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第 0 章 &nbsp; 前言
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第 0 章 &nbsp; 前言
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0.1 &nbsp; 关于本书
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0.2 &nbsp; 如何使用本书
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0.3 &nbsp; 小结
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第 1 章 &nbsp; 初识算法
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第 1 章 &nbsp; 初识算法
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1.1 &nbsp; 算法无处不在
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第 2 章 &nbsp; 复杂度分析
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第 2 章 &nbsp; 复杂度分析
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2.1 &nbsp; 算法效率评估
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2.2 &nbsp; 迭代与递归
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2.3 &nbsp; 时间复杂度
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2.4 &nbsp; 空间复杂度
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第 3 章 &nbsp; 数据结构
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3.1 &nbsp; 数据结构分类
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3.2 &nbsp; 基本数据类型
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3.3 &nbsp; 数字编码 *
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3.4 &nbsp; 字符编码 *
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第 4 章 &nbsp; 数组与链表
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4.1 &nbsp; 数组
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4.2 &nbsp; 链表
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4.3 &nbsp; 列表
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4.4 &nbsp; 内存与缓存 *
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4.5 &nbsp; 小结
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第 5 章 &nbsp; 栈与队列
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5.1 &nbsp; 栈
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5.2 &nbsp; 队列
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5.3 &nbsp; 双向队列
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第 6 章 &nbsp; 哈希表
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第 6 章 &nbsp; 哈希表
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6.1 &nbsp; 哈希表
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6.2 &nbsp; 哈希冲突
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6.3 &nbsp; 哈希算法
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6.4 &nbsp; 小结
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第 7 章 &nbsp; 树
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第 7 章 &nbsp; 树
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7.1 &nbsp; 二叉树
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7.2 &nbsp; 二叉树遍历
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7.3 &nbsp; 二叉树数组表示
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7.4 &nbsp; 二叉搜索树
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7.5 &nbsp; AVL 树 *
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7.6 &nbsp; 小结
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第 8 章 &nbsp; 堆
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第 8 章 &nbsp; 堆
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8.1 &nbsp; 堆
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8.2 &nbsp; 建堆操作
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8.3 &nbsp; Top-k 问题
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第 9 章 &nbsp; 图
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第 9 章 &nbsp; 图
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9.1 &nbsp; 图
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9.2 &nbsp; 图基础操作
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9.3 &nbsp; 图的遍历
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第 10 章 &nbsp; 搜索
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第 10 章 &nbsp; 搜索
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10.1 &nbsp; 二分查找
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10.2 &nbsp; 二分查找插入点
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10.3 &nbsp; 二分查找边界
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10.4 &nbsp; 哈希优化策略
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10.5 &nbsp; 重识搜索算法
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10.6 &nbsp; 小结
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第 11 章 &nbsp; 排序
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11.1 &nbsp; 排序算法
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11.2 &nbsp; 选择排序
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11.3 &nbsp; 冒泡排序
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11.4 &nbsp; 插入排序
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11.5 &nbsp; 快速排序
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11.6 &nbsp; 归并排序
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11.7 &nbsp; 堆排序
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11.8 &nbsp; 桶排序
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11.9 &nbsp; 计数排序
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11.10 &nbsp; 基数排序
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11.11 &nbsp; 小结
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第 12 章 &nbsp; 分治
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12.1 &nbsp; 分治算法
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12.2 &nbsp; 分治搜索策略
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12.3 &nbsp; 构建树问题
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12.4 &nbsp; 汉诺塔问题
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12.5 &nbsp; 小结
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第 13 章 &nbsp; 回溯
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13.1 &nbsp; 回溯算法
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13.2 &nbsp; 全排列问题
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13.3 &nbsp; 子集和问题
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13.4 &nbsp; N 皇后问题
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13.5 &nbsp; 小结
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第 14 章 &nbsp; 动态规划
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14.1 &nbsp; 初探动态规划
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14.2 &nbsp; DP 问题特性
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14.3 &nbsp; DP 解题思路
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14.4 &nbsp; 0-1 背包问题
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14.5 &nbsp; 完全背包问题
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14.6 &nbsp; 编辑距离问题
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14.7 &nbsp; 小结
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第 15 章 &nbsp; 贪心
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15.1 &nbsp; 贪心算法
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15.2 &nbsp; 分数背包问题
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15.3 &nbsp; 最大容量问题
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15.4 &nbsp; 最大切分乘积问题
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15.5 &nbsp; 小结
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第 16 章 &nbsp; 附录
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16.1 &nbsp; 编程环境安装
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16.2 &nbsp; 一起参与创作
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<h2 align="center" style="margin-top: 25px;">《 Hello 算法 》</h2>
<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><img src="index.assets/hello_algo_hero.jpg" class="cover-image" style="width: 100%; margin-top: 27px;"></p>
<div style="display: flex;">
<div class="admonition quote" style="flex: 1; margin-right: 0.4rem;">
<p class="admonition-title">Quote</p>
<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>
<p><strong>—— 邓俊辉，清华大学计算机系教授</strong></p>
</div>
<div class="admonition quote" style="flex: 1; margin-left: 0.4rem;">
<p class="admonition-title">Quote</p>
<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>
<p><strong>—— 李沐，亚马逊资深首席科学家</strong></p>
</div>
</div>
<hr />
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<div style="flex: 1; margin: 0 2rem; display: flex; flex-direction: column; align-items: center;">
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<h3>动画图解</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;">内容清晰易懂</br>学习曲线平滑</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>
<p align="center">“一图胜千言”</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>一键运行</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>
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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>
</div>
</div>
<div class="admonition quote">
<p align="center">"Talk is cheap. Show me the code."</p>
<p align="center">“少吹牛，看代码”</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>互助学习</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>
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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>
</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">"追风赶月莫停留"</p>
<p align="center">“平芜尽处是春山”</p>
</div>
<hr />
<h3 align="center"> 序 </h3>
<p>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。</p>
<p>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得满头是包，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。</p>
<p>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。</p>
<p>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。</p>
<h3 align="left"> 作者 </h3>
<p>靳宇栋 (<a href="https://leetcode.cn/u/jyd/">Krahets</a>)，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<a href="https://leetcode.cn/leetbook/detail/illustration-of-algorithm/">《图解算法数据结构》</a>已被订阅 30 万本。</p>
<hr />
<h3 align="center"> 贡献 </h3>
<p>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）：</p>
<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>
<p>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。</p>
<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>
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