mirror of
https://github.moeyy.xyz/https://github.com/trekhleb/javascript-algorithms.git
synced 2024-11-14 06:52:59 +08:00
221 lines
13 KiB
Markdown
221 lines
13 KiB
Markdown
# JavaScript 演算法與資料結構
|
||
|
||
[](https://travis-ci.org/trekhleb/javascript-algorithms)
|
||
[](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:_
|
||
[_English_](https://github.com/trekhleb/javascript-algorithms/),
|
||
[_简体中文_](README.zh-CN.md),
|
||
[_한국어_](README.ko-KR.md),
|
||
[_Polski_](README.pl-PL.md),
|
||
[_Français_](README.fr-FR.md),
|
||
[_Español_](README.es-ES.md),
|
||
[_Português_](README.pt-BR.md)
|
||
|
||
> We’re writing a book that will clearly explain, in detail, the main algorithms.
|
||
If you’d like to be notified when the “JavaScript Algorithms” book
|
||
launches, [click here](https://upscri.be/402324/).
|
||
|
||
## 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。
|
||
|
||
* [鏈結串列](src/data-structures/linked-list)
|
||
* [貯列](src/data-structures/queue)
|
||
* [堆疊](src/data-structures/stack)
|
||
* [雜湊表](src/data-structures/hash-table)
|
||
* [堆](src/data-structures/heap)
|
||
* [優先貯列](src/data-structures/priority-queue)
|
||
* [字典樹](src/data-structures/trie)
|
||
* [樹](src/data-structures/tree)
|
||
* [二元搜尋樹](src/data-structures/tree/binary-search-tree)
|
||
* [AVL樹](src/data-structures/tree/avl-tree)
|
||
* [紅黑樹](src/data-structures/tree/red-black-tree)
|
||
* [圖](src/data-structures/graph) (有向跟無向皆包含)
|
||
* [互斥集](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](src/algorithms/math/factorial)
|
||
* [費伯納西數列](src/algorithms/math/fibonacci)
|
||
* [Primality Test](src/algorithms/math/primality-test) (排除法)
|
||
* [歐幾里得算法](src/algorithms/math/euclidean-algorithm) - 計算最大公因數 (GCD)
|
||
* [最小公倍數](src/algorithms/math/least-common-multiple) (LCM)
|
||
* [整數拆分](src/algorithms/math/integer-partition)
|
||
* **集合**
|
||
* [笛卡爾積](src/algorithms/sets/cartesian-product) - 多個集合的乘積
|
||
* [冪集合](src/algorithms/sets/power-set) - 所有集合的子集合
|
||
* [排列](src/algorithms/sets/permutations) (有/無重複)
|
||
* [组合](src/algorithms/sets/combinations) (有/無重複)
|
||
* [洗牌算法](src/algorithms/sets/fisher-yates) - 隨機置換一有限序列
|
||
* [最長共同子序列](src/algorithms/sets/longest-common-subsequence) (LCS)
|
||
* [最長遞增子序列](src/algorithms/sets/longest-increasing-subsequence)
|
||
* [Shortest Common Supersequence](src/algorithms/sets/shortest-common-supersequence) (SCS)
|
||
* [背包問題](src/algorithms/sets/knapsack-problem) - "0/1" and "Unbound" ones
|
||
* [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
|
||
* **字串**
|
||
* [萊文斯坦距離](src/algorithms/string/levenshtein-distance) - 兩序列間的最小編輯距離
|
||
* [漢明距離](src/algorithms/string/hamming-distance) - number of positions at which the symbols are different
|
||
* [KMP 演算法](src/algorithms/string/knuth-morris-pratt) - 子字串搜尋
|
||
* [Rabin Karp 演算法](src/algorithms/string/rabin-karp) - 子字串搜尋
|
||
* [最長共通子序列](src/algorithms/string/longest-common-substring)
|
||
* **搜尋**
|
||
* [二元搜尋](src/algorithms/search/binary-search)
|
||
* **排序**
|
||
* [氣泡排序](src/algorithms/sorting/bubble-sort)
|
||
* [選擇排序](src/algorithms/sorting/selection-sort)
|
||
* [插入排序](src/algorithms/sorting/insertion-sort)
|
||
* [堆排序](src/algorithms/sorting/heap-sort)
|
||
* [合併排序](src/algorithms/sorting/merge-sort)
|
||
* [快速排序](src/algorithms/sorting/quick-sort)
|
||
* [希爾排序](src/algorithms/sorting/shell-sort)
|
||
* **樹**
|
||
* [深度優先搜尋](src/algorithms/tree/depth-first-search) (DFS)
|
||
* [廣度優先搜尋](src/algorithms/tree/breadth-first-search) (BFS)
|
||
* **圖**
|
||
* [深度優先搜尋](src/algorithms/graph/depth-first-search) (DFS)
|
||
* [廣度優先搜尋](src/algorithms/graph/breadth-first-search) (BFS)
|
||
* [Dijkstra 演算法](src/algorithms/graph/dijkstra) - 找到所有圖頂點的最短路徑
|
||
* [Bellman-Ford 演算法](src/algorithms/graph/bellman-ford) - 找到所有圖頂點的最短路徑
|
||
* [Detect Cycle](src/algorithms/graph/detect-cycle) - for both directed and undirected graphs (DFS and Disjoint Set based versions)
|
||
* [Prim’s 演算法](src/algorithms/graph/prim) - finding Minimum Spanning Tree (MST) for weighted undirected graph
|
||
* [Kruskal’s 演算法](src/algorithms/graph/kruskal) - finding Minimum Spanning Tree (MST) for weighted undirected graph
|
||
* [拓撲排序](src/algorithms/graph/topological-sorting) - DFS method
|
||
* [關節點](src/algorithms/graph/articulation-points) - Tarjan's algorithm (DFS based)
|
||
* [橋](src/algorithms/graph/bridges) - DFS based algorithm
|
||
* [尤拉路徑及尤拉環](src/algorithms/graph/eulerian-path) - Fleury's algorithm - Visit every edge exactly once
|
||
* [漢彌爾頓環](src/algorithms/graph/hamiltonian-cycle) - Visit every vertex exactly once
|
||
* [強連通組件](src/algorithms/graph/strongly-connected-components) - Kosaraju's algorithm
|
||
* [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
|
||
* [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
|
||
* **未分類**
|
||
* [河內塔](src/algorithms/uncategorized/hanoi-tower)
|
||
* [N-皇后問題](src/algorithms/uncategorized/n-queens)
|
||
* [騎士走棋盤](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](src/algorithms/sets/maximum-subarray)
|
||
* [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
|
||
* **貪婪法** - choose the best option at the current time, without any consideration for the future
|
||
* [未定背包問題](src/algorithms/sets/knapsack-problem)
|
||
* [Dijkstra 演算法](src/algorithms/graph/dijkstra) - 找到所有圖頂點的最短路徑
|
||
* [Prim’s 演算法](src/algorithms/graph/prim) - finding Minimum Spanning Tree (MST) for weighted undirected graph
|
||
* [Kruskal’s 演算法](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](src/algorithms/search/binary-search)
|
||
* [河內塔](src/algorithms/uncategorized/hanoi-tower)
|
||
* [歐幾里得演算法](src/algorithms/math/euclidean-algorithm) - calculate the Greatest Common Divisor (GCD)
|
||
* [排列](src/algorithms/sets/permutations) (有/無重複)
|
||
* [组合](src/algorithms/sets/combinations) (有/無重複)
|
||
* [合併排序](src/algorithms/sorting/merge-sort)
|
||
* [快速排序](src/algorithms/sorting/quick-sort)
|
||
* [樹深度優先搜尋](src/algorithms/tree/depth-first-search) (DFS)
|
||
* [圖深度優先搜尋](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](src/algorithms/math/fibonacci)
|
||
* [萊溫斯坦距離](src/algorithms/string/levenshtein-distance) - minimum edit distance between two sequences
|
||
* [最長共同子序列](src/algorithms/sets/longest-common-subsequence) (LCS)
|
||
* [最長共同子字串](src/algorithms/string/longest-common-substring)
|
||
* [最長遞增子序列](src/algorithms/sets/longest-increasing-subsequence)
|
||
* [最短共同子序列](src/algorithms/sets/shortest-common-supersequence)
|
||
* [0/1背包問題](src/algorithms/sets/knapsack-problem)
|
||
* [整數拆分](src/algorithms/math/integer-partition)
|
||
* [最大子序列](src/algorithms/sets/maximum-subarray)
|
||
* [Bellman-Ford 演算法](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](src/algorithms/graph/hamiltonian-cycle) - Visit every vertex exactly once
|
||
* [N-皇后問題](src/algorithms/uncategorized/n-queens)
|
||
* [騎士走棋盤](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 -- '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 -- '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。
|
||
|
||
|
||
|
||
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) |
|
||
|
||
### 陣列排序演算法複雜度
|
||
|
||
| 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 |
|