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---
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comments: true
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glightbox: false
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hide:
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- footer
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- toc
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- edit
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---
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<div class="header-img-div" style="max-width: 500px;">
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<img src="index.assets/conceptual_rendering.png" style="width: 37%; height: auto;">
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<img src="index.assets/hello_algo_mindmap_tp.png" style="width: 63%; height: auto;">
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</div>
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<h2 align="center">《 Hello 算法 》</h2>
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<p align="center">动画图解、一键运行的数据结构与算法教程</p>
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<p align="center">
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<a href="https://github.com/krahets/hello-algo">
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<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">
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</a>
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<a href="https://github.com/krahets/hello-algo/releases">
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<img alt="GitHub all releases" src="https://img.shields.io/github/downloads/krahets/hello-algo/total?style=social&logo=gitbook&logoColor=black&label=Downloads">
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</a>
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<a href="https://github.com/krahets/hello-algo">
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<img alt="GitHub contributors" src="https://img.shields.io/github/contributors-anon/krahets/hello-algo?style=social&logo=git&logoColor=%23101010">
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</a>
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</p>
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<p align="center">
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<a href="https://www.hello-algo.com/chapter_preface/" class="rounded-button">
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<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>
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开始阅读
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</a>
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<a href="https://github.com/krahets/hello-algo" class="rounded-button">
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<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>
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下载代码
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</a>
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<a href="https://github.com/krahets/hello-algo/releases" class="rounded-button">
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<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>
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下载 PDF
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</a>
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</p>
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<p align="center">
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<img src="https://img.shields.io/badge/Python-snow?logo=python&logoColor=3776AB">
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<img src="https://img.shields.io/badge/C%2B%2B-snow?logo=c%2B%2B&logoColor=00599C">
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<img src="https://img.shields.io/badge/Java-snow?logo=coffeescript&logoColor=FC4C02">
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<img src="https://img.shields.io/badge/C%23-snow?logo=csharp&logoColor=512BD4">
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<img src="https://img.shields.io/badge/Go-snow?logo=go&logoColor=00ADD8">
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<img src="https://img.shields.io/badge/Swift-snow?logo=swift&logoColor=F05138">
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<img src="https://img.shields.io/badge/JavaScript-snow?logo=javascript&logoColor=E9CE30">
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<img src="https://img.shields.io/badge/TypeScript-snow?logo=typescript&logoColor=3178C6">
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<img src="https://img.shields.io/badge/Dart-snow?logo=dart&logoColor=0175C2">
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<img src="https://img.shields.io/badge/Rust-snow?logo=rust&logoColor=000000">
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<img src="https://img.shields.io/badge/C-snow?logo=c&logoColor=A8B9CC">
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<img src="https://img.shields.io/badge/Zig-snow?logo=zig&logoColor=F7A41D">
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<img src="https://img.shields.io/badge/Stay%20Tuned-snow">
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</p>
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---
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<h3 align="center">推荐语</h3>
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<div style="display: flex;">
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<div class="admonition quote" style="flex: 1; margin-right: 0.4rem;">
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<p class="admonition-title">Quote</p>
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<p>“一本通俗易懂的数据结构与算法入门书，引导读者手脑并用地学习，强烈推荐算法初学者阅读。”</p>
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<p><strong>—— 邓俊辉，清华大学计算机系教授</strong></p>
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</div>
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<div class="admonition quote" style="flex: 1; margin-left: 0.4rem;">
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<p class="admonition-title">Quote</p>
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<p>“如果我当年学数据结构与算法的时候有《Hello 算法》，学起来应该会简单 10 倍！”</p>
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<p><strong>—— 李沐，亚马逊资深首席科学家</strong></p>
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</div>
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</div>
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---
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<div style="display: flex; align-items: center; margin: 2rem auto;">
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<div style="flex: 1; margin: 0 2rem; display: flex; flex-direction: column; align-items: center;">
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<div style="display: flex; flex-direction: column; align-items: center;">
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<h3>动画图解</h3>
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<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>
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</div>
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<p style="text-align: center;">内容清晰易懂</br>学习曲线平滑</p>
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</div>
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<img src="index.assets/animation.gif" class="cover-image" style="flex-shrink: 0; width: auto; max-width: 50%; border-radius: 0.5rem;">
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</div>
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<div class="admonition quote">
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<p align="center">"A picture is worth a thousand words."</p>
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<p align="center">“一图胜千言”</p>
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</div>
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<div style="display: flex; align-items: center; margin: 2rem auto;">
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<img src="index.assets/running_code.gif" class="cover-image" style="flex-shrink: 0; width: auto; max-width: 50%; border-radius: 0.5rem;">
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<div style="flex: 1; margin: 0 2rem; display: flex; flex-direction: column; align-items: center;">
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<div style="display: flex; flex-direction: column; align-items: center;">
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<h3>一键运行</h3>
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<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>
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</div>
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<p style="text-align: center;">十余种编程语言</br>代码可直接运行</p>
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</div>
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</div>
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<div class="admonition quote">
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<p align="center">"Talk is cheap. Show me the code."</p>
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<p align="center">“少吹牛，看代码”</p>
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</div>
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<div style="display: flex; align-items: center; margin: 2rem auto;">
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<div style="flex: 1; margin: 0 2rem; display: flex; flex-direction: column; align-items: center;">
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<div style="display: flex; flex-direction: column; align-items: center;">
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<h3>互助学习</h3>
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<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>
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</div>
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<p style="text-align: center;">欢迎讨论与提问</br>读者间携手共进</p>
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</div>
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<img src="index.assets/comment.gif" class="cover-image" style="flex-shrink: 0; width: auto; max-width: 50%; border-radius: 0.5rem;">
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</div>
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<div class="admonition quote">
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<p align="center">"追风赶月莫停留"</p>
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<p align="center">“平芜尽处是春山”</p>
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</div>
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---
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<h3 align="center"> 序 </h3>
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两年前，我在力扣上分享了“剑指 Offer”系列题解，受到了许多同学的喜爱和支持。在与读者交流期间，我最常收到的一个问题是“如何入门算法”。逐渐地，我对这个问题产生了浓厚的兴趣。
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两眼一抹黑地刷题似乎是最受欢迎的方法，简单直接且有效。然而刷题就如同玩“扫雷”游戏，自学能力强的同学能够顺利将地雷逐个排掉，而基础不足的同学很可能被炸的满头是包，并在挫折中步步退缩。通读教材也是一种常见做法，但对于面向求职的同学来说，毕业季、投递简历、准备笔试面试已经消耗了大部分精力，啃厚重的书往往变成了一项艰巨的挑战。
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如果你也面临类似的困扰，那么很幸运这本书找到了你。本书是我对这个问题给出的答案，即使不是最优解，也至少是一次积极的尝试。本书虽然不足以让你直接拿到 Offer ，但会引导你探索数据结构与算法的“知识地图”，带你了解不同“地雷”的形状、大小和分布位置，让你掌握各种“排雷方法”。有了这些本领，相信你可以更加自如地刷题和阅读文献，逐步构建起完整的知识体系。
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我深深赞同费曼教授所言：“Knowledge isn't free. You have to pay attention.”从这个意义上看，这本书并非完全“免费”。为了不辜负你为本书所付出的宝贵“注意力”，我会尽我所能，投入最大的“注意力”来完成这本书的创作。
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<h3 align="left"> 作者 </h3>
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靳宇栋 ([Krahets](https://leetcode.cn/u/jyd/))，大厂高级算法工程师，上海交通大学硕士。力扣（LeetCode）全网阅读量最高博主，发表的[《图解算法数据结构》](https://leetcode.cn/leetbook/detail/illustration-of-algorithm/)已被订阅 30 万本。
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---
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<h3 align="center"> 贡献 </h3>
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本书在开源社区众多贡献者的共同努力下不断完善。感谢每一位投入时间与精力的撰稿人，他们是（按照 GitHub 自动生成的顺序排列）：
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<p align="center">
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<a href="https://github.com/krahets/hello-algo/graphs/contributors">
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<img width="550" src="https://contrib.rocks/image?repo=krahets/hello-algo">
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</a>
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</p>
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本书的代码审阅工作由 codingonion、Gonglja、gvenusleo、hpstory、justin‐tse、krahets、night-cruise、nuomi1 和 Reanon 完成（按照首字母顺序排列）。感谢他们付出的时间与精力，正是他们确保了各语言代码的规范与统一。
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<div class="center-table">
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<table style="border: none;">
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<tbody>
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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</tbody>
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</table>
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</div>
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