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第 0 章 前言
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第 0 章 前言
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0.1 关于本书
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0.2 如何使用本书
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0.2 如何使用本书
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目录
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0.2.1 行文风格约定
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0.2.2 在动画图解中高效学习
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0.2.3 在代码实践中加深理解
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0.2.4 在提问讨论中共同成长
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0.2.5 算法学习路线
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0.3 小结
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< a href = "../../chapter_introduction/" class = "md-nav__link " >
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第 1 章 初识算法
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第 1 章 初识算法
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1.1 算法无处不在
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1.2 算法是什么
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1.3 小结
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< a href = "../../chapter_computational_complexity/" class = "md-nav__link " >
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第 2 章 复杂度分析
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第 2 章 复杂度分析
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2.1 算法效率评估
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2.2 迭代与递归
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2.3 时间复杂度
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2.4 空间复杂度
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2.5 小结
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第 3 章 数据结构
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第 3 章 数据结构
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3.1 数据结构分类
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3.2 基本数据类型
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3.3 数字编码 *
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3.4 字符编码 *
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3.5 小结
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< a href = "../../chapter_array_and_linkedlist/" class = "md-nav__link " >
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第 4 章 数组与链表
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第 4 章 数组与链表
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4.1 数组
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4.2 链表
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4.3 列表
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4.4 内存与缓存 *
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4.5 小结
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第 5 章 栈与队列
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第 5 章 栈与队列
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5.1 栈
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5.2 队列
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5.3 双向队列
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5.4 小结
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第 6 章 哈希表
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第 6 章 哈希表
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6.1 哈希表
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6.2 哈希冲突
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6.3 哈希算法
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6.4 小结
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第 7 章 树
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第 7 章 树
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7.1 二叉树
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7.2 二叉树遍历
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7.3 二叉树数组表示
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7.4 二叉搜索树
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7.5 AVL 树 *
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7.6 小结
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< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z" / > < / svg >
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第 8 章 堆
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第 8 章 堆
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8.1 堆
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8.2 建堆操作
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8.3 Top-K 问题
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8.4 小结
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< a href = "../../chapter_graph/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z" / > < / svg >
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第 9 章 图
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第 9 章 图
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9.1 图
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9.2 图基础操作
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9.3 图的遍历
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9.4 小结
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< a href = "../../chapter_searching/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z" / > < / svg >
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第 10 章 搜索
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第 10 章 搜索
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10.1 二分查找
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10.2 二分查找插入点
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10.3 二分查找边界
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10.4 哈希优化策略
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10.5 重识搜索算法
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10.6 小结
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< a href = "../../chapter_sorting/" class = "md-nav__link " >
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第 11 章 排序
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第 11 章 排序
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11.1 排序算法
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11.2 选择排序
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11.3 冒泡排序
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11.4 插入排序
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11.5 快速排序
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11.6 归并排序
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11.7 堆排序
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11.8 桶排序
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11.9 计数排序
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11.10 基数排序
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11.11 小结
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< a href = "../../chapter_divide_and_conquer/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z" / > < / svg >
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第 12 章 分治
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第 12 章 分治
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12.1 分治算法
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12.2 分治搜索策略
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12.3 构建树问题
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12.4 汉诺塔问题
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12.5 小结
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< a href = "../../chapter_backtracking/" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z" / > < / svg >
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第 13 章 回溯
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第 13 章 回溯
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13.1 回溯算法
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13.2 全排列问题
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13.3 子集和问题
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13.4 N 皇后问题
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13.5 小结
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< a href = "../../chapter_dynamic_programming/" class = "md-nav__link " >
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第 14 章 动态规划
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第 14 章 动态规划
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14.1 初探动态规划
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14.2 DP 问题特性
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14.3 DP 解题思路
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14.4 0-1 背包问题
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14.5 完全背包问题
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14.6 编辑距离问题
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14.7 小结
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第 15 章 贪心
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15.1 贪心算法
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15.4 最大切分乘积问题
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第 16 章 附录
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0.2.1 行文风格约定
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0.2.3 在代码实践中加深理解
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0.2.4 在提问讨论中共同成长
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0.2.5 算法学习路线
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< li > 专有名词和有特指含义的词句会使用 < code > “双引号”< / code > 标注，以避免歧义。< / li >
< li > 重要专有名词及其英文翻译会用 < code > 「 」< / code > 括号标注，例如 < code > 「数组 array」< / code > 。建议记住它们，以便阅读文献。< / li >
< li > < strong > 加粗的文字< / strong > 表示重点内容或总结性语句，这类文字值得特别关注。< / li >
< li > 当涉及到编程语言之间不一致的名词时，本书均以 Python 为准，例如使用 < span class = "arithmatex" > \(\text{None}\)< / span > 来表示“空”。< / li >
< li > 本书部分放弃了编程语言的注释规范，以换取更加紧凑的内容排版。注释主要分为三种类型：标题注释、内容注释、多行注释。< / li >
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< div class = "tabbed-set tabbed-alternate" data-tabs = "1:12" > < input checked = "checked" id = "__tabbed_1_1" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_2" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_3" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_4" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_5" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_6" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_7" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_8" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_9" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_10" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_11" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_12" name = "__tabbed_1" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_1_1" > Python< / label > < label for = "__tabbed_1_2" > C++< / label > < label for = "__tabbed_1_3" > Java< / label > < label for = "__tabbed_1_4" > C#< / label > < label for = "__tabbed_1_5" > Go< / label > < label for = "__tabbed_1_6" > Swift< / label > < label for = "__tabbed_1_7" > JS< / label > < label for = "__tabbed_1_8" > TS< / label > < label for = "__tabbed_1_9" > Dart< / label > < label for = "__tabbed_1_10" > Rust< / label > < label for = "__tabbed_1_11" > C< / label > < label for = "__tabbed_1_12" > Zig< / label > < / div >
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< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-0-1" name = "__codelineno-0-1" href = "#__codelineno-0-1" > < / a > < span class = "sd" > " " " 标题注释，用于标注函数、类、测试样例等" " " < / span >
< a id = "__codelineno-0-2" name = "__codelineno-0-2" href = "#__codelineno-0-2" > < / a >
< a id = "__codelineno-0-3" name = "__codelineno-0-3" href = "#__codelineno-0-3" > < / a > < span class = "c1" > # 内容注释，用于详解代码< / span >
< a id = "__codelineno-0-4" name = "__codelineno-0-4" href = "#__codelineno-0-4" > < / a >
< a id = "__codelineno-0-5" name = "__codelineno-0-5" href = "#__codelineno-0-5" > < / a > < span class = "sd" > " " " < / span >
< a id = "__codelineno-0-6" name = "__codelineno-0-6" href = "#__codelineno-0-6" > < / a > < span class = "sd" > 多行< / span >
< a id = "__codelineno-0-7" name = "__codelineno-0-7" href = "#__codelineno-0-7" > < / a > < span class = "sd" > 注释< / span >
< a id = "__codelineno-0-8" name = "__codelineno-0-8" href = "#__codelineno-0-8" > < / a > < span class = "sd" > " " " < / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-1-1" name = "__codelineno-1-1" href = "#__codelineno-1-1" > < / a > < span class = "cm" > /* 标题注释，用于标注函数、类、测试样例等 */< / span >
< a id = "__codelineno-1-2" name = "__codelineno-1-2" href = "#__codelineno-1-2" > < / a >
< a id = "__codelineno-1-3" name = "__codelineno-1-3" href = "#__codelineno-1-3" > < / a > < span class = "c1" > // 内容注释，用于详解代码< / span >
< a id = "__codelineno-1-4" name = "__codelineno-1-4" href = "#__codelineno-1-4" > < / a >
< a id = "__codelineno-1-5" name = "__codelineno-1-5" href = "#__codelineno-1-5" > < / a > < span class = "cm" > /**< / span >
< a id = "__codelineno-1-6" name = "__codelineno-1-6" href = "#__codelineno-1-6" > < / a > < span class = "cm" > * 多行< / span >
< a id = "__codelineno-1-7" name = "__codelineno-1-7" href = "#__codelineno-1-7" > < / a > < span class = "cm" > * 注释< / span >
< a id = "__codelineno-1-8" name = "__codelineno-1-8" href = "#__codelineno-1-8" > < / a > < span class = "cm" > */< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-2-1" name = "__codelineno-2-1" href = "#__codelineno-2-1" > < / a > < span class = "cm" > /* 标题注释，用于标注函数、类、测试样例等 */< / span >
< a id = "__codelineno-2-2" name = "__codelineno-2-2" href = "#__codelineno-2-2" > < / a >
< a id = "__codelineno-2-3" name = "__codelineno-2-3" href = "#__codelineno-2-3" > < / a > < span class = "c1" > // 内容注释，用于详解代码< / span >
< a id = "__codelineno-2-4" name = "__codelineno-2-4" href = "#__codelineno-2-4" > < / a >
< a id = "__codelineno-2-5" name = "__codelineno-2-5" href = "#__codelineno-2-5" > < / a > < span class = "cm" > /**< / span >
< a id = "__codelineno-2-6" name = "__codelineno-2-6" href = "#__codelineno-2-6" > < / a > < span class = "cm" > * 多行< / span >
< a id = "__codelineno-2-7" name = "__codelineno-2-7" href = "#__codelineno-2-7" > < / a > < span class = "cm" > * 注释< / span >
< a id = "__codelineno-2-8" name = "__codelineno-2-8" href = "#__codelineno-2-8" > < / a > < span class = "cm" > */< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-3-1" name = "__codelineno-3-1" href = "#__codelineno-3-1" > < / a > < span class = "cm" > /* 标题注释，用于标注函数、类、测试样例等 */< / span >
< a id = "__codelineno-3-2" name = "__codelineno-3-2" href = "#__codelineno-3-2" > < / a >
< a id = "__codelineno-3-3" name = "__codelineno-3-3" href = "#__codelineno-3-3" > < / a > < span class = "c1" > // 内容注释，用于详解代码< / span >
< a id = "__codelineno-3-4" name = "__codelineno-3-4" href = "#__codelineno-3-4" > < / a >
< a id = "__codelineno-3-5" name = "__codelineno-3-5" href = "#__codelineno-3-5" > < / a > < span class = "cm" > /**< / span >
< a id = "__codelineno-3-6" name = "__codelineno-3-6" href = "#__codelineno-3-6" > < / a > < span class = "cm" > * 多行< / span >
< a id = "__codelineno-3-7" name = "__codelineno-3-7" href = "#__codelineno-3-7" > < / a > < span class = "cm" > * 注释< / span >
< a id = "__codelineno-3-8" name = "__codelineno-3-8" href = "#__codelineno-3-8" > < / a > < span class = "cm" > */< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-4-1" name = "__codelineno-4-1" href = "#__codelineno-4-1" > < / a > < span class = "cm" > /* 标题注释，用于标注函数、类、测试样例等 */< / span >
< a id = "__codelineno-4-2" name = "__codelineno-4-2" href = "#__codelineno-4-2" > < / a >
< a id = "__codelineno-4-3" name = "__codelineno-4-3" href = "#__codelineno-4-3" > < / a > < span class = "c1" > // 内容注释，用于详解代码< / span >
< a id = "__codelineno-4-4" name = "__codelineno-4-4" href = "#__codelineno-4-4" > < / a >
< a id = "__codelineno-4-5" name = "__codelineno-4-5" href = "#__codelineno-4-5" > < / a > < span class = "cm" > /**< / span >
< a id = "__codelineno-4-6" name = "__codelineno-4-6" href = "#__codelineno-4-6" > < / a > < span class = "cm" > * 多行< / span >
< a id = "__codelineno-4-7" name = "__codelineno-4-7" href = "#__codelineno-4-7" > < / a > < span class = "cm" > * 注释< / span >
< a id = "__codelineno-4-8" name = "__codelineno-4-8" href = "#__codelineno-4-8" > < / a > < span class = "cm" > */< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-5-1" name = "__codelineno-5-1" href = "#__codelineno-5-1" > < / a > < span class = "cm" > /* 标题注释，用于标注函数、类、测试样例等 */< / span >
< a id = "__codelineno-5-2" name = "__codelineno-5-2" href = "#__codelineno-5-2" > < / a >
< a id = "__codelineno-5-3" name = "__codelineno-5-3" href = "#__codelineno-5-3" > < / a > < span class = "c1" > // 内容注释，用于详解代码< / span >
< a id = "__codelineno-5-4" name = "__codelineno-5-4" href = "#__codelineno-5-4" > < / a >
< a id = "__codelineno-5-5" name = "__codelineno-5-5" href = "#__codelineno-5-5" > < / a > < span class = "cm" > /**< / span >
< a id = "__codelineno-5-6" name = "__codelineno-5-6" href = "#__codelineno-5-6" > < / a > < span class = "cm" > * 多行< / span >
< a id = "__codelineno-5-7" name = "__codelineno-5-7" href = "#__codelineno-5-7" > < / a > < span class = "cm" > * 注释< / span >
< a id = "__codelineno-5-8" name = "__codelineno-5-8" href = "#__codelineno-5-8" > < / a > < span class = "cm" > */< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-6-1" name = "__codelineno-6-1" href = "#__codelineno-6-1" > < / a > < span class = "cm" > /* 标题注释，用于标注函数、类、测试样例等 */< / span >
< a id = "__codelineno-6-2" name = "__codelineno-6-2" href = "#__codelineno-6-2" > < / a >
< a id = "__codelineno-6-3" name = "__codelineno-6-3" href = "#__codelineno-6-3" > < / a > < span class = "c1" > // 内容注释，用于详解代码< / span >
< a id = "__codelineno-6-4" name = "__codelineno-6-4" href = "#__codelineno-6-4" > < / a >
< a id = "__codelineno-6-5" name = "__codelineno-6-5" href = "#__codelineno-6-5" > < / a > < span class = "cm" > /**< / span >
< a id = "__codelineno-6-6" name = "__codelineno-6-6" href = "#__codelineno-6-6" > < / a > < span class = "cm" > * 多行< / span >
< a id = "__codelineno-6-7" name = "__codelineno-6-7" href = "#__codelineno-6-7" > < / a > < span class = "cm" > * 注释< / span >
< a id = "__codelineno-6-8" name = "__codelineno-6-8" href = "#__codelineno-6-8" > < / a > < span class = "cm" > */< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-7-1" name = "__codelineno-7-1" href = "#__codelineno-7-1" > < / a > < span class = "cm" > /* 标题注释，用于标注函数、类、测试样例等 */< / span >
< a id = "__codelineno-7-2" name = "__codelineno-7-2" href = "#__codelineno-7-2" > < / a >
< a id = "__codelineno-7-3" name = "__codelineno-7-3" href = "#__codelineno-7-3" > < / a > < span class = "c1" > // 内容注释，用于详解代码< / span >
< a id = "__codelineno-7-4" name = "__codelineno-7-4" href = "#__codelineno-7-4" > < / a >
< a id = "__codelineno-7-5" name = "__codelineno-7-5" href = "#__codelineno-7-5" > < / a > < span class = "cm" > /**< / span >
< a id = "__codelineno-7-6" name = "__codelineno-7-6" href = "#__codelineno-7-6" > < / a > < span class = "cm" > * 多行< / span >
< a id = "__codelineno-7-7" name = "__codelineno-7-7" href = "#__codelineno-7-7" > < / a > < span class = "cm" > * 注释< / span >
< a id = "__codelineno-7-8" name = "__codelineno-7-8" href = "#__codelineno-7-8" > < / a > < span class = "cm" > */< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-8-1" name = "__codelineno-8-1" href = "#__codelineno-8-1" > < / a > < span class = "cm" > /* 标题注释，用于标注函数、类、测试样例等 */< / span >
< a id = "__codelineno-8-2" name = "__codelineno-8-2" href = "#__codelineno-8-2" > < / a >
< a id = "__codelineno-8-3" name = "__codelineno-8-3" href = "#__codelineno-8-3" > < / a > < span class = "c1" > // 内容注释，用于详解代码< / span >
< a id = "__codelineno-8-4" name = "__codelineno-8-4" href = "#__codelineno-8-4" > < / a >
< a id = "__codelineno-8-5" name = "__codelineno-8-5" href = "#__codelineno-8-5" > < / a > < span class = "cm" > /**< / span >
< a id = "__codelineno-8-6" name = "__codelineno-8-6" href = "#__codelineno-8-6" > < / a > < span class = "cm" > * 多行< / span >
< a id = "__codelineno-8-7" name = "__codelineno-8-7" href = "#__codelineno-8-7" > < / a > < span class = "cm" > * 注释< / span >
< a id = "__codelineno-8-8" name = "__codelineno-8-8" href = "#__codelineno-8-8" > < / a > < span class = "cm" > */< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-9-1" name = "__codelineno-9-1" href = "#__codelineno-9-1" > < / a > < span class = "cm" > /* 标题注释，用于标注函数、类、测试样例等 */< / span >
< a id = "__codelineno-9-2" name = "__codelineno-9-2" href = "#__codelineno-9-2" > < / a >
< a id = "__codelineno-9-3" name = "__codelineno-9-3" href = "#__codelineno-9-3" > < / a > < span class = "c1" > // 内容注释，用于详解代码< / span >
< a id = "__codelineno-9-4" name = "__codelineno-9-4" href = "#__codelineno-9-4" > < / a >
< a id = "__codelineno-9-5" name = "__codelineno-9-5" href = "#__codelineno-9-5" > < / a > < span class = "sd" > /**< / span >
< a id = "__codelineno-9-6" name = "__codelineno-9-6" href = "#__codelineno-9-6" > < / a > < span class = "sd" > * 多行< / span >
< a id = "__codelineno-9-7" name = "__codelineno-9-7" href = "#__codelineno-9-7" > < / a > < span class = "sd" > * 注释< / span >
< a id = "__codelineno-9-8" name = "__codelineno-9-8" href = "#__codelineno-9-8" > < / a > < span class = "sd" > */< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-10-1" name = "__codelineno-10-1" href = "#__codelineno-10-1" > < / a > < span class = "cm" > /* 标题注释，用于标注函数、类、测试样例等 */< / span >
< a id = "__codelineno-10-2" name = "__codelineno-10-2" href = "#__codelineno-10-2" > < / a >
< a id = "__codelineno-10-3" name = "__codelineno-10-3" href = "#__codelineno-10-3" > < / a > < span class = "c1" > // 内容注释，用于详解代码< / span >
< a id = "__codelineno-10-4" name = "__codelineno-10-4" href = "#__codelineno-10-4" > < / a >
< a id = "__codelineno-10-5" name = "__codelineno-10-5" href = "#__codelineno-10-5" > < / a > < span class = "cm" > /**< / span >
< a id = "__codelineno-10-6" name = "__codelineno-10-6" href = "#__codelineno-10-6" > < / a > < span class = "cm" > * 多行< / span >
< a id = "__codelineno-10-7" name = "__codelineno-10-7" href = "#__codelineno-10-7" > < / a > < span class = "cm" > * 注释< / span >
< a id = "__codelineno-10-8" name = "__codelineno-10-8" href = "#__codelineno-10-8" > < / a > < span class = "cm" > */< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-11-1" name = "__codelineno-11-1" href = "#__codelineno-11-1" > < / a > < span class = "c1" > // 标题注释，用于标注函数、类、测试样例等< / span >
< a id = "__codelineno-11-2" name = "__codelineno-11-2" href = "#__codelineno-11-2" > < / a >
< a id = "__codelineno-11-3" name = "__codelineno-11-3" href = "#__codelineno-11-3" > < / a > < span class = "c1" > // 内容注释，用于详解代码< / span >
< a id = "__codelineno-11-4" name = "__codelineno-11-4" href = "#__codelineno-11-4" > < / a >
< a id = "__codelineno-11-5" name = "__codelineno-11-5" href = "#__codelineno-11-5" > < / a > < span class = "c1" > // 多行< / span >
< a id = "__codelineno-11-6" name = "__codelineno-11-6" href = "#__codelineno-11-6" > < / a > < span class = "c1" > // 注释< / span >
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< h2 id = "022" > 0.2.2 在动画图解中高效学习< a class = "headerlink" href = "#022" title = "Permanent link" > ¶ < / a > < / h2 >
< p > 相较于文字，视频和图片具有更高的信息密度和结构化程度，更易于理解。在本书中，< strong > 重点和难点知识将主要通过动画和图解形式展示< / strong > ，而文字则作为动画和图片的解释与补充。< / p >
< p > 如果你在阅读本书时，发现某段内容提供了图 0-2 所示的动画或图解，< strong > 请以图为主、以文字为辅< / strong > ，综合两者来理解内容。< / p >
< p > < a class = "glightbox" href = "../../index.assets/animation.gif" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "动画图解示例" class = "animation-figure" src = "../../index.assets/animation.gif" / > < / a > < / p >
< p align = "center" > 图 0-2 动画图解示例 < / p >
< h2 id = "023" > 0.2.3 在代码实践中加深理解< a class = "headerlink" href = "#023" title = "Permanent link" > ¶ < / a > < / h2 >
< p > 本书的配套代码被托管在 < a href = "https://github.com/krahets/hello-algo" > GitHub 仓库< / a > 。如图 0-3 所示，< strong > 源代码附有测试样例，可一键运行< / strong > 。< / p >
< p > 如果时间允许，< strong > 建议你参照代码自行敲一遍< / strong > 。如果学习时间有限，请至少通读并运行所有代码。< / p >
< p > 与阅读代码相比，编写代码的过程往往能带来更多收获。< strong > 动手学，才是真的学< / strong > 。< / p >
< p > < a class = "glightbox" href = "../../index.assets/running_code.gif" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "运行代码示例" class = "animation-figure" src = "../../index.assets/running_code.gif" / > < / a > < / p >
< p align = "center" > 图 0-3 运行代码示例 < / p >
< p > 运行代码的前置工作主要分为三步。< / p >
< p > < strong > 第一步：安装本地编程环境< / strong > 。请参照< a href = "https://www.hello-algo.com/chapter_appendix/installation/" > 附录教程< / a > 进行安装，如果已安装则可跳过此步骤。< / p >
< p > < strong > 第二步：克隆或下载代码仓< / strong > 。如果已经安装 < a href = "https://git-scm.com/downloads" > Git< / a > ，可以通过以下命令克隆本仓库。< / p >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-12-1" name = "__codelineno-12-1" href = "#__codelineno-12-1" > < / a > git< span class = "w" > < / span > clone< span class = "w" > < / span > https://github.com/krahets/hello-algo.git
< / code > < / pre > < / div >
< p > 当然，你也可以在图 0-4 所示的位置， ， < / p >
< p > < a class = "glightbox" href = "../suggestions.assets/download_code.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "克隆仓库与下载代码" class = "animation-figure" src = "../suggestions.assets/download_code.png" / > < / a > < / p >
< p align = "center" > 图 0-4 克隆仓库与下载代码 < / p >
< p > < strong > 第三步：运行源代码< / strong > 。如图 0-5 所示，对于顶部标有文件名称的代码块，我们可以在仓库的 < code > codes< / code > 文件夹内找到对应的源代码文件。源代码文件可一键运行，将帮助你节省不必要的调试时间，让你能够专注于学习内容。< / p >
< p > < a class = "glightbox" href = "../suggestions.assets/code_md_to_repo.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "代码块与对应的源代码文件" class = "animation-figure" src = "../suggestions.assets/code_md_to_repo.png" / > < / a > < / p >
< p align = "center" > 图 0-5 代码块与对应的源代码文件 < / p >
< h2 id = "024" > 0.2.4 在提问讨论中共同成长< a class = "headerlink" href = "#024" title = "Permanent link" > ¶ < / a > < / h2 >
< p > 在阅读本书时，请不要轻易跳过那些没学明白的知识点。< strong > 欢迎在评论区提出你的问题< / strong > ，我和小伙伴们将竭诚为你解答，一般情况下可在两天内回复。< / p >
< p > 如图 0-6 所示，每篇文章的底部都配有评论区。希望你能多关注评论区的内容。一方面，你可以了解大家遇到的问题，从而查漏补缺，激发更深入的思考。另一方面，期待你能慷慨地回答其他小伙伴的问题，分享您的见解，帮助他人进步。< / p >
< p > < a class = "glightbox" href = "../../index.assets/comment.gif" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "评论区示例" class = "animation-figure" src = "../../index.assets/comment.gif" / > < / a > < / p >
< p align = "center" > 图 0-6 评论区示例 < / p >
< h2 id = "025" > 0.2.5 算法学习路线< a class = "headerlink" href = "#025" title = "Permanent link" > ¶ < / a > < / h2 >
< p > 从总体上看，我们可以将学习数据结构与算法的过程划分为三个阶段。< / p >
< ol >
< li > < strong > 算法入门< / strong > 。我们需要熟悉各种数据结构的特点和用法，学习不同算法的原理、流程、用途和效率等方面内容。< / li >
< li > < strong > 刷算法题< / strong > 。建议从热门题目开刷，如< a href = "https://leetcode.cn/studyplan/coding-interviews/" > 剑指 Offer< / a > 和< a href = "https://leetcode.cn/studyplan/top-100-liked/" > LeetCode Hot 100< / a > ，先积累至少 100 道题目，熟悉主流的算法问题。初次刷题时，“知识遗忘”可能是一个挑战，但请放心，这是很正常的。我们可以按照“艾宾浩斯遗忘曲线”来复习题目，通常在进行 3-5 轮的重复后，就能将其牢记在心。< / li >
< li > < strong > 搭建知识体系< / strong > 。在学习方面，我们可以阅读算法专栏文章、解题框架和算法教材，以不断丰富知识体系。在刷题方面，可以尝试采用进阶刷题策略，如按专题分类、一题多解、一解多题等，相关的刷题心得可以在各个社区找到。< / li >
< / ol >
< p > 如图 0-7 所示，本书内容主要涵盖“第一阶段”，旨在帮助你更高效地展开第二和第三阶段的学习。< / p >
< p > < a class = "glightbox" href = "../suggestions.assets/learning_route.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "算法学习路线" class = "animation-figure" src = "../suggestions.assets/learning_route.png" / > < / a > < / p >
< p align = "center" > 图 0-7 算法学习路线 < / p >
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