> 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/graph-traversal.md).

# 图的遍历与连通块

### 图的 DFS

```cpp
vector<int> adj[N];
bool vis[N];

void dfs(int u) {
    vis[u] = true;
    cout << u << " ";
    for (int v : adj[u])
        if (!vis[v]) dfs(v);
}
```

### 图的 BFS

```cpp
void bfs(int s) {
    queue<int> q;
    q.push(s); vis[s] = true;
    while (!q.empty()) {
        int u = q.front(); q.pop();
        cout << u << " ";
        for (int v : adj[u])
            if (!vis[v]) { vis[v] = true; q.push(v); }
    }
}
```

### 连通块（泛洪 floodfill）

遍历所有顶点，未访问的即为一个新连通块：

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

### 复杂度

邻接表下 DFS/BFS 均为 **O(n + m)**；邻接矩阵为 O(n²)。

### 应用

* 判断连通性 / 求连通块个数
* 迷宫、岛屿数量（二维网格 floodfill）
* 二分图判定（染色）


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