From e26e986557e637793bf429e92f6ee42b36b64483 Mon Sep 17 00:00:00 2001 From: Kevin Date: Sat, 26 May 2018 05:33:01 +0800 Subject: [PATCH] Finish main part of translation (#18) * add chinese overview * translate * add * translate english --- README.md | 1 + Readme.zh-TW.md | 211 ++++++++++++++++++++++++++++++++++++++++++++++++ 2 files changed, 212 insertions(+) create mode 100644 Readme.zh-TW.md diff --git a/README.md b/README.md index 630097c7..9096e26b 100644 --- a/README.md +++ b/README.md @@ -11,6 +11,7 @@ with related explanations and links for further reading and YouTube videos. _Read this in other languages:_ [简体中文](https://github.com/trekhleb/javascript-algorithms/blob/master/README.zh-CN.md) +_Read this in Traditional Chinese:_ [繁體中文](https://github.com/trekhleb/javascript-algorithms/blob/master/README.zh-TW.md) ## Data Structures diff --git a/Readme.zh-TW.md b/Readme.zh-TW.md new file mode 100644 index 00000000..05878252 --- /dev/null +++ b/Readme.zh-TW.md @@ -0,0 +1,211 @@ +# 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) + +## 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) + * 紅黑樹 + * 後綴樹 + * 線段樹 或 間隔樹 + * 樹狀數組或二叉索引樹 +* [Graph 圖](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/graph) (有向跟無向皆包含) +* [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 + +* **數學類** + * [階層](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/factorial) + * [費伯納西數列](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) (排除法) + * [歐幾里得算法](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/euclidean-algorithm) - 計算最大公因數 (GCD) + * [最小公倍數](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/least-common-multiple) (LCM) + * [整數拆分](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/integer-partition) +* **集合** + * [笛卡爾積](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/cartesian-product) - 多個集合的乘積 + * [冪集合](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/power-set) - 所有集合的子集合 + * [排列](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/permutations) (有/無重複) + * [组合](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/combinations) (有/無重複) + * [洗牌算法](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/fisher-yates) - 隨機置換一有限序列 + * [最長共同子序列](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/longest-common-subsequnce) (LCS) + * [最長遞增子序列](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) + * [背包問題](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/knapsack-problem) - "0/1" and "Unbound" ones + * [最大子序列問題](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/maximum-subarray) - 暴力法以及動態編程的(Kadane's)版本 +* **字串** + * [萊文斯坦距離](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/levenshtein-distance) - 兩序列間的最小編輯距離 + * [漢明距離](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/hamming-distance) - number of positions at which the symbols are different + * [KMP 演算法](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/knuth-morris-pratt) - 子字串搜尋 + * [Rabin Karp 演算法](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/rabin-karp) - 子字串搜尋 + * [最長共通子序列](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/longest-common-substring) +* **搜尋** + * [二元搜尋](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/search/binary-search) +* **排序** + * [氣泡排序](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/bubble-sort) + * [選擇排序](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/selection-sort) + * [插入排序](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/insertion-sort) + * [堆排序](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/heap-sort) + * [合併排序](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/merge-sort) + * [快速排序](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/quick-sort) + * [希爾排序](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/shell-sort) +* **樹** + * [深度優先搜尋](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/tree/depth-first-search) (DFS) + * [廣度優先搜尋](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/tree/breadth-first-search) (BFS) +* **圖** + * [深度優先搜尋](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/depth-first-search) (DFS) + * [廣度優先搜尋](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/breadth-first-search) (BFS) + * [Dijkstra 演算法](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/dijkstra) - 找到所有圖頂點的最短路徑 + * [Bellman-Ford 演算法](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/bellman-ford) - 找到所有圖頂點的最短路徑 + * [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 演算法](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/prim) - finding Minimum Spanning Tree (MST) for weighted undirected graph + * [Kruskal’s 演算法](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/kruskal) - finding Minimum Spanning Tree (MST) for weighted undirected graph + * [拓撲排序](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/topological-sorting) - DFS method + * [關節點](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/articulation-points) - Tarjan's algorithm (DFS based) + * [橋](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/bridges) - DFS based algorithm + * [尤拉路徑及尤拉環](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/eulerian-path) - Fleury's algorithm - Visit every edge exactly once + * [漢彌爾頓環](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/hamiltonian-cycle) - Visit every vertex exactly once + * [強連通組件](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/strongly-connected-components) - Kosaraju's algorithm + * [旅行推銷員問題](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** + * [河內塔](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/uncategorized/hanoi-tower) + * [N-皇后問題](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/uncategorized/n-queens) + * [騎士走棋盤](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/uncategorized/knight-tour) + +### 演算法範型 + +演算法的範型是一個泛用方法或設計一類底層演算法的方式。它是一個比演算法的概念更高階的抽象化，就像是演算法是比電腦程式更高階的抽象化。 + +* **暴力法** - 尋遍所有的可能解然後選取最好的解 + * [最大子序列](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/maximum-subarray) + * [旅行推銷員問題](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 +* **貪婪法** - choose the best option at the current time, without any consideration for the future + * [未定背包問題](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/knapsack-problem) + * [Dijkstra 演算法](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/dijkstra) - 找到所有圖頂點的最短路徑 + * [Prim’s 演算法](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/prim) - finding Minimum Spanning Tree (MST) for weighted undirected graph + * [Kruskal’s 演算法](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/kruskal) - finding Minimum Spanning Tree (MST) for weighted undirected graph +* **分治法** - divide the problem into smaller parts and then solve those parts + * [二元搜尋](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/search/binary-search) + * [河內塔](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/uncategorized/hanoi-tower) + * [歐幾里得演算法](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/euclidean-algorithm) - calculate the Greatest Common Divisor (GCD) + * [排列](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/permutations) (有/無重複) + * [组合](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/combinations) (有/無重複) + * [合併排序](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/merge-sort) + * [快速排序](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/quick-sort) + * [樹深度優先搜尋](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/tree/depth-first-search) (DFS) + * [圖深度優先搜尋](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/depth-first-search) (DFS) +* **動態編程** - build up to a solution using previously found sub-solutions + * [費伯納西數列](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/fibonacci) + * [萊溫斯坦距離](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/levenshtein-distance) - minimum edit distance between two sequences + * [最長共同子序列](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/longest-common-subsequnce) (LCS) + * [最長共同子字串](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/longest-common-substring) + * [最長遞增子序列](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/longest-increasing-subsequence) + * [最短共同子序列](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/shortest-common-supersequence) + * [0/1背包問題](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/knapsack-problem) + * [整數拆分](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/integer-partition) + * [最大子序列](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/maximum-subarray) + * [Bellman-Ford 演算法](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/bellman-ford) - finding shortest path to all graph vertices +* **回溯法** - 用類似暴力法來嘗試產生所有可能解，但每次只在能滿足所有測試條件，且只有繼續產生子序列方案來產生的解決方案。否則回溯並尋找不同路徑的解決方案。 + * [漢彌爾頓迴路](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/hamiltonian-cycle) - Visit every vertex exactly once + * [N-皇后問題](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/uncategorized/n-queens) + * [騎士走棋盤](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' +``` +**練習場** + +你可以透過在`./src/playground/playground.js`裡面的檔案練習資料結構以及演算法，並且撰寫在`./src/playground/__test__/playground.test.js`裡面的測試程式。 + +接著直接執行下列的指令來測試你練習的 code 是否如預期運作： + +``` +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 + +特別用大 O 標記演算法增長度的排序。 + +![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/). + +下列列出幾個常用的 Big O 標記以及其不同大小資料量輸入後的運算效能比較。 + +| Big O 標記 | 10個資料量需花費的時間 | 100個資料量需花費的時間 | 1000個資料量需花費的時間 | +| -------------- | ---------------------------- | ----------------------------- | ------------------------------- | +| **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 | + +### 資料結構運作複雜度 + +| 資料結構 | 存取 | 搜尋 | 插入 | 刪除 | +| ----------------------- | :-------: | :-------: | :-------: | :-------: | +| **陣列** | 1 | n | n | n | +| **堆疊** | n | n | 1 | 1 | +| **貯列** | n | n | 1 | 1 | +| **鏈結串列** | n | n | 1 | 1 | +| **雜湊表** | - | n | n | n | +| **二元搜尋樹** | n | n | n | n | +| **B-Tree** | log(n) | log(n) | log(n) | log(n) | +| **紅黑樹** | log(n) | log(n) | log(n) | log(n) | +| **AVL Tree** | log(n) | log(n) | log(n) | log(n) | + +### 陣列搜尋演算法複雜度 + +| 名稱 | 最佳 | 平均 | 最差 | 記憶體 | 穩定 | +| --------------------- | :-------: | :-------: | :-----------: | :-------: | :-------: | +| **氣派排序** | n | n^2 | n^2 | 1 | Yes | +| **插入排序** | n | n^2 | n^2 | 1 | Yes | +| **選擇排序** | n^2 | n^2 | n^2 | 1 | No | +| **Heap 排序** | n log(n) | n log(n) | n log(n) | 1 | No | +| **合併排序** | n log(n) | n log(n) | n log(n) | n | Yes | +| **快速排序** | n log(n) | n log(n) | n^2 | log(n) | No | +| **希爾排序** | n log(n) | 由gap sequence決定 | n (log(n))^2 | 1 | No |