refactor: Replace 结点 with 节点 (#452)
* Replace 结点 with 节点 Update the footnotes in the figures * Update mindmap * Reduce the size of the mindmap.png
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@@ -12,7 +12,7 @@ $$
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那么,图与其他数据结构的关系是什么?如果我们把「顶点」看作结点,把「边」看作连接各个结点的指针,则可将「图」看作是一种从「链表」拓展而来的数据结构。**相较于线性关系(链表)和分治关系(树),网络关系(图)的自由度更高,从而更为复杂**。
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那么,图与其他数据结构的关系是什么?如果我们把「顶点」看作节点,把「边」看作连接各个节点的指针,则可将「图」看作是一种从「链表」拓展而来的数据结构。**相较于线性关系(链表)和分治关系(树),网络关系(图)的自由度更高,从而更为复杂**。
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## 图常见类型
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### 邻接表
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「邻接表 Adjacency List」使用 $n$ 个链表来表示图,链表结点表示顶点。第 $i$ 条链表对应顶点 $i$ ,其中存储了该顶点的所有邻接顶点(即与该顶点相连的顶点)。
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「邻接表 Adjacency List」使用 $n$ 个链表来表示图,链表节点表示顶点。第 $i$ 条链表对应顶点 $i$ ,其中存储了该顶点的所有邻接顶点(即与该顶点相连的顶点)。
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- **添加边**:在顶点对应链表的末尾添加边即可,使用 $O(1)$ 时间。因为是无向图,所以需要同时添加两个方向的边。
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- **删除边**:在顶点对应链表中查找并删除指定边,使用 $O(m)$ 时间。在无向图中,需要同时删除两个方向的边。
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- **添加顶点**:在邻接表中添加一个链表,并将新增顶点作为链表头结点,使用 $O(1)$ 时间。
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- **添加顶点**:在邻接表中添加一个链表,并将新增顶点作为链表头节点,使用 $O(1)$ 时间。
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- **删除顶点**:需遍历整个邻接表,删除包含指定顶点的所有边,使用 $O(1)$ 时间。
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- **初始化**:在邻接表中创建 $n$ 个顶点和 $2m$ 条边,使用 $O(n + m)$ 时间。
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=== "删除顶点"
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以下是基于邻接表实现图的代码示例。细心的同学可能注意到,**我们在邻接表中使用 `Vertex` 结点类来表示顶点**,这样做的原因有:
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以下是基于邻接表实现图的代码示例。细心的同学可能注意到,**我们在邻接表中使用 `Vertex` 节点类来表示顶点**,这样做的原因有:
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- 如果我们选择通过顶点值来区分不同顶点,那么值重复的顶点将无法被区分。
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- 如果类似邻接矩阵那样,使用顶点列表索引来区分不同顶点。那么,假设我们想要删除索引为 $i$ 的顶点,则需要遍历整个邻接表,将其中 $> i$ 的索引全部减 $1$,这样操作效率较低。
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@@ -22,7 +22,7 @@ BFS 通常借助「队列」来实现。队列具有“先入先出”的性质
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2. 在循环的每轮迭代中,弹出队首顶点并记录访问,然后将该顶点的所有邻接顶点加入到队列尾部;
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3. 循环步骤 `2.` ,直到所有顶点被访问完成后结束;
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为了防止重复遍历顶点,我们需要借助一个哈希表 `visited` 来记录哪些结点已被访问。
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为了防止重复遍历顶点,我们需要借助一个哈希表 `visited` 来记录哪些节点已被访问。
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=== "Java"
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