From 2364de7061e7b22be777d9740a4f22418e7c2d4a Mon Sep 17 00:00:00 2001 From: Kevin Date: Fri, 25 May 2018 12:44:22 +0800 Subject: [PATCH] add chinese overview (#17) --- Readme.zh-TW.md | 218 ++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 218 insertions(+) create mode 100644 Readme.zh-TW.md diff --git a/Readme.zh-TW.md b/Readme.zh-TW.md new file mode 100644 index 00000000..df155308 --- /dev/null +++ b/Readme.zh-TW.md @@ -0,0 +1,218 @@ +# JavaScript 演算法與資料結構 + +[![build status](https://travis-ci.org/trekhleb/javascript-algorithms.svg?branch=master)](https://travis-ci.org/trekhleb/javascript-algorithms) +[![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms) + +這個知識庫包含許多 JavaScript 的資料結構與演算法的基礎範例。 +每個演算法和資料結構都有其個別的文件，內有相關的解釋以及更多相關的文章或Youtube影片連結。 + +_Read this in other languages:_ [简体中文](https://github.com/trekhleb/javascript-algorithms/blob/master/README.zh-CN.md) + +_Read this in other languages:_ [繁體中文](https://github.com/trekhleb/javascript-algorithms/blob/master/README.zh-TW.md) + +## 資料結構 + +資料結構是一個電腦用來組織和排序資料的特定方式，透過這樣的方式資料可以有效率地被讀取以及修改。更精確地說，一個資料結構是一個資料值的集合、彼此間的關係，函數或者運作可以應用於資料上。 + +* [Linked List 鏈結串列](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/linked-list) +* [Queue 貯列](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/queue) +* [Stack 堆疊](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/stack) +* [Hash Table 雜湊表](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/hash-table) +* [Heap 堆](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/heap) +* [Priority Queue 優先貯列](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/priority-queue) +* [Trie 字典樹](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/trie) +* [Tree 樹](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/tree) + * [Binary Search Tree 二元搜尋樹](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/tree/binary-search-tree) + * [AVL Tree AVL樹](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/tree/avl-tree) + * Red-Black Tree + * Suffix Tree + * Segment Tree or Interval Tree + * Binary Indexed Tree or Fenwick Tree +* [Graph 圖](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/graph) (both directed and undirected) +* [Disjoint Set 互斥集](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/disjoint-set) + +## 演算法 + +演算法是一個如何解決一類問題的非模糊規格。演算法是一個具有精確地定義了一系列運作的規則的集合 + +### 演算法議題分類 TODO + +* **數學類** + * [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) +* **集合** + * [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 the 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 +* **字串** + * [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) +* **搜尋** + * [Binary Search](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/search/binary-search) +* **排序** + * [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) + * [Shellsort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/shell-sort) +* **樹** + * [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) +* **圖** + * [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 +* **未分類** + * [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 to 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 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** + +## 如何使用本知識庫 + +**安裝所有必須套件** + +``` +npm install +``` + +**執行所有測試** +``` +npm test +``` + +**以名稱執行該測試** +``` +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' +``` + +## 有用的資訊 + +### 參考 + +[▶ Data Structures and Algorithms on YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8) + +### 大 O 標記 + +Order of growth of algorithms specified in Big O notation. + +![Big O 表](https://github.com/trekhleb/javascript-algorithms/blob/master/assets/big-o-graph.png?raw=true) + +資料來源: [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 | +| ----------------------- | :-------: | :-------: | :-------: | :-------: | +| **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 | +| **Binary Search Tree** | n | n | n | 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 | +| --------------------- | :-------: | :-------: | :-----------: | :-------: | :-------: | +| **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 |