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Hello 算法
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0. 写在前面
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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. 复杂度分析
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2.1. 算法效率评估
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2.3. 空间复杂度
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2.5. 小结
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3.3. 小结
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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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5.2. 队列
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5.4. 小结
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6. 散列表
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6. 散列表
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6.2. 哈希冲突处理
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< li > 图由顶点和边组成，可以表示为一组顶点和一组边构成的集合。< / li >
< li > 相比线性关系（链表）和分治关系（树），网络关系（图）的自由度更高，也从而更为复杂。< / li >
< li > 有向图的边存在方向，连通图中的任意顶点都可达，有权图的每条边都包含权重变量。< / li >
< li > 邻接矩阵使用方阵来表示图，每一行（列）代表一个顶点，矩阵元素代表边，使用 < span class = "arithmatex" > \(1\)< / span > 或 < span class = "arithmatex" > \(0\)< / span > 来表示两个顶点之间有边或无边。邻接矩阵的增删查操作效率很高，但占用空间大。< / 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。邻接表相对邻接矩阵更加节省空间，但由于需要通过遍历链表来查找边，因此时间效率较低。< / li >
< li > 当邻接表中的链表过长时，可以将其转化为红黑树或哈希表，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 > 图可以用于建模各类现实系统，例如社交网络、地铁线路等。< / li >
< 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 >
< 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，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、无路可走再回头的搜索方式，常基于递归来实现。< / li >
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