图的最小生成树之普里姆Prim算法

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源代码如下：
#include<iostream>using namespace std;#define MAX_VERTEX_NUM 20#define infinity 9typedef int QElemType; typedef int EdgeData;typedef char VertexData;typedef struct {    VertexData verlist[MAX_VERTEX_NUM];            //顶点表     EdgeData edge[MAX_VERTEX_NUM][MAX_VERTEX_NUM]; //邻接矩阵--可试为边之间的关系      int vexnum,edgenum;                          //顶点数和边数}MTGraph;void printMTGragh(MTGraph *G){int i,j;for (i = 1 ; i <= G->vexnum ; i++){for (j = 1 ; j <= G->vexnum ; j++)cout<<G->edge[i][j]<<" ";cout<<endl;}//Prim(G,G->edge);}void Prim(MTGraph *G){             //集合V-U的顶点尚未加入最小生成树中，集合U则已加入 int lowcost[MAX_VERTEX_NUM+1]; //用来保存集合V-U中各顶点与集合U中顶点最短边的权值，   // lowcost[v] = infinity 表示顶点V已加入了最小生成树中    int closest[MAX_VERTEX_NUM+1]; //用来保存依附于该边的在集合U的顶点// 该边：集合V-U中各顶点与集合U中顶点最短边int i,j,k,h,min;//printMTGragh(G);for(i = 2;i<=G->vexnum;i++){lowcost[i] = G->edge[1][i];closest[i] = 1;  //将定点1加入集合U中 }for(i = 2;i<=G->vexnum;i++){min = 9 ;k = i;for(j=2;j<=G->vexnum;j++)if(lowcost[j] < min && lowcost[j]!=0){min = lowcost[j]; //在 lowcost中取最小边 k = j;}cout<<"将第"<<i<<"个元素放入集合U中时，Lowcost原序列：";for(h = 2;h<=G->vexnum;h++)cout<<lowcost[h]<<" ";cout<<endl;cout<<"("<<k<<","<<closest[k]<<")"<<endl; //输出顶点K与之对应的权值 cout<<"取出的顶点为:"<<k<<"将顶点"<<k<<"与顶点"<<closest[k]<<"相连"<<endl; lowcost[k] = 0;  //将顶点K置于集合U中 for(j=2;j<=G->vexnum;j++) //调整数组lowcost和 cloestif(G->edge[k][j]<lowcost[j]){lowcost[j] = G->edge[k][j];closest[j] = k;}cout<<"将第"<<i<<"个元素放入集合U中时，Lowcost更新后的序列：";for(h = 2;h<=G->vexnum;h++)cout<<lowcost[h]<<" ";cout<<endl;}}  //时间复杂度O(n^2) //建立图的邻接矩阵 void createMTGraph(MTGraph *G){ int i,j,k,w;cout<<"输入顶点数和边数如（5 7）"<<endl;cin>>G->vexnum>>G->edgenum;cout<<"输入顶点信息,如（A B C D...）"<<endl;for(i = 0 ; i<G->vexnum;i++)cin>>G->verlist[i];for(i = 0 ; i<=G->vexnum;i++)for(j = 0 ; j<=G->vexnum;j++)G->edge[i][j] = infinity;cout<<"输入边(i,j)上的权值w,如(i j w)"<<endl; for(k=0;k<G->edgenum;k++){ cin>>i>>j>>w; G->edge[i][j] = w; G->edge[j][i] = w; }}main(){MTGraph *G ;G = new MTGraph();createMTGraph(G);printMTGragh(G);Prim(G);system("pause");}
程序运行后的结果
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