6.3

import heapq

def prim(graph, start):
num_nodes = len(graph)
visited = [False] * num_nodes
min_heap = [(0, start, -1)]
mst_cost = 0
mst_edges = []

while min_heap:
    weight, u, parent = heapq.heappop(min_heap)
    if visited[u]:
        continue
    visited[u] = True
    mst_cost += weight
    if parent!= -1:
        mst_edges.append((parent, u, weight))

    for v in range(num_nodes):
        if not visited[v] and graph[u][v]!= 0:
            heapq.heappush(min_heap, (graph[u][v], v, u))

return mst_cost, mst_edges

graph = [
[0, 20, 0, 0, 15, 0],
[20, 0, 20, 60, 25, 0],
[0, 20, 0, 30, 18, 0],
[0, 60, 30, 0, 35, 10],
[0, 0, 0, 10, 15, 0]
]

mst_cost, mst_edges = prim(graph, 0)
print("Prim 算法生成的最小生成树的成本:", mst_cost)
print("Prim 算法生成的最小生成树的边:", mst_edges)

print("学号：3022")