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‎README.zh-CN.md

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# JavaScript 算法与数据结构
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[![build status](https://travis-ci.org/trekhleb/javascript-algorithms.svg?branch=master)](https://travis-ci.org/trekhleb/javascript-algorithms)
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[![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms)
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本仓库包含了多种基于 JavaScript 的算法与数据结构。
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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。
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## 数据结构
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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。
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* [链表](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/linked-list)
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* [队列](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/queue)
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* [栈](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/stack)
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* [哈希表](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/hash-table)
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* [堆](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/heap)
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* [优先队列](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/priority-queue)
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* [字典树](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/trie)
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* [树](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/tree)
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* [二分查找](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/tree/binary-search-tree)
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* [AVL 树](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/tree/avl-tree)
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* 红黑树
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* 后缀树
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* 线段树 或 间隔树
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* 二叉索引树
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* [图](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/graph) (有向图与无向图)
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* [并查集](https://github.com/trekhleb/javascript-algorithms/tree/master/src/data-structures/disjoint-set)
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## 算法
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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。
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### 算法主题
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* **数学**
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* [阶乘](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/factorial)
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* [斐波那契数](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/fibonacci)
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* [素数检测](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/primality-test) (排除法)
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* [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）
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* [最小公倍数](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/least-common-multiple) (LCM)
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* [整数拆分](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/integer-partition)
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* **集合**
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* [笛卡尔积](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/cartesian-product) - 多集合结果
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* [幂集](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/power-set) - 该集合的所有子集
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* [排列](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/permutations) (有/无重复)
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* [组合](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/combinations) (有/无重复)
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* [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
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* [最长公共子序列](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/longest-common-subsequnce) (LCS)
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* [最长递增子序列](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/longest-increasing-subsequence)
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* [Shortest Common Supersequence](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/shortest-common-supersequence) (SCS)
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* [背包问题](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/knapsack-problem) - "0/1" and "Unbound" ones
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* [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
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* **字符串**
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* [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
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* [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
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* [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
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* [字符串快速查找](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/rabin-karp) - 子串搜索
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* [最长公共子串](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/longest-common-substring)
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* **搜索**
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* [二分查找](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/search/binary-search)
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* **排序**
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* [冒泡排序](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/bubble-sort)
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* [选择排序](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/selection-sort)
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* [插入排序](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/insertion-sort)
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* [堆排序](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/heap-sort)
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* [归并排序](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/merge-sort)
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* [快速排序](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/quick-sort)
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* [希尔排序](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/shell-sort)
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* **树**
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* [深度优先搜索](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/tree/depth-first-search) (DFS)
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* [广度优先搜索](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/tree/breadth-first-search) (BFS)
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* **图**
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* [深度优先搜索](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/depth-first-search) (DFS)
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* [广度优先搜索](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/breadth-first-search) (BFS)
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* [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
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* [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
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* [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）
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* [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）
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* [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）
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* [拓撲排序](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/topological-sorting) - DFS 方法
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* [关节点](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/articulation-points) - Tarjan算法（基于DFS）
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* [桥](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/bridges) - 基于DFS的算法
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* [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
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* [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
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* [强连通分量](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/strongly-connected-components) - Kosaraju算法
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* [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
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* **未分类**
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* [汉诺塔](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/uncategorized/hanoi-tower)
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* [八皇后问题](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/uncategorized/n-queens)
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* [骑士巡逻](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/uncategorized/knight-tour)
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### 算法范式
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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
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算法是比计算机程序更高的抽象。
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* **BF算法** - 查找所有可能性并选择最佳解决方案
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* [最大子数列](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/maximum-subarray)
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* [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
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* **贪心法** - 在当前选择最佳选项，不考虑以后情况
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* [背包问题](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/knapsack-problem)
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* [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
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* [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）
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* [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）
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* **分治法** - 将问题分成较小的部分，然后解决这些部分
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* [二分查找](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/search/binary-search)
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* [汉诺塔](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/uncategorized/hanoi-tower)
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* [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）
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* [排列](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/permutations) (有/无重复)
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* [组合](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/combinations) (有/无重复)
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* [归并排序](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/merge-sort)
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* [Quicksort](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sorting/quick-sort)
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* [树深度优先搜索](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/tree/depth-first-search) (DFS)
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* [图深度优先搜索](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/depth-first-search) (DFS)
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* **动态编程** - 使用以前找到的子解决方案构建解决方案
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* [斐波那契数](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/fibonacci)
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* [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
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* [最长公共子序列](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/longest-common-subsequnce) (LCS)
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* [最长公共子串](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/longest-common-substring)
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* [最长递增子序列](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/longest-increasing-subsequence)
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* [最短公共子序列](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/shortest-common-supersequence)
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* [0-1背包问题](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/knapsack-problem)
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* [整数拆分](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/integer-partition)
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* [最大子数列](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/maximum-subarray)
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* [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
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* **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。
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* [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
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* [八皇后问题](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/uncategorized/n-queens)
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* [骑士巡逻](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/uncategorized/knight-tour)
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* **B & B**
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## 如何使用本仓库
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**安装依赖**
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```
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npm install
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```
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**执行测试**
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```
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npm test
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```
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**按照名称执行测试**
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```
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npm test -- -t 'LinkedList'
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```
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**Playground**
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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。
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然后，只需运行以下命令来测试你的 Playground 是否按无误:
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```
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npm test -- -t 'playground'
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```
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## 有用的信息
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### 引用
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[▶ YouTube](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8)
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### 大O符号
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大O符号中指定的算法的增长顺序。
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![Big O graphs](https://github.com/trekhleb/javascript-algorithms/blob/master/assets/big-o-graph.png?raw=true)
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源: [Big O Cheat Sheet](http://bigocheatsheet.com/).
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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。
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| 大O标记法 | 计算10个元素 | 计算100个元素 | 计算1000个元素 |
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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 | 60 | 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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### 数据结构操作的复杂性
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| 数据结构 | 连接 | 查找 | 插入 | 删除 |
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| ----------------------- | :-------: | :-------: | :-------: | :-------: |
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| **数组** | 1 | n | n | n |
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| **栈** | n | n | 1 | 1 |
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| **队列** | n | n | 1 | 1 |
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| **链表** | n | n | 1 | 1 |
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| **哈希表** | - | n | n | n |
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| **二分查找树** | n | n | n | n |
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| **B树** | log(n) | log(n) | log(n) | log(n) |
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| **红黑树** | log(n) | log(n) | log(n) | log(n) |
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| **AVL树** | log(n) | log(n) | log(n) | log(n) |
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### 数组排序算法的复杂性
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| 名称 | 最优 | 平均 | 最坏 | 内存 | 稳定 |
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| --------------------- | :-------: | :-------: | :-----------: | :-------: | :-------: |
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| **冒泡排序** | 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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| **选择排序** | n^2 | n^2 | n^2 | 1 | No |
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| **堆排序** | n log(n) | n log(n) | n log(n) | 1 | No |
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| **归并排序** | 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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| **希尔排序** | n log(n) | 取决于差距序列 | n (log(n))^2 | 1 | No |

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