对于任给的一张无向带权连通图，求出其最小生成树。

题目要求:

(1)编程创建一幅图
(2)输出创建的图
(3)编写Prim算法代码，实现图的最小生成树求解，且输出最小生成树
(4)编写Kruskal算法代码，实现图的最小生成树求解，且输出最小生成树
(5)编写菜单，允许用户选择相应操作

代码如下:

#include <iostream>
#include <queue>
#include <algorithm>
using namespace std;
const int maxVertexNum = 30;//最大顶点数
const int noEdge = 99999999;//用来记录两个顶点之间没有边
const int ERROR = -1;//发生错误class Graph
{
private :class Edge{public :int v1;int v2;int w;};int edgeNum;//边数int vertexNum;//顶点数int vertexs[maxVertexNum][maxVertexNum];//邻接矩阵bool vis[maxVertexNum];//用来标记是否访问过该顶点int dist[maxVertexNum];//prim算法中用来记录该结点离最小生成树的距离int parent[maxVertexNum];//prim算法中用到Edge edge[maxVertexNum];//用来记录边，方便输出int totalWeight;//最小权重和int set[maxVertexNum];//kruskal算法中，集合数组，利用并查集算法，来判断是否构成回路Edge kEdge[maxVertexNum];//kruskal算法中所用，用来记录创建的图的信息，在用kruskal算法时，不是用邻接矩阵存储的图，而是用了这个结构体数组来存储public:void menu(){char c;while (true){cout << "--------邻接矩阵存储的图--------------" << endl;cout << "--------输入 c 创建图-----------------" << endl;cout << "--------输入 p 输出图-----------------" << endl;cout << "--------输入 r 使用prim算法-----------" << endl;cout << "--------输入 k 使用kruskal算法--------" << endl;cout << "--------输入 e 退出程序---------------" << endl;cout << "---------顶点从0开始------------------" << endl;cin >> c;switch (c){case 'c':buildGraph();cout << "创建完毕,按任意键继续" << endl;c = getchar();//吃回车c = getchar();//吃任意键system("cls");//刷新屏幕break;case 'p':printGraph();cout << "输出完毕,按任意键继续" << endl;c = getchar();c = getchar();system("cls");break;case 'r':prim();cout << "输出完毕,按任意键继续" << endl;c = getchar();c = getchar();system("cls");break;case 'k':kruskal();cout << "输出完毕,按任意键继续" << endl;c = getchar();c = getchar();system("cls");break;case 'e':return;}}}Graph() :vertexNum(0), edgeNum(0){initVis();for (int i = 0; i < maxVertexNum; i++){for (int j = 0; j < maxVertexNum; j++){vertexs[i][j] = noEdge;}}}private:void initSet(){for (int i = 0; i < vertexNum; i++) set[i] = i;}void Union(int root1, int root2){int x = Find(root1);int y = Find(root2);if (x != y){set[x] = y;}}int Find(int x){if (set[x] != x) return Find(set[x]);else return x;}void initVis(){for (int i = 0; i < maxVertexNum; i++){vis[i] = false;}}void buildGraph(){cout << "请输入节点数和边数" << endl;cin >> vertexNum >> edgeNum;int e1, e2;int w;for (int i = 0; i < edgeNum; i++){cin >> e1 >> e2>>w;vertexs[e1][e2] = w;vertexs[e2][e1] = w;kEdge[i].v1 = e1;kEdge[i].v2 = e2;kEdge[i].w = w;}}void printGraph(){for (int i = 0; i < vertexNum; i++){vis[i] = true;for (int j = 0; j < vertexNum; j++){if (!vis[j]&&vertexs[i][j] != noEdge){cout << i << " - " << j <<" = "<<vertexs[i][j]<< endl;}}}initVis();}int findMinDist(){int minVertex;int minDist = noEdge;for (int i = 0; i < vertexNum; i++){if (dist[i] != 0 && dist[i] < minDist){minDist = dist[i];minVertex = i;}}if (minDist < noEdge) return minVertex;else return ERROR;}void prim(){for (int i = 0; i < vertexNum; i++){dist[i] = vertexs[0][i];parent[i] = 0;}totalWeight = 0;int cnt = 0;dist[0] = 0;parent[0] = -1;cnt++;int v;while (true){v = findMinDist();if (v == ERROR) break;edge[cnt].v1 = parent[v];edge[cnt].v2 = v;edge[cnt].w = dist[v];totalWeight += dist[v];dist[v] = 0;cnt++;for (int w = 0; w < vertexNum; w++){if (dist[w] != 0 && vertexs[v][w] < noEdge){dist[w] = vertexs[v][w];parent[w] = v;}}}if (cnt < vertexNum){cout << "此图不连通" << endl;}else{for (int i = 1; i < cnt; i++){cout << edge[i].v1 << " - " << edge[i].v2 << " = " << edge[i].w << endl;}cout <<"totalWeight = " <<totalWeight << endl;}}//所有普通类成员函数，都不能以函数指针的方式作为其他函数的入口函数。//所以这里的cmp函数要加上staticstatic bool cmp(Edge a, Edge b){return a.w < b.w;}void kruskal(){initSet();sort(kEdge,kEdge+edgeNum,cmp);int cnt = 0;int idx = 0;totalWeight = 0;while (cnt < vertexNum - 1 && idx < edgeNum){int v1 = kEdge[idx].v1;int v2 = kEdge[idx].v2;if (Find(v1) != Find(v2)){edge[cnt].v1 = v1;edge[cnt].v2 = v2;edge[cnt].w = kEdge[cnt].w;totalWeight += edge[cnt].w;cnt++;Union(v1, v2);}idx++;}if (cnt < vertexNum - 1){cout << "此图不连通" << endl;}else{for (int i = 0; i < vertexNum - 1; i++){cout << edge[i].v1 << " - " << edge[i].v2 << " = " << edge[i].w << endl;}cout << "totalWeight = " << totalWeight << endl;}}};int main()
{Graph g;g.menu();return 0;
}

示例：