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217 lines
13 KiB
Markdown
217 lines
13 KiB
Markdown
# JavaScript 演算法與資料結構
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[](https://travis-ci.org/trekhleb/javascript-algorithms)
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[](https://codecov.io/gh/trekhleb/javascript-algorithms)
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這個知識庫包含許多 JavaScript 的資料結構與演算法的基礎範例。
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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。
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_Read this in other languages:_
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[_English_](https://github.com/trekhleb/javascript-algorithms/),
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[_简体中文_](README.zh-CN.md),
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[_한국어_](README.ko-KR.md),
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[_Polski_](README.pl-PL.md),
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[_Français_](README.fr-FR.md),
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[_Español_](README.es-ES.md),
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[_Português_](README.pt-BR.md)
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## 資料結構
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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。
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* [鏈結串列](src/data-structures/linked-list)
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* [貯列](src/data-structures/queue)
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* [堆疊](src/data-structures/stack)
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* [雜湊表](src/data-structures/hash-table)
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* [堆](src/data-structures/heap)
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* [優先貯列](src/data-structures/priority-queue)
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* [字典樹](src/data-structures/trie)
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* [樹](src/data-structures/tree)
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* [二元搜尋樹](src/data-structures/tree/binary-search-tree)
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* [AVL樹](src/data-structures/tree/avl-tree)
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* [紅黑樹](src/data-structures/tree/red-black-tree)
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* [圖](src/data-structures/graph) (有向跟無向皆包含)
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* [互斥集](src/data-structures/disjoint-set)
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## 演算法
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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
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### 演算法議題分類
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* **數學類**
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* [階層](src/algorithms/math/factorial)
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* [費伯納西數列](src/algorithms/math/fibonacci)
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* [Primality Test](src/algorithms/math/primality-test) (排除法)
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* [歐幾里得算法](src/algorithms/math/euclidean-algorithm) - 計算最大公因數 (GCD)
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* [最小公倍數](src/algorithms/math/least-common-multiple) (LCM)
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* [整數拆分](src/algorithms/math/integer-partition)
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* **集合**
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* [笛卡爾積](src/algorithms/sets/cartesian-product) - 多個集合的乘積
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* [冪集合](src/algorithms/sets/power-set) - 所有集合的子集合
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* [排列](src/algorithms/sets/permutations) (有/無重複)
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* [组合](src/algorithms/sets/combinations) (有/無重複)
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* [洗牌算法](src/algorithms/sets/fisher-yates) - 隨機置換一有限序列
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* [最長共同子序列](src/algorithms/sets/longest-common-subsequence) (LCS)
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* [最長遞增子序列](src/algorithms/sets/longest-increasing-subsequence)
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* [Shortest Common Supersequence](src/algorithms/sets/shortest-common-supersequence) (SCS)
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* [背包問題](src/algorithms/sets/knapsack-problem) - "0/1" and "Unbound" ones
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* [最大子序列問題](src/algorithms/sets/maximum-subarray) - 暴力法以及動態編程的(Kadane's)版本
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* **字串**
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* [萊文斯坦距離](src/algorithms/string/levenshtein-distance) - 兩序列間的最小編輯距離
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* [漢明距離](src/algorithms/string/hamming-distance) - number of positions at which the symbols are different
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* [KMP 演算法](src/algorithms/string/knuth-morris-pratt) - 子字串搜尋
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* [Rabin Karp 演算法](src/algorithms/string/rabin-karp) - 子字串搜尋
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* [最長共通子序列](src/algorithms/string/longest-common-substring)
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* **搜尋**
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* [二元搜尋](src/algorithms/search/binary-search)
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* **排序**
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* [氣泡排序](src/algorithms/sorting/bubble-sort)
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* [選擇排序](src/algorithms/sorting/selection-sort)
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* [插入排序](src/algorithms/sorting/insertion-sort)
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* [堆排序](src/algorithms/sorting/heap-sort)
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* [合併排序](src/algorithms/sorting/merge-sort)
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* [快速排序](src/algorithms/sorting/quick-sort)
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* [希爾排序](src/algorithms/sorting/shell-sort)
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* **樹**
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* [深度優先搜尋](src/algorithms/tree/depth-first-search) (DFS)
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* [廣度優先搜尋](src/algorithms/tree/breadth-first-search) (BFS)
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* **圖**
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* [深度優先搜尋](src/algorithms/graph/depth-first-search) (DFS)
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* [廣度優先搜尋](src/algorithms/graph/breadth-first-search) (BFS)
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* [Dijkstra 演算法](src/algorithms/graph/dijkstra) - 找到所有圖頂點的最短路徑
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* [Bellman-Ford 演算法](src/algorithms/graph/bellman-ford) - 找到所有圖頂點的最短路徑
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* [Detect Cycle](src/algorithms/graph/detect-cycle) - for both directed and undirected graphs (DFS and Disjoint Set based versions)
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* [Prim’s 演算法](src/algorithms/graph/prim) - finding Minimum Spanning Tree (MST) for weighted undirected graph
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* [Kruskal’s 演算法](src/algorithms/graph/kruskal) - finding Minimum Spanning Tree (MST) for weighted undirected graph
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* [拓撲排序](src/algorithms/graph/topological-sorting) - DFS method
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* [關節點](src/algorithms/graph/articulation-points) - Tarjan's algorithm (DFS based)
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* [橋](src/algorithms/graph/bridges) - DFS based algorithm
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* [尤拉路徑及尤拉環](src/algorithms/graph/eulerian-path) - Fleury's algorithm - Visit every edge exactly once
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* [漢彌爾頓環](src/algorithms/graph/hamiltonian-cycle) - Visit every vertex exactly once
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* [強連通組件](src/algorithms/graph/strongly-connected-components) - Kosaraju's algorithm
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* [旅行推銷員問題](src/algorithms/graph/travelling-salesman) - shortest possible route that visits each city and returns to the origin city
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* [Floyd-Warshall algorithm](src/algorithms/graph/floyd-warshall) - 一次循环可以找出所有頂點之间的最短路徑
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* **未分類**
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* [河內塔](src/algorithms/uncategorized/hanoi-tower)
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* [N-皇后問題](src/algorithms/uncategorized/n-queens)
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* [騎士走棋盤](src/algorithms/uncategorized/knight-tour)
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### 演算法範型
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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。
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* **暴力法** - 尋遍所有的可能解然後選取最好的解
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* [最大子序列](src/algorithms/sets/maximum-subarray)
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* [旅行推銷員問題](src/algorithms/graph/travelling-salesman) - shortest possible route that visits each city and returns to the origin city
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* **貪婪法** - choose the best option at the current time, without any consideration for the future
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* [未定背包問題](src/algorithms/sets/knapsack-problem)
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* [Dijkstra 演算法](src/algorithms/graph/dijkstra) - 找到所有圖頂點的最短路徑
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* [Prim’s 演算法](src/algorithms/graph/prim) - finding Minimum Spanning Tree (MST) for weighted undirected graph
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* [Kruskal’s 演算法](src/algorithms/graph/kruskal) - finding Minimum Spanning Tree (MST) for weighted undirected graph
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* **分治法** - divide the problem into smaller parts and then solve those parts
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* [二元搜尋](src/algorithms/search/binary-search)
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* [河內塔](src/algorithms/uncategorized/hanoi-tower)
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* [歐幾里得演算法](src/algorithms/math/euclidean-algorithm) - calculate the Greatest Common Divisor (GCD)
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* [排列](src/algorithms/sets/permutations) (有/無重複)
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* [组合](src/algorithms/sets/combinations) (有/無重複)
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* [合併排序](src/algorithms/sorting/merge-sort)
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* [快速排序](src/algorithms/sorting/quick-sort)
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* [樹深度優先搜尋](src/algorithms/tree/depth-first-search) (DFS)
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* [圖深度優先搜尋](src/algorithms/graph/depth-first-search) (DFS)
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* **動態編程** - build up to a solution using previously found sub-solutions
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* [費伯納西數列](src/algorithms/math/fibonacci)
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* [萊溫斯坦距離](src/algorithms/string/levenshtein-distance) - minimum edit distance between two sequences
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* [最長共同子序列](src/algorithms/sets/longest-common-subsequence) (LCS)
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* [最長共同子字串](src/algorithms/string/longest-common-substring)
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* [最長遞增子序列](src/algorithms/sets/longest-increasing-subsequence)
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* [最短共同子序列](src/algorithms/sets/shortest-common-supersequence)
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* [0/1背包問題](src/algorithms/sets/knapsack-problem)
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* [整數拆分](src/algorithms/math/integer-partition)
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* [最大子序列](src/algorithms/sets/maximum-subarray)
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* [Bellman-Ford 演算法](src/algorithms/graph/bellman-ford) - finding shortest path to all graph vertices
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* **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。
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* [漢彌爾頓迴路](src/algorithms/graph/hamiltonian-cycle) - Visit every vertex exactly once
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* [N-皇后問題](src/algorithms/uncategorized/n-queens)
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* [騎士走棋盤](src/algorithms/uncategorized/knight-tour)
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* **Branch & Bound**
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## 如何使用本知識庫
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**安裝所有必須套件**
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```
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npm install
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```
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**執行所有測試**
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```
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npm test
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```
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**以名稱執行該測試**
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```
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npm test -- 'LinkedList'
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```
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**練習場**
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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。
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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：
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```
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npm test -- 'playground'
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```
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## 有用的資訊
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### 參考
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[▶ Data Structures and Algorithms on YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
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### 大 O 標記
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特別用大 O 標記演算法增長度的排序。
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資料來源: [Big O Cheat Sheet](http://bigocheatsheet.com/).
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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。
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| 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 |
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| -------------- | ---------------------------- | ----------------------------- | ------------------------------- |
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| **O(1)** | 1 | 1 | 1 |
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| **O(log N)** | 3 | 6 | 9 |
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| **O(N)** | 10 | 100 | 1000 |
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| **O(N log N)** | 30 | 600 | 9000 |
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| **O(N^2)** | 100 | 10000 | 1000000 |
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| **O(2^N)** | 1024 | 1.26e+29 | 1.07e+301 |
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| **O(N!)** | 3628800 | 9.3e+157 | 4.02e+2567 |
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### 資料結構運作複雜度
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| 資料結構 | 存取 | 搜尋 | 插入 | 刪除 |
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| ----------------------- | :-------: | :-------: | :-------: | :-------: |
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| **陣列** | 1 | n | n | n |
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| **堆疊** | n | n | 1 | 1 |
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| **貯列** | n | n | 1 | 1 |
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| **鏈結串列** | n | n | 1 | 1 |
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| **雜湊表** | - | n | n | n |
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| **二元搜尋樹** | n | n | n | n |
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| **B-Tree** | log(n) | log(n) | log(n) | log(n) |
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| **紅黑樹** | log(n) | log(n) | log(n) | log(n) |
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| **AVL Tree** | log(n) | log(n) | log(n) | log(n) |
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### 陣列排序演算法複雜度
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| 名稱 | 最佳 | 平均 | 最差 | 記憶體 | 穩定 |
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| ---------------------- | :-------: | :-------: | :-----------: | :-------: | :-------: |
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| **氣派排序** | n | n^2 | n^2 | 1 | Yes |
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| **插入排序** | n | n^2 | n^2 | 1 | Yes |
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| **選擇排序** | n^2 | n^2 | n^2 | 1 | No |
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| **Heap 排序** | n log(n) | n log(n) | n log(n) | 1 | No |
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| **合併排序** | n log(n) | n log(n) | n log(n) | n | Yes |
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| **快速排序** | n log(n) | n log(n) | n^2 | log(n) | No |
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| **希爾排序** | n log(n) | 由gap sequence決定 | n (log(n))^2 | 1 | No |
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