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#include

#include

#include

#define INFINITY 30000//权值最大值

#define max_vertex_num 20//最大顶点数

typedef struct{

int arcs[max_vertex_num][max_vertex_num]; //邻接矩阵

int vexnum,arnum;//图当前的顶点和边数

}Graph;

typedef struct{

int adjvex;//某顶点与已构造好部分生成树的顶点之间权值最小的顶点

int lowcost;//某顶点与已构造好部分生成树的顶点之间的最小权值

}ClosEdge;//用prim算法求最小生成树的辅助数组

void CreateGraph(Graph g)//生成邻接矩阵

{

int i,j;

int start,end,weight;

for(i=1;i<=g.vexnum;i++)

for(j=1;j<=g.vexnum;j++)

g.arcs[i][j]=INFINITY;//矩阵初始化

printf("输入每条边的两个关联顶点编号和其权值：\n");

for(i=1;i<=g.arnum;i++)

{

scanf("%d %d %d",&start,&end,&weight);

g.arcs[start][end]=weight;

g.arcs[end][start]=weight;

}

}

int minimun(ClosEdge cl[],int vnum)//在辅助数组中选择权值最小的顶点并返回其位置

{

int i;

int w,p;

w=INFINITY;

for(i=1;i<=vnum;i++)

{

if(cl[i].lowcost!=0&&cl[i].lowcost

{

w=cl[i].lowcost;

p=i;

}

}

return p;

}

void MiniSpanTree_PRIM(Graph g,int u)

{

ClosEdge closedge[max_vertex_num];

int i,j,k;

printf("最小生成树:\n");

for(j=1;j<=g.vexnum;j++)//辅助数组初始化

{

if(j!=u)

{

closedge[j].adjvex=u;

closedge[j].lowcost=g.arcs[u][j];

}

}

closedge[u].lowcost=0;//初始，U={u} ；

for(i=1;i

{

k=minimun(closedge,g.vexnum);//求生成树的下一个顶点

printf("%d %d\n",closedge[k].adjvex,k);

closedge[k].lowcost=0;//第k个顶点并入U集

for(j=1;j<=g.vexnum;j++)//新顶点并入后重新选择最小边

{

if(g.arcs[k][j]

{

closedge[j].adjvex=k;

closedge[j].lowcost=g.arcs[k][j];

}

}

}

}

int main()

{

Graph g;

char jx='y';

int u;

while(jx!='N'&&jx!='n')

{

printf("请输入图的顶点和边数:\n");

scanf("%d %d",&g.vexnum,&g.arnum);

CreateGraph(g);

printf("请输入构造最小生成树的开始顶点:\n");

scanf("%d",&u);

MiniSpanTree_PRIM(g,u);

printf("最小生成树构造完毕，继续进行吗?\n");

scanf("%c",&jx);

}

return 0;

}