《算法图论：BFS/DFS 实战（迷宫问题 + 拓扑排序）》（442）
### 《算法图论：BFS/DFS 实战（迷宫问题 + 拓扑排序）》 🚀
在图论算法中，**广度优先搜索（BFS）**和**深度优先搜索（DFS）**是两大经典遍历方法，它们不仅能解决基础的路径查找问题，还能应用于更复杂的场景，比如**迷宫问题**和**拓扑排序**。
#### 🧩 迷宫问题：BFS vs DFS
假设有一个二维迷宫，`0`代表通路，`1`代表墙壁，我们需要从起点`(0,0)`走到终点`(n-1,n-1)`。
- **BFS** 🌀：逐层扩展，**保证找到最短路径**。用队列实现，适合无权图的最短路径问题。
- **DFS** 🌊：一路走到底再回溯，用栈（递归）实现，**可能更快找到一条路径**，但不一定最短。
**代码片段（BFS迷宫）**：
```python
from collections import deque
def bfs_maze(maze):
queue = deque([(0, 0)])
while queue:
x, y = queue.popleft()
if (x, y) == (n-1, n-1):
return True
for dx, dy in [(0,1), (1,0), (0,-1), (-1,0)]:
nx, ny = x+dx, y+dy
if 0<=nx<n and 0<=ny<n and maze[nx][ny]==0:
queue.append((nx, ny))
return False
```
#### 📊 拓扑排序：DFS的经典应用
拓扑排序用于**有向无环图（DAG）**的任务调度，比如课程依赖关系。DFS的后序遍历反转结果就是拓扑序！
**代码片段（DFS拓扑排序）**：
```python
def topo_sort(graph):
visited, stack = set(), []
def dfs(node):
visited.add(node)
for neighbor in graph[node]:
if neighbor not in visited:
dfs(neighbor)
stack.append(node) # 后序压栈
for node in graph:
if node not in visited:
dfs(node)
return stack[::-1] # 反转结果
```
#### 总结 🎯
- **BFS**：最短路径、扩散问题（如社交网络层级关系）。
- **DFS**：拓扑排序、连通性检测、回溯问题。
掌握这两种算法，就能轻松应对大多数图论挑战啦！💪
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