diff --git a/README.zh-CN.md b/README.zh-CN.md new file mode 100644 index 00000000..5a815e3d --- /dev/null +++ b/README.zh-CN.md @@ -0,0 +1,212 @@ +# 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。 + +## 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 | 60 | 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 |