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< title > 9.4 < / title >
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跳转至
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Hello 算法
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9.4 小结
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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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0.3 小结
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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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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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第 4 章 数组与链表
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第 4 章 数组与链表
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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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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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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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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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9.4 小结
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目录
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1. 重点回顾
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2. Q & A
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< 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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< a href = "../../chapter_searching/searching_algorithm_revisited/" class = "md-nav__link" >
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10.5 重识搜索算法
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10.6 小结
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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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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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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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第 16 章 附录
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16.1 编程环境安装
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16.2 一起参与创作
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1. 重点回顾
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< li > 图由顶点和边组成，可以被表示为一组顶点和一组边构成的集合。< / li >
< li > 相较于线性关系（链表）和分治关系（树），网络关系（图）具有更高的自由度，因而更为复杂。< / li >
< li > 有向图的边具有方向性，连通图中的任意顶点均可达，有权图的每条边都包含权重变量。< / li >
< li > 邻接矩阵利用矩阵来表示图，每一行（列）代表一个顶点，矩阵元素代表边，用 < span class = "arithmatex" > \(1\)< / span > 或 < span class = "arithmatex" > \(0\)< / span > 表示两个顶点之间有边或无边。邻接矩阵在增删查操作上效率很高，但空间占用较多。< / li >
< li > 邻接表使用多个链表来表示图，第 < span class = "arithmatex" > \(i\)< / span > 条链表对应顶点 < span class = "arithmatex" > \(i\)< / span > ，其中存储了该顶点的所有邻接顶点。邻接表相对于邻接矩阵更加节省空间，但由于需要遍历链表来查找边，时间效率较低。< / li >
< li > 当邻接表中的链表过长时，可以将其转换为红黑树或哈希表，从而提升查询效率。< / li >
< li > 从算法思想角度分析，邻接矩阵体现“以空间换时间”，邻接表体现“以时间换空间”。< / li >
< li > 图可用于建模各类现实系统，如社交网络、地铁线路等。< / li >
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< li > 树是图的一种特例，树的遍历也是图的遍历的一种特例。< / li >
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< li > 图的广度优先遍历是一种由近及远、层层扩张的搜索方式，通常借助队列实现。< / li >
< li > 图的深度优先遍历是一种优先走到底、无路可走时再回溯的搜索方式，常基于递归来实现。< / li >
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< / ul >
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< h3 id = "2-q-a" > 2. Q & A< a class = "headerlink" href = "#2-q-a" title = "Permanent link" > ¶ < / a > < / h3 >
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< div class = "admonition question" >
< p class = "admonition-title" > 路径的定义是顶点序列还是边序列？< / p >
< p > 维基百科上不同语言版本的定义不一致： ， ：
在本文中，路径被认为是一个边序列，而不是一个顶点序列。这是因为两个顶点之间可能存在多条边连接，此时每条边都对应一条路径。< / p >
< / div >
< div class = "admonition question" >
< p class = "admonition-title" > 非连通图中，是否会有无法遍历到的点？< / p >
< p > 在非连通图中，从某个顶点出发，至少有一个顶点无法到达。遍历非连通图需要设置多个起点，以遍历到图的所有连通分量。< / p >
< / div >
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< p class = "admonition-title" > 在邻接表中，“与该顶点相连的所有顶点”的顶点顺序是否有要求？< / p >
< p > 可以是任意顺序。但在实际应用中，可能会需要按照指定规则来排序，比如按照顶点添加的次序、或者按照顶点值大小的顺序等等，这样可以有助于快速查找“带有某种极值”的顶点。< / p >
< / div >
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