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3.1. 数据结构分类
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0. 写在前面
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0.1. 关于本书
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1. 引言
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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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2. 复杂度分析
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2.1. 算法效率评估
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2.2. 时间复杂度
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2.3. 空间复杂度
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2.4. 小结
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3. 数据结构简介
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3.1. 数据结构分类
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3.1. 数据结构分类
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目录
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3.1.1. 逻辑结构：线性与非线性
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3.1.2. 物理结构：连续与离散
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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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4. 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. 小结
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5. 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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6. 散列表
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6.1. 哈希表（ ）
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6.2. 哈希冲突（ ）
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6.4. 小结
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7. 树
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7.1. 二叉树
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7.5. AVL 树 *
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7.6. 小结
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8. 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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9. 图
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9.2. 图基础操作
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9.4. 小结
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11.7. 堆排序
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11.10. 基数排序
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11.11. 小结
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12.4. N 皇后问题
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13.1. 编程环境安装
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13.2. 一起参与创作
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3.1.1. 逻辑结构：线性与非线性
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3.1.2. 物理结构：连续与离散
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< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M10 20H6V4h7v5h5v3.1l2-2V8l-6-6H6c-1.1 0-2 .9-2 2v16c0 1.1.9 2 2 2h4v-2m10.2-7c.1 0 .3.1.4.2l1.3 1.3c.2.2.2.6 0 .8l-1 1-2.1-2.1 1-1c.1-.1.2-.2.4-.2m0 3.9L14.1 23H12v-2.1l6.1-6.1 2.1 2.1Z" / > < / svg >
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< h1 id = "31" > 3.1. 数据结构分类< a class = "headerlink" href = "#31" title = "Permanent link" > ¶ < / a > < / h1 >
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< p > 数据结构可以从逻辑结构和物理结构两个维度进行分类。< / p >
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< h2 id = "311" > 3.1.1. 逻辑结构：线性与非线性< a class = "headerlink" href = "#311" title = "Permanent link" > ¶ < / a > < / h2 >
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< p > < strong > 「逻辑结构」揭示了数据元素之间的逻辑关系< / strong > 。在数组和链表中，数据按照顺序依次排列，体现了数据之间的线性关系；而在树中，数据从顶部向下按层次排列，表现出祖先与后代之间的派生关系；图则由节点和边构成，反映了复杂的网络关系。< / p >
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< p > 逻辑结构通常分为「线性」和「非线性」两类。线性结构比较直观，指数据在逻辑关系上呈线性排列；非线性结构则相反，呈非线性排列，例如网状或树状结构。< / p >
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< ul >
< li > < strong > 线性数据结构< / strong > ：数组、链表、栈、队列、哈希表；< / li >
< li > < strong > 非线性数据结构< / strong > ：树、图、堆、哈希表；< / li >
< / ul >
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< p > < img alt = "线性与非线性数据结构" src = "../classification_of_data_structure.assets/classification_logic_structure.png" / > < / p >
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< p align = "center" > Fig. 线性与非线性数据结构 < / p >
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< h2 id = "312" > 3.1.2. 物理结构：连续与离散< a class = "headerlink" href = "#312" title = "Permanent link" > ¶ < / a > < / h2 >
< p > 在计算机中，内存和硬盘是两种主要的存储硬件设备。「硬盘」主要用于长期存储数据，容量较大（通常可达到 TB 级别）、速度较慢。「内存」用于运行程序时暂存数据，速度较快，但容量较小（通常为 GB 级别）。< / p >
< p > < strong > 在算法运行过程中，相关数据都存储在内存中< / strong > 。下图展示了一个计算机内存条，其中每个黑色方块都包含一块内存空间。我们可以将内存想象成一个巨大的 Excel 表格，其中每个单元格都可以存储 1 byte 的数据，在算法运行时，所有数据都被存储在这些单元格中。< / p >
< p > < strong > 系统通过「内存地址 Memory Location」来访问目标内存位置的数据< / strong > 。计算机根据特定规则为表格中的每个单元格分配编号，确保每个内存空间都有唯一的内存地址。有了这些地址，程序便可以访问内存中的数据。< / p >
< p > < img alt = "内存条、内存空间、内存地址" src = "../classification_of_data_structure.assets/computer_memory_location.png" / > < / p >
< p align = "center" > Fig. 内存条、内存空间、内存地址 < / p >
< p > 内存是所有程序的共享资源，当内存被某个程序占用时，其他程序无法同时使用。< strong > 因此，在数据结构与算法的设计中，内存资源是一个重要的考虑因素< / strong > 。例如，算法所占用的内存峰值不应超过系统剩余空闲内存；如果运行的程序很多并且缺少大量连续的内存空间，那么所选用的数据结构必须能够存储在离散的内存空间内。< / p >
< p > < strong > 「物理结构」反映了数据在计算机内存中的存储方式< / strong > ，可分为数组的连续空间存储和链表的离散空间存储。物理结构从底层决定了数据的访问、更新、增删等操作方法，同时在时间效率和空间效率方面呈现出互补的特点。< / p >
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< p > < img alt = "连续空间存储与离散空间存储" src = "../classification_of_data_structure.assets/classification_phisical_structure.png" / > < / p >
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< p align = "center" > Fig. 连续空间存储与离散空间存储 < / p >
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< p > < strong > 所有数据结构都是基于数组、链表或二者的组合实现的< / strong > 。例如，栈和队列既可以使用数组实现，也可以使用链表实现；而哈希表的实现可能同时包含数组和链表。< / p >
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< ul >
< li > < strong > 基于数组可实现< / strong > ：栈、队列、哈希表、树、堆、图、矩阵、张量（维度 < span class = "arithmatex" > \(\geq 3\)< / span > 的数组）等；< / li >
< li > < strong > 基于链表可实现< / strong > ：栈、队列、哈希表、树、堆、图等；< / li >
< / ul >
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< p > 基于数组实现的数据结构也被称为「静态数据结构」，这意味着此类数据结构在初始化后长度不可变。相对应地，基于链表实现的数据结构被称为「动态数据结构」，这类数据结构在初始化后，仍可以在程序运行过程中对其长度进行调整。< / p >
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< div class = "admonition tip" >
< p class = "admonition-title" > Tip< / p >
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< p > 如若感觉理解物理结构有困难，建议先阅读下一章“数组与链表”，然后再回头理解物理结构的含义。数组与链表是其他所有数据结构的基石，建议你投入更多时间深入了解这两种基本数据结构。< / p >
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< / div >
< h2 id = "__comments" > 评论< / h2 >
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