知乎高赞，如何系统地学习算法？

ゞ浴缸里的玫瑰 2022-10-06 00:57 224阅读 0赞

大家好，我是程序员吴师兄，之前我在知乎写过一个回答**如何系统地学习算法**，截至目前已经收获了 1w 的赞同，今天特定整理一下，分享给 C 站的小伙伴们，**有帮助记得点赞哟**。

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2tleHVhbnhpdTExNjM_size_16_color_FFFFFF_t_70]

以下为原文。

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**不 BB，直接上干货，非科班出生，毕业工作后才开始学算法，到目前学了 4 年 ！！！**

为了让你对数据结构和算法能有个全面的认识，我画了一张图，里面几乎涵盖了所有数据结构和算法书籍中都会讲到的知识点。

![img][]

这里面有10个数据结构：数组、链表、栈、队列、散列表、二叉树、堆、跳表、图、Trie 树；10个算法：递归、排序、二分查找、搜索、哈希算法、贪心算法、分治算法、回溯算法、动态规划、字符串匹配算法。

掌握了这些基础的数据结构和算法，再学更加复杂的数据结构和算法，就会非常容易、非常快。

### **1、复杂度分析** ###

[看动画轻松理解时间复杂度（一）][Link 1]

[看动画轻松理解时间复杂度（二）][Link 1]

[冰与火之歌：「时间」与「空间」复杂度][Link 2]

[每个程序员都应该收藏的算法复杂度速查表][Link 3]

### **2、基本算法思想** ###

[五分钟了解一下什么是「贪心算法 」][Link 4]

[有了四步解题法模板，再也不害怕动态规划！][Link 5]

[（进阶版）有了四步解题法模板，再也不害怕动态规划！][Link 6]

[（再进阶版）有了四步解题法模板，再也不害怕动态规划！][Link 6]

[浅谈什么是分治算法][Link 7]

[看动画轻松理解「递归」与「动态规划」][Link 8]

[浅谈什么是动态规划以及相关的「股票」算法题][Link 9]

[深度解析「正则表达式匹配」：从暴力解法到动态规划][Link 10]

### **3、排序算法** ###

[「多图警告」手撕排序算法 – iOS进阶必备][_ iOS]

[十大经典排序算法动画与解析，看我就够了！（配代码完全版）][Link 11]

[这或许是东半球分析十大排序算法最好的一篇文章][Link 12]

### **4、搜索** ###

[几道和「广度优先搜索」有关的算法面试题][Link 13]

[初识广度优先搜索与解题套路][Link 14]

[从简单二叉树问题重新来看深度优先搜索][Link 15]

### **5、查找** ###

[二分查找算法详解][Link 16]

[一网打尽！二分查找解题模版与题型全面解析][Link 17]

[面试官，我会写二分查找法！对，没有 bug 的那种！][bug]

### **6、字符串匹配** ###

[动画：BM 算法中的坏字符规则与好后缀规则][BM]

[动画：七分钟理解什么是KMP算法][KMP]

[动画：什么是 BF 算法 ？][BF _]

[动态规划之 KMP 算法详解（配代码版）][KMP 1]

### **7、线性表** ###

[如何高效对有序数组/链表去重？][Link 18]

[超详细！详解一道高频算法题：数组中的第 K 个最大元素][K]

[一道简单的数组遍历题，加上四个条件后感觉无从下手][Link 19]

[数组特性的妙用！如何找到「缺失的第一个正数」][Link 20]

[剑指 offer 第一题：二维数组中的查找][offer]

[动画：什么是单调栈？][Link 21]

[在数据结构中穿针引线：链表实现栈和队列][Link 22]

[从简单的线性数据结构开始：栈与队列][Link 23]

[五分钟学算法小知识：用栈实现队列/用队列实现栈][Link 24]

[几道和「堆栈、队列」有关的面试算法题][Link 25]

[超详细！图解「合并 K 个排序链表」][K 1]

[动画：面试如何轻松手写链表？][Link 26]

[LeetCode 上最难的链表算法题，没有之一！][LeetCode]

[链表算法面试问题？看我就够了！][Link 27]

[看动画轻松理解「链表」实现「LRU缓存淘汰算法」][LRU]

[从简单的线性数据结构开始：穿针引线的链表（一）][Link 28]

[在数据结构中穿针引线：链表实现栈和队列][Link 22]

### **8、散列表** ###

[五分钟速读：什么是散列表（哈希表）？][Link 29]

[什么是哈希洪水攻击（Hash-Flooding Attack）？][Hash-Flooding Attack]

[几道和散列（哈希）表有关的面试题][Link 30]

[如何判断一个元素在亿级数据中是否存在？][Link 31]

### **9、树** ###

[面试前准备：二叉树高频面试题和答案][Link 32]

[懵逼树上懵逼果：学习二分搜索树][Link 33]

[LeetCode 二叉树问题小总结][LeetCode 1]

[从简单二叉树问题重新来看深度优先搜索][Link 15]

[几道和「二叉树」有关的算法面试题][Link 34]

[详解什么是平衡二叉树（AVL）（修订补充版）][AVL]

[【面试现场】为什么 MySQL 数据库要用B+树存储索引？][MySQL _B]

[字典树概念与题型解析][Link 35]

[面试官：为什么 MySQL 的索引要使用 B+ 树，而不是其它树？比如 B 树？][MySQL _ B_ _ B]

[心里没点 B 树。。。][B]

[数据结构与算法——最小生成树][Link 36]

[植树节，程序猿种的那些树][Link 37]

[数据结构与算法——2-3-4树][2-3-4]

[数据结构与算法——2-3树][2-3]

[看动画轻松理解「Trie树」][Trie]

### **10、图** ###

[浅谈什么是图拓扑排序][Link 38]

[数据结构与算法——图论基础与图存储结构][Link 39]

[数据结构与算法：三十张图弄懂「图的两种遍历方式」][Link 40]

[数据结构与算法——图最短路径][Link 41]

### **总结** ###

学习数据结构和算法的过程，是非常好的思维训练的过程，所以，千万不要被动地记忆，要多辩证地思考，多问为什么。

如果你一直这么坚持做，你会发现，等你学完之后，写代码的时候就会不由自主地考虑到很多性能方面的事情，时间复杂度、空间复杂度非常高的垃圾代码出现的次数就会越来越少。

你的编程内功就真正得到了修炼。大家加油：）

## 作者简介 ##

> 作者：大家好，我是程序员吴师兄，在 GitHub 上开源了一个项目 LeetCodeAnimation，目前有 60k star，通过动画的形式讲解算法，已经帮助成千上万的程序员入门算法了，欢迎关注公众号「五分钟学算法」，和我们一起学习算法。  
> 转载说明：未获得授权，禁止转载

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[K 1]: https://link.zhihu.com/?target=http%3A//mp.weixin.qq.com/s%3F__biz%3DMzUyNjQxNjYyMg%3D%3D%26mid%3D2247486890%26idx%3D2%26sn%3D8ce4eb1d150a5333942ed86350d4eed3%26chksm%3Dfa0e622bcd79eb3d2ac14d76351400253f8ab2cf908fc16939fc9ce58cbc0be24eb1197ddd8d%26scene%3D21%23wechat_redirect
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[LeetCode]: https://link.zhihu.com/?target=http%3A//mp.weixin.qq.com/s%3F__biz%3DMzUyNjQxNjYyMg%3D%3D%26mid%3D2247485110%26idx%3D1%26sn%3D93950a8445ce1d45d0633093b9127240%26chksm%3Dfa0e6937cd79e021003c333a19bebd00cddec60472cadb8dc66629523eee9c66c5eaef6c8798%26scene%3D21%23wechat_redirect
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[Link 29]: https://link.zhihu.com/?target=http%3A//mp.weixin.qq.com/s%3F__biz%3DMzUyNjQxNjYyMg%3D%3D%26mid%3D2247486499%26idx%3D4%26sn%3D7c9aee095ec972b1af842788c545d309%26chksm%3Dfa0e63a2cd79eab47649274533063bea75550d97aa55f60856f02037bc2f6b657270630f214b%26scene%3D21%23wechat_redirect
[Hash-Flooding Attack]: https://link.zhihu.com/?target=http%3A//mp.weixin.qq.com/s%3F__biz%3DMzUyNjQxNjYyMg%3D%3D%26mid%3D2247485591%26idx%3D1%26sn%3D54cde6fab4f11a0478f0c6447069d47c%26chksm%3Dfa0e6716cd79ee00e3502116a4f2999ee9648b99999317d450d9d6ee8ebef8cf4d39f2f79372%26scene%3D21%23wechat_redirect
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[LeetCode 1]: https://link.zhihu.com/?target=http%3A//mp.weixin.qq.com/s%3F__biz%3DMzUyNjQxNjYyMg%3D%3D%26mid%3D2247486350%26idx%3D3%26sn%3Df847d84a0c2553d2854b37b6202cb923%26chksm%3Dfa0e640fcd79ed19006e12d9d4e330fca44db451413a5870de3758515be60f387d43a1f80ef1%26scene%3D21%23wechat_redirect
[Link 34]: https://link.zhihu.com/?target=http%3A//mp.weixin.qq.com/s%3F__biz%3DMzUyNjQxNjYyMg%3D%3D%26mid%3D2247484985%26idx%3D1%26sn%3D93343d355abf36c77a361c9931cbe2d1%26chksm%3Dfa0e69b8cd79e0ae1e6b57665a456da5f421cc92fe6934337f1eb1e18c3fd6a3c1adc8ca88c2%26scene%3D21%23wechat_redirect
[AVL]: https://link.zhihu.com/?target=http%3A//mp.weixin.qq.com/s%3F__biz%3DMzUyNjQxNjYyMg%3D%3D%26mid%3D2247484608%26idx%3D1%26sn%3D68b96e6e65a048da54177b6e95b02676%26chksm%3Dfa0e6b41cd79e257daa1f276e0921ed4a060c9caf964e4131f68010ae2a9b8211f56af866fed%26scene%3D21%23wechat_redirect
[MySQL _B]: https://link.zhihu.com/?target=http%3A//mp.weixin.qq.com/s%3F__biz%3DMzUyNjQxNjYyMg%3D%3D%26mid%3D2247486680%26idx%3D1%26sn%3Dfec210ee18e81448e9e5245be7ebe03f%26chksm%3Dfa0e6359cd79ea4f1f138d979c10160f3c62cca7fa36e38f896ef4434983cff5dd544ccf0799%26scene%3D21%23wechat_redirect
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[MySQL _ B_ _ B]: https://link.zhihu.com/?target=http%3A//mp.weixin.qq.com/s%3F__biz%3DMzUyNjQxNjYyMg%3D%3D%26mid%3D2247486359%26idx%3D2%26sn%3Ddaf49d25a38e1440d932c92ca618de09%26chksm%3Dfa0e6416cd79ed000dadbda01d801977e410e505ea91331e42e7ed2990eda12272441ee9bb75%26scene%3D21%23wechat_redirect
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[2-3-4]: https://link.zhihu.com/?target=http%3A//mp.weixin.qq.com/s%3F__biz%3DMzUyNjQxNjYyMg%3D%3D%26mid%3D2247484706%26idx%3D1%26sn%3D645713dba123f71a014dcc1204083293%26chksm%3Dfa0e6aa3cd79e3b5b2ebf903a52bd90f6728e9def50da80eb0ee5aa3aa9f6e940c9822217fe2%26scene%3D21%23wechat_redirect
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[Trie]: https://link.zhihu.com/?target=http%3A//mp.weixin.qq.com/s%3F__biz%3DMzUyNjQxNjYyMg%3D%3D%26mid%3D2247484383%26idx%3D1%26sn%3Dbc555e97f42b56aa8697ec71d92dc79d%26chksm%3Dfa0e6c5ecd79e548a10d493979b58cb3530eab4c83533d09c463da67d870a24a1acddef4dad4%26scene%3D21%23wechat_redirect
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