给定17*17的邻接矩阵用python编写prim算法求最小生成树从而求解最小路径问题并给出运行结果
时间: 2023-07-22 19:09:48 浏览: 82
好的,我可以给您提供一个Python实现的Prim算法求解最小生成树的代码。首先,需要先构造邻接矩阵,以下是一个示例邻接矩阵:
```
graph = [[0, 2, 0, 6, 0],
[2, 0, 3, 8, 5],
[0, 3, 0, 0, 7],
[6, 8, 0, 0, 9],
[0, 5, 7, 9, 0]]
```
其中,0表示两个节点之间没有连边,其他数字表示边的权值。接下来,可以使用以下代码实现Prim算法求解最小生成树:
```python
INF = float('inf')
def prim(graph):
n = len(graph)
# 初始化距离和集合
dist = [INF] * n
visited = [False] * n
# 从第一个节点开始
dist[0] = 0
# 计算最小生成树的边和权值
for i in range(n):
# 寻找最小距离的节点
u = minDist(dist, visited)
visited[u] = True
# 更新最小距离
for v in range(n):
if graph[u][v] > 0 and not visited[v] and graph[u][v] < dist[v]:
dist[v] = graph[u][v]
# 计算最小生成树的权值
weight = sum(dist)
return weight
# 找到距离集合最近的节点
def minDist(dist, visited):
minDist = INF
minIndex = -1
for i in range(len(dist)):
if not visited[i] and dist[i] < minDist:
minDist = dist[i]
minIndex = i
return minIndex
```
最后,调用prim函数即可得到最小生成树的权值。
```python
graph = [[0, 2, 0, 6, 0],
[2, 0, 3, 8, 5],
[0, 3, 0, 0, 7],
[6, 8, 0, 0, 9],
[0, 5, 7, 9, 0]]
print(prim(graph))
```
输出结果为:16。
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