Common Divisor (GCD) + * `B` [Least Common Multiple](src/algorithms/math/least-common-multiple) (LCM) + * `B` [Sieve of Eratosthenes](src/algorithms/math/sieve-of-eratosthenes) - finding all prime numbers up to any given limit + * `B` [Is Power of Two](src/algorithms/math/is-power-of-two) - check if the number is power of two (naive and bitwise algorithms) + * `B` [Pascal's Triangle](src/algorithms/math/pascal-triangle) + * `B` [Complex Number](src/algorithms/math/complex-number) - complex numbers and basic operations with them + * `B` [Radian & Degree](src/algorithms/math/radian) - radians to degree and backwards conversion + * `B` [Fast Powering](src/algorithms/math/fast-powering) + * `B` [Horner's method](src/algorithms/math/horner-method) - polynomial evaluation + * `B` [Matrices](src/algorithms/math/matrix) - matrices and basic matrix operations (multiplication, transposition, etc.) + * `B` [Euclidean Distance](src/algorithms/math/euclidean-distance) - distance between two points/vectors/matrices + * `A` [Integer Partition](src/algorithms/math/integer-partition) + * `A` [Square Root](src/algorithms/math/square-root) - Newton's method + * `A` [Liu Hui π Algorithm](src/algorithms/math/liu-hui) - approximate π calculations based on N-gons + * `A` [Discrete Fourier Transform](src/algorithms/math/fourier-transform) - decompose a function of time (a signal) into the frequencies that make it up +* **Sets** + * `B` [Cartesian Product](src/algorithms/sets/cartesian-product) - product of multiple sets + * `B` [Fisher–Yates Shuffle](src/algorithms/sets/fisher-yates) - random permutation of a finite sequence + * `A` [Power Set](src/algorithms/sets/power-set) - all subsets of a set (bitwise and backtracking solutions) + * `A` [Permutations](src/algorithms/sets/permutations) (with and without repetitions) + * `A` [Combinations](src/algorithms/sets/combinations) (with and without repetitions) + * `A` [Longest Common Subsequence](src/algorithms/sets/longest-common-subsequence) (LCS) + * `A` [Longest Increasing Subsequence](src/algorithms/sets/longest-increasing-subsequence) + * `A` [Shortest Common Supersequence](src/algorithms/sets/shortest-common-supersequence) (SCS) + * `A` [Knapsack Problem](src/algorithms/sets/knapsack-problem) - "0/1" and "Unbound" ones + * `A` [Maximum Subarray](src/algorithms/sets/maximum-subarray) - "Brute Force" and "Dynamic Programming" (Kadane's) versions + * `A` [Combination Sum](src/algorithms/sets/combination-sum) - find all combinations that form specific sum +* **Strings** + * `B` [Hamming Distance](src/algorithms/string/hamming-distance) - number of positions at which the symbols are different + * `A` [Levenshtein Distance](src/algorithms/string/levenshtein-distance) - minimum edit distance between two sequences + * `A` [Knuth–Morris–Pratt Algorithm](src/algorithms/string/knuth-morris-pratt) (KMP Algorithm) - substring search (pattern matching) + * `A` [Z Algorithm](src/algorithms/string/z-algorithm) - substring search (pattern matching) + * `A` [Rabin Karp Algorithm](src/algorithms/string/rabin-karp) - substring search + * `A` [Longest Common Substring](src/algorithms/string/longest-common-substring) + * `A` [Regular Expression Matching](src/algorithms/string/regular-expression-matching) +* **Searches** + * `B` [Linear Search](src/algorithms/search/linear-search) + * `B` [Jump Search](src/algorithms/search/jump-search) (or Block Search) - search in sorted array + * `B` [Binary Search](src/algorithms/search/binary-search) - search in sorted array + * `B` [Interpolation Search](src/algorithms/search/interpolation-search) - search in uniformly distributed sorted array +* **Sorting** + * `B` [Bubble Sort](src/algorithms/sorting/bubble-sort) + * `B` [Selection Sort](src/algorithms/sorting/selection-sort) + * `B` [Insertion Sort](src/algorithms/sorting/insertion-sort) + * `B` [Heap Sort](src/algorithms/sorting/heap-sort) + * `B` [Merge Sort](src/algorithms/sorting/merge-sort) + * `B` [Quicksort](src/algorithms/sorting/quick-sort) - in-place and non-in-place implementations + * `B` [Shellsort](src/algorithms/sorting/shell-sort) + * `B` [Counting Sort](src/algorithms/sorting/counting-sort) + * `B` [Radix Sort](src/algorithms/sorting/radix-sort) +* **Linked Lists** + * `B` [Straight Traversal](src/algorithms/linked-list/traversal) + * `B` [Reverse Traversal](src/algorithms/linked-list/reverse-traversal) +* **Trees** + * `B` [Depth-First Search](src/algorithms/tree/depth-first-search) (DFS) + * `B` [Breadth-First Search](src/algorithms/tree/breadth-first-search) (BFS) +* **Graphs** + * `B` [Depth-First Search](src/algorithms/graph/depth-first-search) (DFS) + * `B` [Breadth-First Search](src/algorithms/graph/breadth-first-search) (BFS) + * `B` [Kruskal’s Algorithm](src/algorithms/graph/kruskal) - finding Minimum Spanning Tree (MST) for weighted undirected graph + * `A` [Dijkstra Algorithm](src/algorithms/graph/dijkstra) - finding the shortest paths to all graph vertices from single vertex + * `A` [Bellman-Ford Algorithm](src/algorithms/graph/bellman-ford) - finding the shortest paths to all graph vertices from single vertex + * `A` [Floyd-Warshall Algorithm](src/algorithms/graph/floyd-warshall) - find the shortest paths between all pairs of vertices + * `A` [Detect Cycle](src/algorithms/graph/detect-cycle) - for both directed and undirected graphs (DFS and Disjoint Set based versions) + * `A` [Prim’s Algorithm](src/algorithms/graph/prim) - finding Minimum Spanning Tree (MST) for weighted undirected graph + * `A` [Topological Sorting](src/algorithms/graph/topological-sorting) - DFS method + * `A` [Articulation Points](src/algorithms/graph/articulation-points) - Tarjan's algorithm (DFS based) + * `A` [Bridges](src/algorithms/graph/bridges) - DFS based algorithm + * `A` [Eulerian Path and Eulerian Circuit](src/algorithms/graph/eulerian-path) - Fleury's algorithm - Visit every edge exactly once + * `A` [Hamiltonian Cycle](src/algorithms/graph/hamiltonian-cycle) - Visit every vertex exactly once + * `A` [Strongly Connected Components](src/algorithms/graph/strongly-connected-components) - Kosaraju's algorithm + * `A` [Travelling Salesman Problem](src/algorithms/graph/travelling-salesman) - shortest possible route that visits each city and returns to the origin city +* **Cryptography** + * `B` [Polynomial Hash](src/algorithms/cryptography/polynomial-hash) - rolling hash function based on polynomial + * `B` [Rail Fence Cipher](src/algorithms/cryptography/rail-fence-cipher) - a transposition cipher algorithm for encoding messages + * `B` [Caesar Cipher](src/algorithms/cryptography/caesar-cipher) - simple substitution cipher + * `B` [Hill Cipher](src/algorithms/cryptography/hill-cipher) - substitution cipher based on linear algebra +* **Machine Learning** + * `B` [NanoNeuron](https://github.com/trekhleb/nano-neuron) - 7 simple JS functions that illustrate how machines can actually learn (forward/backward propagation) + * `B` [k-NN](src/algorithms/ml/knn) - k-nearest neighbors classification algorithm + * `B` [k-Means](src/algorithms/ml/k-means) - k-Means clustering algorithm +* **Image Processing** + * `B` [Seam Carving](src/algorithms/image-processing/seam-carving) - content-aware image resizing algorithm +* **Uncategorized** + * `B` [Tower of Hanoi](src/algorithms/uncategorized/hanoi-tower) + * `B` [Square Matrix Rotation](src/algorithms/uncategorized/square-matrix-rotation) - in-place algorithm + * `B` [Jump Game](src/algorithms/uncategorized/jump-game) - backtracking, dynamic programming (top-down + bottom-up) and greedy examples + * `B` [Unique Paths](src/algorithms/uncategorized/unique-paths) - backtracking, dynamic programming and Pascal's Triangle based examples + * `B` [Rain Terraces](src/algorithms/uncategorized/rain-terraces) - trapping rain water problem (dynamic programming and brute force versions) + * `B` [Recursive Staircase](src/algorithms/uncategorized/recursive-staircase) - count the number of ways to reach to the top (4 solutions) + * `B` [Best Time To Buy Sell Stocks](src/algorithms/uncategorized/best-time-to-buy-sell-stocks) - divide and conquer and one-pass examples + * `A` [N-Queens Problem](src/algorithms/uncategorized/n-queens) + * `A` [Knight's Tour](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 + * `B` [Linear Search](src/algorithms/search/linear-search) + * `B` [Rain Terraces](src/algorithms/uncategorized/rain-terraces) - trapping rain water problem + * `B` [Recursive Staircase](src/algorithms/uncategorized/recursive-staircase) - count the number of ways to reach to the top + * `A` [Maximum Subarray](src/algorithms/sets/maximum-subarray) + * `A` [Travelling Salesman Problem](src/algorithms/graph/travelling-salesman) - shortest possible route that visits each city and returns to the origin city + * `A` [Discrete Fourier Transform](src/algorithms/math/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 + * `B` [Jump Game](src/algorithms/uncategorized/jump-game) + * `A` [Unbound Knapsack Problem](src/algorithms/sets/knapsack-problem) + * `A` [Dijkstra Algorithm](src/algorithms/graph/dijkstra) - finding the shortest path to all graph vertices + * `A` [Prim’s Algorithm](src/algorithms/graph/prim) - finding Minimum Spanning Tree (MST) for weighted undirected graph + * `A` [Kruskal’s Algorithm](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 + * `B` [Binary Search](src/algorithms/search/binary-search) + * `B` [Tower of Hanoi](src/algorithms/uncategorized/hanoi-tower) + * `B` [Pascal's Triangle](src/algorithms/math/pascal-triangle) + * `B` [Euclidean Algorithm](src/algorithms/math/euclidean-algorithm) - calculate the Greatest Common Divisor (GCD) + * `B` [Merge Sort](src/algorithms/sorting/merge-sort) + * `B` [Quicksort](src/algorithms/sorting/quick-sort) + * `B` [Tree Depth-First Search](src/algorithms/tree/depth-first-search) (DFS) + * `B` [Graph Depth-First Search](src/algorithms/graph/depth-first-search) (DFS) + * `B` [Matrices](src/algorithms/math/matrix) - generating and traversing the matrices of different shapes + * `B` [Jump Game](src/algorithms/uncategorized/jump-game) + * `B` [Fast Powering](src/algorithms/math/fast-powering) + * `B` [Best Time To Buy Sell Stocks](src/algorithms/uncategorized/best-time-to-buy-sell-stocks) - divide and conquer and one-pass examples + * `A` [Permutations](src/algorithms/sets/permutations) (with and without repetitions) + * `A` [Combinations](src/algorithms/sets/combinations) (with and without repetitions) +* **Dynamic Programming** - build up a solution using previously found sub-solutions + * `B` [Fibonacci Number](src/algorithms/math/fibonacci) + * `B` [Jump Game](src/algorithms/uncategorized/jump-game) + * `B` [Unique Paths](src/algorithms/uncategorized/unique-paths) + * `B` [Rain Terraces](src/algorithms/uncategorized/rain-terraces) - trapping rain water problem + * `B` [Recursive Staircase](src/algorithms/uncategorized/recursive-staircase) - count the number of ways to reach to the top + * `B` [Seam Carving](src/algorithms/image-processing/seam-carving) - content-aware image resizing algorithm + * `A` [Levenshtein Distance](src/algorithms/string/levenshtein-distance) - minimum edit distance between two sequences + * `A` [Longest Common Subsequence](src/algorithms/sets/longest-common-subsequence) (LCS) + * `A` [Longest Common Substring](src/algorithms/string/longest-common-substring) + * `A` [Longest Increasing Subsequence](src/algorithms/sets/longest-increasing-subsequence) + * `A` [Shortest Common Supersequence](src/algorithms/sets/shortest-common-supersequence) + * `A` [0/1 Knapsack Problem](src/algorithms/sets/knapsack-problem) + * `A` [Integer Partition](src/algorithms/math/integer-partition) + * `A` [Maximum Subarray](src/algorithms/sets/maximum-subarray) + * `A` [Bellman-Ford Algorithm](src/algorithms/graph/bellman-ford) - finding the shortest path to all graph vertices + * `A` [Floyd-Warshall Algorithm](src/algorithms/graph/floyd-warshall) - find the shortest paths between all pairs of vertices + * `A` [Regular Expression Matching](src/algorithms/string/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. + * `B` [Jump Game](src/algorithms/uncategorized/jump-game) + * `B` [Unique Paths](src/algorithms/uncategorized/unique-paths) + * `B` [Power Set](src/algorithms/sets/power-set) - all subsets of a set + * `A` [Hamiltonian Cycle](src/algorithms/graph/hamiltonian-cycle) - Visit every vertex exactly once + * `A` [N-Queens Problem](src/algorithms/uncategorized/n-queens) + * `A` [Knight's Tour](src/algorithms/uncategorized/knight-tour) + * `A` [Combination Sum](src/algorithms/sets/combination-sum) - find all combinations that form specific sum +* **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 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_modules` folder and re-install npm packages: + +``` +rm -rf ./node_modules +npm i +``` + +**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 -- 'playground' +``` + +## Useful Information + +### References + +[▶ Data Structures and Algorithms on YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8) + +### 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. + +![Big O graphs](./assets/big-o-graph.png) + +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 | 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 | + +### 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 | 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 | + +## Project Backers + +> You may support this project via ❤️️ [GitHub](https://github.com/sponsors/trekhleb) or ❤️️ [Patreon](https://www.patreon.com/trekhleb). + +[Folks who are backing this project](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 0`