> 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/dfs.md).

# 深度优先搜索

### 搜索思想

深度优先搜索（DFS）沿着一条路径走到底，走不通再**回溯**到上一个分叉点，尝试其它路径。可用递归或栈实现。

### 回溯的本质

“前进 → 标记 → 探索 → 撤销标记 → 返回”。撤销标记就是回溯的关键。

### 网格 DFS 模板

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

void dfs(int x, int y) {
    ans++;
    vis[x][y] = true;
    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
            && !vis[nx][ny]) {
            dfs(nx, ny);
        }
    }
}
```

### 求连通块数量

```cpp
int count = 0;
for (int i = 0; i < n; i++)
    for (int j = 0; j < m; j++)
        if (!vis[i][j]) { dfs(i, j); count++; }
```

### DFS vs BFS

|      | DFS           | BFS        |
| ---- | ------------- | ---------- |
| 数据结构 | 递归 / 栈        | 队列         |
| 特点   | 一条路走到底        | 逐层扩展       |
| 适合   | 遍历、连通性、回溯、全排列 | 无权最短路、最少步数 |

### 全排列（回溯 + 撤销标记）

```cpp
void perm(int k) {
    if (k == n) { /* 输出排列 */ return; }
    for (int i = 1; i <= n; i++) {
        if (!used[i]) {
            used[i] = true; ans[k] = i;
            perm(k + 1);
            used[i] = false;      // 回溯
        }
    }
}
```

### 剪枝

在搜索前判断“这条路不可能有解”就提前返回，能大幅提速（如越界、已访问、超过最优解）。


---

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