# JavaScript 算法与数据结构

[![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)

本仓库包含了多种基于 JavaScript 的算法与数据结构。

每种算法和数据结构都有自己的 README 并提供相关说明以及进一步阅读和 YouTube 视频。

_Read this in other languages:_ [_English_](https://github.com/trekhleb/javascript-algorithms/)

## 数据结构

数据结构是在计算机中组织和存储数据的一种特殊方式，它可以高效地访问和修改数据。更确切地说，数据结构是数据值的集合，它们之间的关系、函数或操作可以应用于数据。

* [链表](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/linked-list)
* [队列](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/queue)
* [栈](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/stack)
* [哈希表](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/hash-table)
* [堆](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/heap)
* [优先队列](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/priority-queue)
* [字典树](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/trie)
* [树](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/tree)
    * [二分查找](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/tree/binary-search-tree)
    * [AVL 树](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/tree/avl-tree)
    * 红黑树
    * 后缀树
    * 线段树 或 间隔树
    * 二叉索引树
* [图](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/graph) (有向图与无向图)
* [并查集](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/disjoint-set)

## 算法

算法是如何解决一类问题的明确规范。 算法是一组精确定义操作序列的规则。

### 算法主题

* **数学**
  * [阶乘](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/factorial)
  * [斐波那契数](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/fibonacci)
  * [素数检测](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/primality-test) (排除法)
  * [欧几里得算法](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/euclidean-algorithm) - 计算最大公约数（GCD）
  * [最小公倍数](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/least-common-multiple) (LCM)
  * [整数拆分](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/integer-partition)
* **集合**
  * [笛卡尔积](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/cartesian-product) - 多集合结果
  * [幂集](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/power-set) - 该集合的所有子集
  * [排列](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/permutations) (有/无重复)
  * [组合](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/combinations) (有/无重复)
  * [洗牌算法](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/fisher-yates) - 随机置换有限序列
  * [最长公共子序列](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/longest-common-subsequnce) (LCS)
  * [最长递增子序列](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)
  * [背包问题](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/knapsack-problem) - "0/1" and "Unbound" ones
  * [最大子数列问题](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/maximum-subarray) - BF算法 与 动态编程
* **字符串**
  * [莱温斯坦距离](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/levenshtein-distance) - 两个序列之间的最小编辑距离
  * [汉明距离](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/hamming-distance) - 符号不同的位置数
  * [克努斯-莫里斯-普拉特算法](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/knuth-morris-pratt) - 子串搜索
  * [字符串快速查找](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/rabin-karp) - 子串搜索
  * [最长公共子串](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/longest-common-substring)
* **搜索**
  * [二分查找](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/search/binary-search)
* **排序**
  * [冒泡排序](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/bubble-sort)
  * [选择排序](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)
  * [归并排序](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)
  * [希尔排序](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/shell-sort)
* **树**  
  * [深度优先搜索](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/tree/depth-first-search) (DFS)
  * [广度优先搜索](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/tree/breadth-first-search) (BFS)
* **图**
  * [深度优先搜索](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/depth-first-search) (DFS)
  * [广度优先搜索](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/breadth-first-search) (BFS)
  * [戴克斯特拉算法m](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/dijkstra) - 找到所有图顶点的最短路径
  * [贝尔曼-福特算法](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/bellman-ford) - 找到所有图顶点的最短路径
  * [判圈算法](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/detect-cycle) - 对于有向图和无向图（基于DFS和不相交集的版本）
  * [普林演算法](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/prim) - 寻找加权无向图的最小生成树（MST）
  * [克鲁斯克尔演算法](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/kruskal) - 寻找加权无向图的最小生成树（MST）
  * [拓撲排序](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/topological-sorting) - DFS 方法
  * [关节点](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/articulation-points) - Tarjan算法（基于DFS）
  * [桥](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/bridges) - 基于DFS的算法
  * [欧拉路径与一笔画问题](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/eulerian-path) - Fleury的算法 - 一次访问每个边缘
  * [哈密顿图](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/hamiltonian-cycle) - 恰好访问每个顶点一次
  * [强连通分量](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/strongly-connected-components) - Kosaraju算法
  * [旅行推销员问题](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/travelling-salesman) - 尽可能以最短的路线访问每个城市并返回原始城市
* **未分类**  
  * [汉诺塔](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/uncategorized/hanoi-tower)
  * [八皇后问题](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/uncategorized/n-queens)
  * [骑士巡逻](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/uncategorized/knight-tour)

### 算法范式

算法范式是基于类的设计的通用方法或方法的算法。 这是一个比算法概念更高的抽象，就像一个
算法是比计算机程序更高的抽象。

* **BF算法** - 查找所有可能性并选择最佳解决方案
  * [最大子数列](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/maximum-subarray)
  * [旅行推销员问题](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/travelling-salesman) - 尽可能以最短的路线访问每个城市并返回原始城市

* **贪心法** - 在当前选择最佳选项，不考虑以后情况
  * [背包问题](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/knapsack-problem)
  * [戴克斯特拉算法](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/dijkstra) - 找到所有图顶点的最短路径
  * [普里姆算法](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/prim) - 寻找加权无向图的最小生成树（MST）
  * [克鲁斯卡尔算法](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/kruskal) - 寻找加权无向图的最小生成树（MST）
* **分治法** - 将问题分成较小的部分，然后解决这些部分
  * [二分查找](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/search/binary-search)
  * [汉诺塔](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/uncategorized/hanoi-tower)
  * [欧几里得算法](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/euclidean-algorithm) - 计算最大公约数（GCD）
  * [排列](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/permutations) (有/无重复)
  * [组合](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/combinations) (有/无重复)
  * [归并排序](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)
  * [树深度优先搜索](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/tree/depth-first-search) (DFS)
  * [图深度优先搜索](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/depth-first-search) (DFS)
* **动态编程** - 使用以前找到的子解决方案构建解决方案
  * [斐波那契数](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/fibonacci)
  * [莱温斯坦距离](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/levenshtein-distance) - 两个序列之间的最小编辑距离
  * [最长公共子序列](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/longest-common-subsequnce) (LCS)
  * [最长公共子串](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/longest-common-substring)
  * [最长递增子序列](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/longest-increasing-subsequence)
  * [最短公共子序列](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/shortest-common-supersequence)
  * [0-1背包问题](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/knapsack-problem)
  * [整数拆分](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/integer-partition)
  * [最大子数列](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/maximum-subarray)
  * [贝尔曼-福特算法](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/bellman-ford) - 找到所有图顶点的最短路径
* **回溯法** - 类似于 BF算法 试图产生所有可能的解决方案，但每次生成解决方案测试如果它满足所有条件，那么只有继续生成后续解决方案。 否则回溯并继续寻找不同路径的解决方案。
  * [哈密顿图](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/hamiltonian-cycle) - 恰好访问每个顶点一次
  * [八皇后问题](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/uncategorized/n-queens)
  * [骑士巡逻](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/uncategorized/knight-tour)
* **B & B**

## 如何使用本仓库

**安装依赖**
```
npm install
```

**执行测试**
```
npm test
```

**按照名称执行测试**
```
npm test -- -t 'LinkedList'
```

**Playground**

你可以在`./src/playground/playground.js`文件中操作数据结构与算法，并在`./src/playground/__test__/playground.test.js`中编写测试。

然后，只需运行以下命令来测试你的 Playground 是否按无误:

```
npm test -- -t 'playground'
```

## 有用的信息

### 引用

[▶ YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)

### 大O符号

大O符号中指定的算法的增长顺序。

![Big O graphs](https://github.com/trekhleb/javascript-algorithms/blob/master/assets/big-o-graph.png?raw=true)

源: [Big O Cheat Sheet](http://bigocheatsheet.com/).

以下是一些最常用的 大O标记法 列表以及它们与不同大小输入数据的性能比较。

| 大O标记法 | 计算10个元素 | 计算100个元素 | 计算1000个元素  |
| -------------- | ---------------------------- | ----------------------------- | ------------------------------- |
| **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                      |

### 数据结构操作的复杂性

| 数据结构          | 连接    | 查找    | 插入 | 删除  |
| ----------------------- | :-------: | :-------: | :-------: | :-------: |
| **数组**               | 1         | n         | n         | n         |
| **栈**               | n         | n         | 1         | 1         |
| **队列**               | n         | n         | 1         | 1         |
| **链表**         | n         | n         | 1         | 1         |
| **哈希表**          | -         | n         | n         | n         |
| **二分查找树**  | n         | n         | n         | n         |
| **B树**              | log(n)    | log(n)    | log(n)    | log(n)    |
| **红黑树**      | log(n)    | log(n)    | log(n)    | log(n)    |
| **AVL树**            | log(n)    | log(n)    | log(n)    | log(n)    |

### 数组排序算法的复杂性

| 名称                  | 最优      | 平均   | 最坏         | 内存    | 稳定    |
| --------------------- | :-------: | :-------: | :-----------: | :-------: | :-------: |
| **冒泡排序**       | n         | n^2       | n^2           | 1         | Yes       |
| **插入排序**    | n         | n^2       | n^2           | 1         | Yes       |
| **选择排序**    | n^2       | n^2       | n^2           | 1         | No        |
| **堆排序**         | n log(n)  | n log(n)  | n log(n)      | 1         | No        |
| **归并排序**        | 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        |
| **希尔排序**        | n log(n)  | 取决于差距序列   | n (log(n))^2  | 1         | No        |