> For the complete documentation index, see [llms.txt](https://docs.1l.lol/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.1l.lol/graph-theory/connectivity.md).

# 连通性与连通分量

### 无向图

* **连通图**：任意两点间都存在路径
* **连通分量**：无向图的极大连通子图

求法：对每个未访问点做一次 DFS/BFS，一次遍历得到一个分量。

```cpp
int comp = 0;
for (int i = 1; i <= n; i++)
    if (!vis[i]) { dfs(i); comp++; }
```

### 有向图

* **强连通**：任意两点互相可达
* **强连通分量（SCC）**：极大的强连通子图
* **弱连通**：忽略方向后连通

### Tarjan 求强连通分量（初步）

用 DFS 时间戳 dfn 和追溯值 low 找环，配合栈。

### 缩点

把每个强连通分量缩成一个点，得到 **DAG**，再在 DAG 上做拓扑排序 / DP。

### 应用

* 判断连通性
* 缩点后求解（如最长路）
* 2-SAT、网络流等高级算法的基础


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