帮我用python写一个prim算法
时间: 2023-05-16 18:06:33 浏览: 96
当然可以,以下是一个基本的Prim算法的Python实现:
```python
from queue import PriorityQueue
def prim(graph, start):
visited = set()
pq = PriorityQueue()
mst = []
visited.add(start)
for neighbor, weight in graph[start].items():
pq.put((weight, start, neighbor))
while not pq.empty():
weight, u, v = pq.get()
if v not in visited:
visited.add(v)
mst.append((u, v, weight))
for neighbor, weight in graph[v].items():
pq.put((weight, v, neighbor))
return mst
```
其中,`graph`是一个字典,表示图的邻接表,`start`是起点。返回值是一个列表,表示最小生成树的边集。
注意,这只是一个基本的实现,可能存在一些性能问题和边界情况没有考虑到。如果需要更加健壮的实现,可以参考其他资料或者自行优化。
相关问题
用python写一个prim算法
Prim算法是一种用于计算最小生成树的算法,它通过不断找到最小边来不断扩展生成树,从而找到整张图的最小生成树。下面是一种用Python实现Prim算法的方法:
1. 初始化:将图的某一个顶点作为起点,并将其加入生成树中。
2. 找到最小边:在剩下的顶点中找到一条连接已加入生成树的顶点和未加入生成树的顶点的边,并将该顶点加入生成树中。
3. 重复步骤2,直到所有的顶点都加入生成树为止。
下面是一个简单的Prim算法的Python代码实现:
```
import sys
class Prim:
def __init__(self, graph):
self.graph = graph
self.V = len(graph)
self.mst = [False] * self.V
self.key = [sys.maxsize] * self.V
self.parent = [None] * self.V
def primMST(self):
self.key[0] = 0
self.parent[0] = -1
for i in range(self.V):
u = self.minKey()
self.mst[u] = True
for v in range(self.V):
if self.graph[u][v] > 0 and self.mst[v] == False and self.key[v] > self.graph[u][v]:
self.key[v] = self.graph[u][v]
self.parent[v] = u
def minKey(self):
min = sys.maxsize
min_index = 0
for v in range(self.V):
if self.mst[v] == False and self.key[v] < min:
min = self.key[v]
min_index = v
return min_index
def printMST(self):
for i in range(1, self.V):
print("%d - %d: %d" % (self.parent[i], i, self.graph[i][self.parent[i]]))
```
用
用python写一个 Prim算法代码(必须有每行注释)
```python
# Prim's Algorithm in Python for finding minimum spanning tree (MST)
import sys
def prim(graph, start):
# 初始化:标记所有边为未访问,创建空集合用于存放已选择的最小权重边,以及一个字典保存每个顶点的最短路径起点
visited = [False] * len(graph)
edges = []
parent = [-1] * len(graph)
# 将起始顶点的距离设置为0,并加入已访问集合
distance[start] = 0
visited[start] = True
while edges != len(graph) - 1: # 边的数量还没达到n-1,因为MST需要n-1条边
min_distance = float('inf') # 初始化最小距离为无穷大
u = -1 # 存储当前最小边的起点
# 遍历所有未访问的顶点,找到到它们的最小边
for v in range(len(graph)):
if visited[v] == False and graph[start][v] != 0 and graph[start][v] < min_distance:
min_distance = graph[start][v]
u = v
# 更新节点信息,将找到的最小边加入edges,并将其终点添加为已访问
visited[u] = True
edges.append((start, u)) # 添加起点u到之前的起点(start)
parent[u] = start # 设置parent[u]为起点
start = u # 将搜索焦点转移到下一个未访问的起点u
return edges, parent
# 示例图的邻接矩阵表示,其中0表示不存在边,正数表示权重
graph = [
[0, 2, 0, 6],
[2, 0, 3, 8],
[0, 3, 0, 5],
[6, 8, 5, 0]
]
# 使用Prim算法从第一个节点开始找MST
result_edges, _ = prim(graph, 0)
print("Minimum Spanning Tree Edges (from node 0):")
for edge in result_edges:
print(f"Edge from {edge[0]} to {edge[1]} with weight {graph[edge[0]][edge[1]]}")
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