程序实现建立六条边和十二个顶点的有向图G的邻接矩阵和邻接表存储结构,并输出这两种结构,根据邻接表,实现图G从顶点0开始的深度优先遍历和广度优先遍历算法,并输出从顶点5到顶点2的所有长度为3的简单路径,从顶点5到顶点2的最短路径最后销毁图G的邻接表的设计思路
时间: 2024-03-03 09:48:00 浏览: 61
好的,我会根据您的要求进行回答。首先是邻接矩阵和邻接表的存储结构:
邻接矩阵:
```
0 1 2 3 4 5
0 0 1 0 0 0 1
1 0 0 1 0 0 0
2 1 0 0 1 0 0
3 0 0 0 0 1 0
4 0 0 1 0 0 1
5 0 0 0 1 1 0
```
邻接表:
```
0 -> 1 -> 5
1 -> 2
2 -> 0 -> 3
3 -> 4
4 -> 2 -> 5
5 -> 3 -> 4
```
接下来是深度优先遍历和广度优先遍历算法的实现,以及从顶点5到顶点2的所有长度为3的简单路径:
深度优先遍历算法:
```python
def dfs(graph, start):
visited = set()
stack = [start]
while stack:
vertex = stack.pop()
if vertex not in visited:
visited.add(vertex)
stack.extend(graph[vertex] - visited)
return visited
```
广度优先遍历算法:
```python
from collections import deque
def bfs(graph, start):
visited = set()
queue = deque([start])
while queue:
vertex = queue.popleft()
if vertex not in visited:
visited.add(vertex)
queue.extend(graph[vertex] - visited)
return visited
```
从顶点5到顶点2的所有长度为3的简单路径:
```python
def find_all_paths(graph, start, end, path=[]):
path = path + [start]
if start == end:
return [path]
if start not in graph:
return []
paths = []
for node in graph[start]:
if node not in path:
new_paths = find_all_paths(graph, node, end, path)
for p in new_paths:
if len(p) == 4 and p[-1] == end:
paths.append(p)
return paths
```
使用 `find_all_paths(graph, 5, 2)` 即可输出所有长度为3的简单路径。
最后是从顶点5到顶点2的最短路径,可以使用 Dijkstra 算法或者 Floyd 算法,这里给出 Dijkstra 算法的实现:
Dijkstra 算法:
```python
import heapq
def dijkstra(graph, start, end):
heap = [(0, start)]
visited = set()
while heap:
(cost, vertex) = heapq.heappop(heap)
if vertex not in visited:
visited.add(vertex)
if vertex == end:
return cost
for next_vertex, c in graph[vertex].items():
if next_vertex not in visited:
heapq.heappush(heap, (cost + c, next_vertex))
return float("inf")
```
使用 `dijkstra(graph, 5, 2)` 即可输出从顶点5到顶点2的最短路径长度。
最后是邻接表的销毁,只需将所有链表节点释放即可,示例代码如下:
```python
def destroy_graph(graph):
for node in graph:
graph[node] = None
del graph
```
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