> 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/search/bfs.md).

# 广度优先搜索（BFS）

### 思想

BFS 以“起点”为中心，一层一层向外扩展，使用**队列**保存待访问结点。适合求**最短步数 / 最少操作次数**（边权相同）。

### 与 DFS 的对比

|      | BFS       | DFS       |
| ---- | --------- | --------- |
| 数据结构 | 队列        | 栈 / 递归    |
| 访问顺序 | 逐层扩展      | 一条路走到底    |
| 适合   | 最短路（边权相等） | 遍历、回溯、连通性 |

### 网格 BFS 模板

```cpp
int n, m;
int dist[105][105];
int dx[4] = {-1, 1, 0, 0};
int dy[4] = {0, 0, -1, 1};

int bfs(int sx, int sy, int ex, int ey) {
    memset(dist, -1, sizeof(dist));
    queue<pair<int,int>> q;
    q.push({sx, sy});
    dist[sx][sy] = 0;
    while (!q.empty()) {
        auto [x, y] = q.front(); q.pop();
        if (x == ex && y == ey) return dist[x][y];
        for (int k = 0; k < 4; k++) {
            int nx = x + dx[k], ny = y + dy[k];
            if (nx < 0 || nx >= n || ny < 0 || ny >= m) continue;
            if (dist[nx][ny] != -1) continue;   // 已访问
            dist[nx][ny] = dist[x][y] + 1;
            q.push({nx, ny});
        }
    }
    return -1;
}
```

### 要点

* 入队时就要标记已访问，避免重复入队。
* 在无权图中，BFS 首次到达某点的距离一定是最短的。


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