编程实现用邻接矩阵存储的图的最小生成树Prim算法

下面是使用邻接矩阵存储的图的最小生成树Prim算法的Python代码实现：

import sys

class Graph():
    def __init__(self, vertices):
        self.V = vertices
        self.graph = [[0 for column in range(vertices)] for row in range(vertices)]

    def printMST(self, parent):
        print("Edge\tWeight")
        for i in range(1, self.V):
            print(parent[i], "-", i, "\t", self.graph[i][parent[i]])

    def minKey(self, key, mstSet):
        min = sys.maxsize
        for v in range(self.V):
            if key[v] < min and mstSet[v] == False:
                min = key[v]
                min_index = v
        return min_index

    def primMST(self):
        key = [sys.maxsize] * self.V
        parent = [None] * self.V
        key[0] = 0
        mstSet = [False] * self.V
        parent[0] = -1
        for cout in range(self.V):
            u = self.minKey(key, mstSet)
            mstSet[u] = True
            for v in range(self.V):
                if self.graph[u][v] > 0 and mstSet[v] == False and key[v] > self.graph[u][v]:
                    key[v] = self.graph[u][v]
                    parent[v] = u
        self.printMST(parent)

# 测试代码
g = Graph(5)
g.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]]
g.primMST()

这个算法的时间复杂度为O(V^2)，其中V是图中节点的数量。