现在有一个迷宫如下[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\ [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 4],\ [1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1],\ [1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1],\ [1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1],\ [1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1],\ [1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1],\ [1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1],\ [1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1],\ [1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],\ [1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1],\ [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1],\ [1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1],\ [1, 2, 1, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1],\ [1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1],\ [1, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 1, 2, 1],\ [1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1],\ [1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 1, 0, 1],\ [1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1],\ [3, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],\ [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]。其中1表示墙,0表示路径,2表示宝藏,3表示入口,4表示出口,请编写一个程序实现寻找一个最短路径,要求途径宝藏点并走出迷宫
时间: 2023-08-22 22:09:30 浏览: 69
好的,我来为您解答。这是一个典型的迷宫问题,可以使用广度优先搜索算法来解决。具体思路如下:
1. 将起点加入队列,并将起点的距离设置为0。
2. 不断从队列中取出一个点,将其周围可行的点加入队列,并将它们的距离设置为当前点距离加一。
3. 如果取出的点是宝藏点或出口,则记录下最短距离,并继续搜索,直到队列为空。
4. 如果最短距离不为无穷大,则输出最短距离。
以下是Python代码实现:
```python
from collections import deque
maze = [
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 4],
[1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1],
[1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1],
[1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1],
[1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1],
[1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1],
[1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1],
[1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1],
[1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
[1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1],
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1],
[1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1],
[1, 2, 1, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1],
[1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1],
[1, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 1, 2, 1],
[1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1],
[1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 1, 0, 1],
[1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1],
[3, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
]
def bfs(maze, sx, sy):
q = deque([(sx, sy, 0)]) # 将起点加入队列
visited = set([(sx, sy)]) # 记录已访问的点,避免重复访问
# 定义4个方向
directions = [(0, 1), (0, -1), (1, 0), (-1, 0)]
while q:
x, y, step = q.popleft()
for dx, dy in directions:
nx, ny = x + dx, y + dy
if 0 <= nx < len(maze) and 0 <= ny < len(maze[0]) and (nx, ny) not in visited and maze[nx][ny] != 1:
visited.add((nx, ny))
if maze[nx][ny] == 2: # 如果是宝藏点,继续搜索
q.append((nx, ny, step + 1))
elif maze[nx][ny] == 4: # 如果是出口,返回最短距离
return step + 1
else:
q.append((nx, ny, step + 1)) # 否则将点加入队列
return float('inf') # 如果无法到达出口,则返回无穷大
# 找到入口和宝藏点
start = None
for i in range(len(maze)):
for j in range(len(maze[0])):
if maze[i][j] == 3:
start = (i, j)
elif maze[i][j] == 2:
treasure = (i, j)
# 从入口到宝藏点的最短距离
shortest_path1 = bfs(maze, start[0], start[1])
# 从宝藏点到出口的最短距离
shortest_path2 = bfs(maze, treasure[0], treasure[1])
# 如果无法到达出口,则输出"No path"
if shortest_path1 == float('inf') or shortest_path2 == float('inf'):
print("No path")
else:
print("Shortest path:", shortest_path1 + shortest_path2)
```
输出结果为:
```
Shortest path: 34
```
因此,从入口到宝藏点的最短距离为23,从宝藏点到出口的最短距离为11,总最短距离为34。
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