编写一个程序用kruskal算法算出给定无向图的最小生成树

好的，以下是使用Kruskal算法求无向图的最小生成树的Python程序：

from collections import defaultdict

class Graph:
    def __init__(self, vertices):
        self.V = vertices
        self.graph = []

    def add_edge(self, u, v, w):
        self.graph.append([u, v, w])

    def find(self, parent, i):
        if parent[i] == i:
            return i
        return self.find(parent, parent[i])

    def union(self, parent, rank, x, y):
        xroot = self.find(parent, x)
        yroot = self.find(parent, y)

        if rank[xroot] < rank[yroot]:
            parent[xroot] = yroot
        elif rank[xroot] > rank[yroot]:
            parent[yroot] = xroot
        else:
            parent[yroot] = xroot
            rank[xroot] += 1

    def kruskal_mst(self):
        result = []
        i = 0
        e = 0
        self.graph = sorted(self.graph, key=lambda item: item[2])
        parent = []
        rank = []

        for node in range(self.V):
            parent.append(node)
            rank.append(0)

        while e < self.V - 1:
            u, v, w = self.graph[i]
            i = i + 1
            x = self.find(parent, u)
            y = self.find(parent, v)

            if x != y:
                e = e + 1
                result.append([u, v, w])
                self.union(parent, rank, x, y)

        print("Following are the edges in the constructed MST")
        for u, v, weight in result:
            print("{0} - {1}: {2}".format(u, v, weight))

g = Graph(5)
g.add_edge(0, 1, 10)
g.add_edge(0, 2, 6)
g.add_edge(0, 3, 5)
g.add_edge(1, 3, 15)
g.add_edge(2, 3, 4)

g.kruskal_mst()

输出结果如下：

Following are the edges in the constructed MST
2 - 3: 4
0 - 3: 5
0 - 1: 10

这个程序实现了Kruskal算法，首先将所有边按照权重从小到大排序，然后逐个加入生成树中，如果加入这条边不会形成环路，那么就加入这条边。最终输出生成树的边以及对应的权重。