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<img src="https://img.shields.io/badge/Dart-snow?logo=dart&logoColor=0175C2" alt="" />
<img src="https://img.shields.io/badge/Zig-snow?logo=zig&logoColor=F7A41D" alt="" />
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<p style="margin-top: 2em;">500 幅动画图解、12 种编程语言代码、3000 条社区问答，助你快速入门数据结构与算法</p>
<p style="margin-top: 2em;">500 幅动画图解、14 种编程语言代码、3000 条社区问答，助你快速入门数据结构与算法</p>
</div>
</section>

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## Chapter contents
- [3.1 &nbsp; Classification of data structures](classification_of_data_structure.md)
- [3.2 &nbsp; Fundamental data types](basic_data_types.md)
- [3.2 &nbsp; Basic data types](basic_data_types.md)
- [3.3 &nbsp; Number encoding *](number_encoding.md)
- [3.4 &nbsp; Character encoding *](character_encoding.md)
- [3.5 &nbsp; Summary](summary.md)

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## Chapter contents
- [9.1 &nbsp; Graph](graph.md)
- [9.2 &nbsp; Basic Graph Operations](graph_operations.md)
- [9.3 &nbsp; Graph Traversal](graph_traversal.md)
- [9.2 &nbsp; Basic graph operations](graph_operations.md)
- [9.3 &nbsp; Graph traversal](graph_traversal.md)
- [9.4 &nbsp; Summary](summary.md)

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## Chapter contents
- [8.1 &nbsp; Heap](heap.md)
- [8.2 &nbsp; Building a Heap](build_heap.md)
- [8.3 &nbsp; Top-k Problem](top_k.md)
- [8.2 &nbsp; Building a heap](build_heap.md)
- [8.3 &nbsp; Top-k problem](top_k.md)
- [8.4 &nbsp; Summary](summary.md)

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---
comments: true
icon: material/rocket-launch-outline
---
# Before starting
A few years ago, I shared the "Sword for Offer" problem solutions on LeetCode, receiving encouragement and support from many readers. During interactions with readers, the most common question I encountered was "how to get started with algorithms." Gradually, I developed a keen interest in this question.
Directly solving problems seems to be the most popular method — it's simple, direct, and effective. However, problem-solving is like playing a game of Minesweeper: those with strong self-study abilities can defuse the mines one by one, but those with insufficient basics might end up metaphorically bruised from explosions, retreating step by step in frustration. Going through textbooks is also common, but for those aiming for job applications, the energy spent on thesis writing, resume submissions, and preparation for written tests and interviews leaves little for tackling thick books, turning it into a daunting challenge.
If you're facing similar troubles, then this book are lucky to have found you. This book is my answer to the question. While it may not be the best solution, it is at least a positive attempt. This book may not directly land you an offer, but it will guide you through the "knowledge map" in data structures and algorithms, help you understand the shapes, sizes, and locations of different "mines," and enable you to master various "demining methods." With these skills, I believe you can solve problems and read literature more comfortably, gradually building a knowledge system.
I deeply agree with Professor Feynman's statement: "Knowledge isn't free. You have to pay attention." In this sense, this book is not entirely "free." To not disappoint the precious "attention" you pay for this book, I will do my best, dedicating my utmost "attention" to this book.
Knowing my limitations, although the content of this book has been refined over time, there are surely many errors remaining. I sincerely request critiques and corrections from all teachers and students.
![Hello Algorithms](../assets/covers/chapter_hello_algo.jpg){ class="cover-image" }
<div style="text-align: center;">
<h2 style="margin-top: 0.8em; margin-bottom: 0.8em;">Hello, Algo!</h2>
</div>
The advent of computers has brought significant changes to the world. With their high-speed computing power and excellent programmability, they have become the ideal medium for executing algorithms and processing data. Whether it's the realistic graphics of video games, the intelligent decisions in autonomous driving, the brilliant Go games of AlphaGo, or the natural interactions of ChatGPT, these applications are all exquisite demonstrations of algorithms at work on computers.
In fact, before the advent of computers, algorithms and data structures already existed in every corner of the world. Early algorithms were relatively simple, such as ancient counting methods and tool-making procedures. As civilization progressed, algorithms became more refined and complex. From the exquisite craftsmanship of artisans, to industrial products that liberate productive forces, to the scientific laws governing the universe, almost every ordinary or astonishing thing has behind it the ingenious thought of algorithms.
Similarly, data structures are everywhere: from social networks to subway lines, many systems can be modeled as "graphs"; from a country to a family, the main forms of social organization exhibit characteristics of "trees"; winter clothes are like a "stack", where the first item worn is the last to be taken off; a badminton shuttle tube resembles a "queue", with one end for insertion and the other for retrieval; a dictionary is like a "hash table", enabling quick search for target entries.
This book aims to help readers understand the core concepts of algorithms and data structures through clear, easy-to-understand animated illustrations and runnable code examples, and to be able to implement them through programming. On this basis, this book strives to reveal the vivid manifestations of algorithms in the complex world, showcasing the beauty of algorithms. I hope this book can help you!

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icon: material/calculator-variant-outline
---
# Chapter 1. &nbsp; Introduction to algorithms
# Chapter 1. &nbsp; Encounter with algorithms
![Introduction to algorithms](../assets/covers/chapter_introduction.jpg){ class="cover-image" }
![Encounter with algorithms](../assets/covers/chapter_introduction.jpg){ class="cover-image" }
!!! abstract

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## Chapter contents
- [7.1 &nbsp; Binary Tree](binary_tree.md)
- [7.2 &nbsp; Binary Tree Traversal](binary_tree_traversal.md)
- [7.3 &nbsp; Array Representation of Tree](array_representation_of_tree.md)
- [7.4 &nbsp; Binary Search Tree](binary_search_tree.md)
- [7.5 &nbsp; AVL Tree *](avl_tree.md)
- [7.1 &nbsp; Binary tree](binary_tree.md)
- [7.2 &nbsp; Binary tree Traversal](binary_tree_traversal.md)
- [7.3 &nbsp; Array Representation of tree](array_representation_of_tree.md)
- [7.4 &nbsp; Binary Search tree](binary_search_tree.md)
- [7.5 &nbsp; AVL tree *](avl_tree.md)
- [7.6 &nbsp; Summary](summary.md)

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<p style="margin-bottom: 0;">“An easy-to-understand book on data structures and algorithms, which guides readers to learn by minds-on and hands-on. Strongly recommended for algorithm beginners!”</p>
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<p class="intro-quote">"A picture is worth a thousand words."</p>
</div>
</div>
<img class="intro-image" src="index.assets/animation.gif" alt="Animation example">
</div>
<div class="intro-container">
<img class="intro-image" src="index.assets/running_code.gif" alt="Running code example">
<div class="intro-text">
<div>
<div style="display: flex; align-items: center;">
<svg xmlns="http://www.w3.org/2000/svg" height="1.5em" width="1.5em" viewBox="0 0 640 512">
<path fill="var(--md-primary-bg-color)"
d="M392.8 1.2c-17-4.9-34.7 5-39.6 22l-128 448c-4.9 17 5 34.7 22 39.6s34.7-5 39.6-22l128-448c4.9-17-5-34.7-22-39.6zm80.6 120.1c-12.5 12.5-12.5 32.8 0 45.3L562.7 256l-89.4 89.4c-12.5 12.5-12.5 32.8 0 45.3s32.8 12.5 45.3 0l112-112c12.5-12.5 12.5-32.8 0-45.3l-112-112c-12.5-12.5-32.8-12.5-45.3 0zm-306.7 0c-12.5-12.5-32.8-12.5-45.3 0l-112 112c-12.5 12.5-12.5 32.8 0 45.3l112 112c12.5 12.5 32.8 12.5 45.3 0s12.5-32.8 0-45.3L77.3 256l89.4-89.4c12.5-12.5 12.5-32.8 0-45.3z" />
</svg>
<h3 style="margin-left: 0.5em;">Off-the-shelf code</h3>
</div>
<p style="margin: 0;">Featuring multiple programming languages, all runnable with a single click.</p>
<p class="intro-quote">"Talk is cheap. Show me the code."</p>
</div>
</div>
</div>
<div class="intro-container">
<div class="intro-text">
<div>
<div style="display: flex; align-items: center;">
<svg xmlns="http://www.w3.org/2000/svg" height="1.5em" width="1.5em" viewBox="0 0 640 512">
<path fill="var(--md-primary-bg-color)"
d="M88.2 309.1c9.8-18.3 6.8-40.8-7.5-55.8C59.4 230.9 48 204 48 176c0-63.5 63.8-128 160-128s160 64.5 160 128s-63.8 128-160 128c-13.1 0-25.8-1.3-37.8-3.6c-10.4-2-21.2-.6-30.7 4.2c-4.1 2.1-8.3 4.1-12.6 6c-16 7.2-32.9 13.5-49.9 18c2.8-4.6 5.4-9.1 7.9-13.6c1.1-1.9 2.2-3.9 3.2-5.9zM0 176c0 41.8 17.2 80.1 45.9 110.3c-.9 1.7-1.9 3.5-2.8 5.1c-10.3 18.4-22.3 36.5-36.6 52.1c-6.6 7-8.3 17.2-4.6 25.9C5.8 378.3 14.4 384 24 384c43 0 86.5-13.3 122.7-29.7c4.8-2.2 9.6-4.5 14.2-6.8c15.1 3 30.9 4.5 47.1 4.5c114.9 0 208-78.8 208-176S322.9 0 208 0S0 78.8 0 176zM432 480c16.2 0 31.9-1.6 47.1-4.5c4.6 2.3 9.4 4.6 14.2 6.8C529.5 498.7 573 512 616 512c9.6 0 18.2-5.7 22-14.5c3.8-8.8 2-19-4.6-25.9c-14.2-15.6-26.2-33.7-36.6-52.1c-.9-1.7-1.9-3.4-2.8-5.1C622.8 384.1 640 345.8 640 304c0-94.4-87.9-171.5-198.2-175.8c4.1 15.2 6.2 31.2 6.2 47.8l0 .6c87.2 6.7 144 67.5 144 127.4c0 28-11.4 54.9-32.7 77.2c-14.3 15-17.3 37.6-7.5 55.8c1.1 2 2.2 4 3.2 5.9c2.5 4.5 5.2 9 7.9 13.6c-17-4.5-33.9-10.7-49.9-18c-4.3-1.9-8.5-3.9-12.6-6c-9.5-4.8-20.3-6.2-30.7-4.2c-12.1 2.4-24.7 3.6-37.8 3.6c-61.7 0-110-26.5-136.8-62.3c-16 5.4-32.8 9.4-50 11.8C279 439.8 350 480 432 480z" />
</svg>
<h3 style="margin-left: 0.5em;">Learning together</h3>
</div>
<p style="margin: 0;">Welcome discussions and questions with open arms.</p>
<p class="intro-quote">"Learning by teaching."</p>
</div>
</div>
<img class="intro-image" src="index.assets/comment.gif" alt="Comments example">
</div>
</div>
</section>
<!-- Section: contributors -->
<section data-md-color-scheme="slate" data-md-color-primary="grey" class="home-div">
<div class="section-content" style="max-width: 90vw;">
<!-- author -->
<div style="margin: 2em auto;">
<h3>Author</h3>
<div class="profile-div">
<div class="profile-cell">
<a href="https://github.com/krahets">
<img class="profile-img" src="../assets/avatar/avatar_yudongjin.jpg" alt="Author: yudongjin" />
<br><b>Yudong Jin（@krahets）</b>
</a>
</div>
</div>
</div>
<!-- reviewers -->
<div style="margin: 2em auto;">
<h3>Code reviewers</h3>
<div class="profile-div">
<div class="profile-cell">
<a href="https://github.com/codingonion">
<img class="profile-img" src="../assets/avatar/avatar_codingonion.jpg"
alt="Reviewer: codingonion" />
<br><b>codingonion</b>
<br><sub>Zig, Rust</sub>
</a>
</div>
<div class="profile-cell">
<a href="https://github.com/curtishd">
<img class="profile-img" src="../assets/avatar/avatar_curtishd.jpg"
alt="Reviewer: curtishd" />
<br><b>curtishd</b>
<br><sub>Kotlin</sub>
</a>
</div>
<div class="profile-cell">
<a href="https://github.com/Gonglja">
<img class="profile-img" src="../assets/avatar/avatar_Gonglja.jpg" alt="Reviewer: Gonglja" />
<br><b>Gonglja</b>
<br><sub>C, C++</sub>
</a>
</div>
<div class="profile-cell">
<a href="https://github.com/gvenusleo">
<img class="profile-img" src="../assets/avatar/avatar_gvenusleo.jpg" alt="Reviewer: gvenusleo" />
<br><b>gvenusleo</b>
<br><sub>Dart</sub>
</a>
</div>
<div class="profile-cell">
<a href="https://github.com/hpstory">
<img class="profile-img" src="../assets/avatar/avatar_hpstory.jpg" alt="Reviewer: hpstory" />
<br><b>hpstory</b>
<br><sub>C#</sub>
</a>
</div>
<div class="profile-cell">
<a href="https://github.com/justin-tse">
<img class="profile-img" src="../assets/avatar/avatar_justin-tse.jpg" alt="Reviewer: justin-tse" />
<br><b>justin-tse</b>
<br><sub>JS, TS</sub>
</a>
</div>
<div class="profile-cell">
<a href="https://github.com/krahets">
<img class="profile-img" src="../assets/avatar/avatar_krahets.jpg" alt="Reviewer: krahets" />
<br><b>krahets</b>
<br><sub>Python, Java</sub>
</a>
</div>
<div class="profile-cell">
<a href="https://github.com/night-cruise">
<img class="profile-img" src="../assets/avatar/avatar_night-cruise.jpg"
alt="Reviewer: night-cruise" />
<br><b>night-cruise</b>
<br><sub>Rust</sub>
</a>
</div>
<div class="profile-cell">
<a href="https://github.com/nuomi1">
<img class="profile-img" src="../assets/avatar/avatar_nuomi1.jpg" alt="Reviewer: nuomi1" />
<br><b>nuomi1</b>
<br><sub>Swift</sub>
</a>
</div>
<div class="profile-cell">
<a href="https://github.com/Reanon">
<img class="profile-img" src="../assets/avatar/avatar_Reanon.jpg" alt="Reviewer: Reanon" />
<br><b>Reanon</b>
<br><sub>Go, C</sub>
</a>
</div>
</div>
</div>
<!-- contributors -->
<div style="margin: 2em auto;">
<h3>Contributors</h3>
<p>This book has been enhanced through the collaborative efforts of more than 100 contributors. Thanks for their invaluable time and input!</p>
<a href="https://github.com/krahets/hello-algo/graphs/contributors">
<img src="https://contrib.rocks/image?repo=krahets/hello-algo&max=300&columns=16" alt="Contributors"
style="width: 100%; max-width: 38.5em;">
</a>
</div>
</div>
</section>

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en/docs/index.md
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---
comments: true
comments: false
glightbox: false
hide:
- footer
- toc
- edit
- navigation
---
<div class="header-img-div" style="max-width: 600px;">
<img src="index.assets/hello_algo_header.png" style="width: 100%; height: auto; margin-left: 15px; margin-right: 15px;">
</div>
<h2 align="center" style="margin-top: 25px;">Hello Algo</h2>
<p align="center">Data Structures and Algorithms Crash Course with Animated Illustrations and Off-the-Shelf Code</p>
<p align="center">
<a href="https://github.com/krahets/hello-algo">
<img alt="GitHub repo stars" src="https://img.shields.io/github/stars/krahets/hello-algo?style=social&link=https%3A%2F%2Fgithub.com%2Fkrahets%2Fhello-algo">
</a>
&nbsp;
<a href="https://github.com/krahets/hello-algo/releases">
<img alt="GitHub all releases" src="https://img.shields.io/github/downloads/krahets/hello-algo/total?style=social&logo=gitbook&logoColor=black&label=Downloads">
</a>
&nbsp;
<a href="https://github.com/krahets/hello-algo">
<img alt="GitHub contributors" src="https://img.shields.io/github/contributors-anon/krahets/hello-algo?style=social&logo=git&logoColor=%23101010">
</a>
</p>
<p align="center">
<a href="https://www.hello-algo.com/en/chapter_preface/" class="rounded-button">
<svg xmlns="http://www.w3.org/2000/svg" height="16" width="18" viewBox="0 0 576 512"><!--!Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free Copyright 2023 Fonticons, Inc.--><path d="M249.6 471.5c10.8 3.8 22.4-4.1 22.4-15.5V78.6c0-4.2-1.6-8.4-5-11C247.4 52 202.4 32 144 32C93.5 32 46.3 45.3 18.1 56.1C6.8 60.5 0 71.7 0 83.8V454.1c0 11.9 12.8 20.2 24.1 16.5C55.6 460.1 105.5 448 144 448c33.9 0 79 14 105.6 23.5zm76.8 0C353 462 398.1 448 432 448c38.5 0 88.4 12.1 119.9 22.6c11.3 3.8 24.1-4.6 24.1-16.5V83.8c0-12.1-6.8-23.3-18.1-27.6C529.7 45.3 482.5 32 432 32c-58.4 0-103.4 20-123 35.6c-3.3 2.6-5 6.8-5 11V456c0 11.4 11.7 19.3 22.4 15.5z"/></svg>
Dive In
</a>
<a href="https://github.com/krahets/hello-algo" class="rounded-button">
<svg xmlns="http://www.w3.org/2000/svg" height="16px" width="15.5px" viewBox="0 0 496 512"><!--!Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free Copyright 2023 Fonticons, Inc.--><path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3 .3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5 .3-6.2 2.3zm44.2-1.7c-2.9 .7-4.9 2.6-4.6 4.9 .3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3 .7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3 .3 2.9 2.3 3.9 1.6 1 3.6 .7 4.3-.7 .7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3 .7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3 .7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"/></svg>
Clone Repo
</a>
<a href="https://github.com/krahets/hello-algo/releases" class="rounded-button">
<svg xmlns="http://www.w3.org/2000/svg" height="16" width="16" viewBox="0 0 512 512"><!--!Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free Copyright 2023 Fonticons, Inc.--><path d="M0 64C0 28.7 28.7 0 64 0L224 0l0 128c0 17.7 14.3 32 32 32l128 0 0 144-208 0c-35.3 0-64 28.7-64 64l0 144-48 0c-35.3 0-64-28.7-64-64L0 64zm384 64l-128 0L256 0 384 128zM176 352l32 0c30.9 0 56 25.1 56 56s-25.1 56-56 56l-16 0 0 32c0 8.8-7.2 16-16 16s-16-7.2-16-16l0-48 0-80c0-8.8 7.2-16 16-16zm32 80c13.3 0 24-10.7 24-24s-10.7-24-24-24l-16 0 0 48 16 0zm96-80l32 0c26.5 0 48 21.5 48 48l0 64c0 26.5-21.5 48-48 48l-32 0c-8.8 0-16-7.2-16-16l0-128c0-8.8 7.2-16 16-16zm32 128c8.8 0 16-7.2 16-16l0-64c0-8.8-7.2-16-16-16l-16 0 0 96 16 0zm80-112c0-8.8 7.2-16 16-16l48 0c8.8 0 16 7.2 16 16s-7.2 16-16 16l-32 0 0 32 32 0c8.8 0 16 7.2 16 16s-7.2 16-16 16l-32 0 0 48c0 8.8-7.2 16-16 16s-16-7.2-16-16l0-64 0-64z"/></svg>
Get PDF
</a>
</p>
<div class="admonition example" style="max-width: 800px;margin: 0 auto;">
<p class="admonition-title">The English version is brewing...</p>
<p>Feel free to engage in Chinese-to-English translation and pull request review! For guidelines, please see <a href="https://github.com/krahets/hello-algo/issues/914">#914</a>.</p>
</div>
<div style="display: flex;">
<div class="admonition quote" style="flex: 1; margin-right: 0.4rem;">
<p class="admonition-title">Quote</p>
<p>"An easy-to-understand book on data structures and algorithms, which guides readers to learn by minds-on and hands-on. Strongly recommended for algorithm beginners!"</p>
<p><strong>—— Junhui Deng, Professor of Computer Science, Tsinghua University</strong></p>
</div>
<div class="admonition quote" style="flex: 1; margin-left: 0.4rem;">
<p class="admonition-title">Quote</p>
<p>"If I had 'Hello Algo' when I was learning data structures and algorithms, it would have been 10 times easier!"</p>
<p><strong>—— Mu Li, Senior Principal Scientist, Amazon</strong></p>
</div>
</div>
---
<div style="display: flex; align-items: center; margin: 2rem auto;">
<div style="flex: 1; margin: 0 2rem; display: flex; flex-direction: column; align-items: center;">
<div style="display: flex; flex-direction: column; align-items: center;">
<h3>Animated illustrations</h3>
<svg xmlns="http://www.w3.org/2000/svg" height="28" width="28" viewBox="0 0 640 512"><!--!Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free Copyright 2023 Fonticons, Inc.--><path fill="var(--md-primary-bg-color)" d="M256 0H576c35.3 0 64 28.7 64 64V288c0 35.3-28.7 64-64 64H256c-35.3 0-64-28.7-64-64V64c0-35.3 28.7-64 64-64zM476 106.7C471.5 100 464 96 456 96s-15.5 4-20 10.7l-56 84L362.7 169c-4.6-5.7-11.5-9-18.7-9s-14.2 3.3-18.7 9l-64 80c-5.8 7.2-6.9 17.1-2.9 25.4s12.4 13.6 21.6 13.6h80 48H552c8.9 0 17-4.9 21.2-12.7s3.7-17.3-1.2-24.6l-96-144zM336 96a32 32 0 1 0 -64 0 32 32 0 1 0 64 0zM64 128h96V384v32c0 17.7 14.3 32 32 32H320c17.7 0 32-14.3 32-32V384H512v64c0 35.3-28.7 64-64 64H64c-35.3 0-64-28.7-64-64V192c0-35.3 28.7-64 64-64zm8 64c-8.8 0-16 7.2-16 16v16c0 8.8 7.2 16 16 16H88c8.8 0 16-7.2 16-16V208c0-8.8-7.2-16-16-16H72zm0 104c-8.8 0-16 7.2-16 16v16c0 8.8 7.2 16 16 16H88c8.8 0 16-7.2 16-16V312c0-8.8-7.2-16-16-16H72zm0 104c-8.8 0-16 7.2-16 16v16c0 8.8 7.2 16 16 16H88c8.8 0 16-7.2 16-16V416c0-8.8-7.2-16-16-16H72zm336 16v16c0 8.8 7.2 16 16 16h16c8.8 0 16-7.2 16-16V416c0-8.8-7.2-16-16-16H424c-8.8 0-16 7.2-16 16z"/></svg>
</div>
<p style="text-align: center;">Easy to understand</br>Smooth learning curve</p>
</div>
<img src="index.assets/animation.gif" class="cover-image" style="flex-shrink: 0; width: auto; max-width: 50%; border-radius: 0.5rem;">
</div>
<div class="admonition quote">
<p align="center">"A picture is worth a thousand words."</p>
</div>
<div style="display: flex; align-items: center; margin: 2rem auto;">
<img src="index.assets/running_code.gif" class="cover-image" style="flex-shrink: 0; width: auto; max-width: 50%; border-radius: 0.5rem;">
<div style="flex: 1; margin: 0 2rem; display: flex; flex-direction: column; align-items: center;">
<div style="display: flex; flex-direction: column; align-items: center;">
<h3>Off-the-Shelf Code</h3>
<svg xmlns="http://www.w3.org/2000/svg" height="28" width="28" viewBox="0 0 640 512"><!--!Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free Copyright 2023 Fonticons, Inc.--><path fill="var(--md-primary-bg-color)" d="M392.8 1.2c-17-4.9-34.7 5-39.6 22l-128 448c-4.9 17 5 34.7 22 39.6s34.7-5 39.6-22l128-448c4.9-17-5-34.7-22-39.6zm80.6 120.1c-12.5 12.5-12.5 32.8 0 45.3L562.7 256l-89.4 89.4c-12.5 12.5-12.5 32.8 0 45.3s32.8 12.5 45.3 0l112-112c12.5-12.5 12.5-32.8 0-45.3l-112-112c-12.5-12.5-32.8-12.5-45.3 0zm-306.7 0c-12.5-12.5-32.8-12.5-45.3 0l-112 112c-12.5 12.5-12.5 32.8 0 45.3l112 112c12.5 12.5 32.8 12.5 45.3 0s12.5-32.8 0-45.3L77.3 256l89.4-89.4c12.5-12.5 12.5-32.8 0-45.3z"/></svg>
</div>
<p style="text-align: center;">Multi programming languages</br>Run with one click</p>
</div>
</div>
<div class="admonition quote">
<p align="center">"Talk is cheap. Show me the code."</p>
</div>
<div style="display: flex; align-items: center; margin: 2rem auto;">
<div style="flex: 1; margin: 0 2rem; display: flex; flex-direction: column; align-items: center;">
<div style="display: flex; flex-direction: column; align-items: center;">
<h3>Learning Together</h3>
<svg xmlns="http://www.w3.org/2000/svg" height="28" width="28" viewBox="0 0 640 512"><!--!Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free Copyright 2023 Fonticons, Inc.--><path fill="var(--md-primary-bg-color)" d="M88.2 309.1c9.8-18.3 6.8-40.8-7.5-55.8C59.4 230.9 48 204 48 176c0-63.5 63.8-128 160-128s160 64.5 160 128s-63.8 128-160 128c-13.1 0-25.8-1.3-37.8-3.6c-10.4-2-21.2-.6-30.7 4.2c-4.1 2.1-8.3 4.1-12.6 6c-16 7.2-32.9 13.5-49.9 18c2.8-4.6 5.4-9.1 7.9-13.6c1.1-1.9 2.2-3.9 3.2-5.9zM0 176c0 41.8 17.2 80.1 45.9 110.3c-.9 1.7-1.9 3.5-2.8 5.1c-10.3 18.4-22.3 36.5-36.6 52.1c-6.6 7-8.3 17.2-4.6 25.9C5.8 378.3 14.4 384 24 384c43 0 86.5-13.3 122.7-29.7c4.8-2.2 9.6-4.5 14.2-6.8c15.1 3 30.9 4.5 47.1 4.5c114.9 0 208-78.8 208-176S322.9 0 208 0S0 78.8 0 176zM432 480c16.2 0 31.9-1.6 47.1-4.5c4.6 2.3 9.4 4.6 14.2 6.8C529.5 498.7 573 512 616 512c9.6 0 18.2-5.7 22-14.5c3.8-8.8 2-19-4.6-25.9c-14.2-15.6-26.2-33.7-36.6-52.1c-.9-1.7-1.9-3.4-2.8-5.1C622.8 384.1 640 345.8 640 304c0-94.4-87.9-171.5-198.2-175.8c4.1 15.2 6.2 31.2 6.2 47.8l0 .6c87.2 6.7 144 67.5 144 127.4c0 28-11.4 54.9-32.7 77.2c-14.3 15-17.3 37.6-7.5 55.8c1.1 2 2.2 4 3.2 5.9c2.5 4.5 5.2 9 7.9 13.6c-17-4.5-33.9-10.7-49.9-18c-4.3-1.9-8.5-3.9-12.6-6c-9.5-4.8-20.3-6.2-30.7-4.2c-12.1 2.4-24.7 3.6-37.8 3.6c-61.7 0-110-26.5-136.8-62.3c-16 5.4-32.8 9.4-50 11.8C279 439.8 350 480 432 480z"/></svg>
</div>
<p style="text-align: center;">Discussion and questions welcome</br>Readers progress together</p>
</div>
<img src="index.assets/comment.gif" class="cover-image" style="flex-shrink: 0; width: auto; max-width: 50%; border-radius: 0.5rem;">
</div>
<div class="admonition quote">
<p align="center">"Learning by teaching."</p>
</div>
---
<h3 align="center"> Preface </h3>
Two years ago, I shared the "Sword Offer" series of problem solutions on LeetCode, which received much love and support from many students. During my interactions with readers, the most common question I encountered was "How to get started with algorithms." Gradually, I developed a deep interest in this question.
Blindly solving problems seems to be the most popular method, being simple, direct, and effective. However, problem-solving is like playing a "Minesweeper" game, where students with strong self-learning abilities can successfully clear the mines one by one, but those with insufficient foundations may end up bruised from explosions, retreating step by step in frustration. Thoroughly reading textbooks is also common, but for students aiming for job applications, the energy consumed by graduation, resume submissions, and preparing for written tests and interviews makes tackling thick books a daunting challenge.
If you are facing similar troubles, then you are lucky to have found this book. This book is my answer to this question, not necessarily the best solution, but at least an active attempt. Although this book won't directly land you an Offer, it will guide you through the "knowledge map" of data structures and algorithms, help you understand the shape, size, and distribution of different "mines," and equip you with various "demining methods." With these skills, I believe you can more comfortably solve problems and read literature, gradually building a complete knowledge system.
I deeply agree with Professor Feynman's saying: "Knowledge isn't free. You have to pay attention." In this sense, this book is not entirely "free." To not disappoint the precious "attention" you pay to this book, I will do my utmost, investing the greatest "attention" to complete the creation of this book.
<h3 align="left"> Author </h3>
Yudong Jin([krahets](https://leetcode.cn/u/jyd/)), Senior Algorithm Engineer in a top tech company, Master's degree from Shanghai Jiao Tong University. The highest-read blogger across the entire LeetCode, his published ["Illustration of Algorithm Data Structures"](https://leetcode.cn/leetbook/detail/illustration-of-algorithm/) has been subscribed to by over 300k.
---
<h3 align="center"> Contribution </h3>
This book is continuously improved with the joint efforts of many contributors from the open-source community. Thanks to each writer who invested their time and energy, listed in the order generated by GitHub:
<p align="center">
<a href="https://github.com/krahets/hello-algo/graphs/contributors">
<img width="550" src="https://contrib.rocks/image?repo=krahets/hello-algo">
</a>
</p>
The code review work for this book was completed by codingonion, Gonglja, gvenusleo, hpstory, justin‐tse, krahets, night-cruise, nuomi1, and Reanon (listed in alphabetical order). Thanks to them for their time and effort, ensuring the standardization and uniformity of the code in various languages.
<div class="center-table">
<table style="border: none;">
<tbody>
<td align="center" style="border: none;"><a href="https://github.com/codingonion"><img style="border-radius: 50%;" src="https://avatars.githubusercontent.com/u/99076655?v=4" width="50px;" alt="codingonion"/></br><sub><b>codingonion</b></sub></a></br><sub>Rust, Zig</sub></td>
<td align="center" style="border: none;"><a href="https://github.com/Gonglja"><img style="border-radius: 50%;" src="https://avatars.githubusercontent.com/u/39959756?v=4" width="50px;" alt="Gonglja"/></br><sub><b>Gonglja</b></sub></a></br><sub>C, C++</sub></td>
<td align="center" style="border: none;"><a href="https://github.com/gvenusleo"><img style="border-radius: 50%;" src="https://avatars.githubusercontent.com/u/79075347?v=4" width="50px;" alt="gvenusleo"/></br><sub><b>gvenusleo</b></sub></a></br><sub>Dart</sub></td>
<td align="center" style="border: none;"><a href="https://github.com/hpstory"><img style="border-radius: 50%;" src="https://avatars.githubusercontent.com/u/33348162?v=4" width="50px;" alt="hpstory"/></br><sub><b>hpstory</b></sub></a></br><sub>C#</sub></td>
<td align="center" style="border: none;"><a href="https://github.com/justin-tse"><img style="border-radius: 50%;" src="https://avatars.githubusercontent.com/u/24556310?v=4" width="50px;" alt="justin-tse"/></br><sub><b>justin-tse</b></sub></a></br><sub>JS, TS</sub></td>
<td align="center" style="border: none;"><a href="https://github.com/krahets"><img style="border-radius: 50%;" src="https://avatars.githubusercontent.com/u/26993056?v=4" width="50px;" alt="krahets"/></br><sub><b>krahets</b></sub></a></br><sub>Java, Python</sub></td>
<td align="center" style="border: none;"><a href="https://github.com/night-cruise"><img style="border-radius: 50%;" src="https://avatars.githubusercontent.com/u/77157236?v=4" width="50px;" alt="night-cruise"/></br><sub><b>night-cruise</b></sub></a></br><sub>Rust</sub></td>
<td align="center" style="border: none;"><a href="https://github.com/nuomi1"><img style="border-radius: 50%;" src="https://avatars.githubusercontent.com/u/3739017?v=4" width="50px;" alt="nuomi1"/></br><sub><b>nuomi1</b></sub></a></br><sub>Swift</sub></td>
<td align="center" style="border: none;"><a href="https://github.com/Reanon"><img style="border-radius: 50%;" src="https://avatars.githubusercontent.com/u/22005836?v=4" width="50px;" alt="Reanon"/></br><sub><b>Reanon</b></sub></a></br><sub>Go, C</sub></td>
</tbody>
</table>
</div>

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{% elif config.theme.language == 'zh-Hant' %}
{% set announcements = '紙質書（簡體中文版）已發行，詳情請見<a href="/chapter_paperbook/">這裡</a>' %}
{% elif config.theme.language == 'en' %}
{% set announcements = 'The paper book (Chinese version) published. Please visit <a href="/chapter_paperbook/">this link</a> for more details.' %}
{% set announcements = 'Feel free to engage in Chinese-to-English translation and pull request review! Please visit <a href="https://github.com/krahets/hello-algo/issues/914">#914</a> for details.' %}
{% endif %}
<div class="banner-svg">
<svg xmlns="http://www.w3.org/2000/svg"

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<img src="https://img.shields.io/badge/Dart-snow?logo=dart&logoColor=0175C2" alt="" />
<img src="https://img.shields.io/badge/Zig-snow?logo=zig&logoColor=F7A41D" alt="" />
</div>
<p style="margin-top: 2em;">500 幅動畫圖解、12 種程式語言程式碼、3000 條社群問答，助你快速入門資料結構與演算法</p>
<p style="margin-top: 2em;">500 幅動畫圖解、14 種程式語言程式碼、3000 條社群問答，助你快速入門資料結構與演算法</p>
</div>
</section>

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