普里姆算法

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <iostream>
using namespace std;
#define max_name 5
#define max_vertex_num 20 //权的上限值
typedef char vertex[max_name];//顶点名字串
typedef int adjmatrix[max_vertex_num][max_vertex_num];//邻接矩阵
typedef struct //定义图
{
vertex vexs[max_vertex_num];
adjmatrix arcs;
int vexnum,arcnum ;
}Graph;

typedef struct
{
vertex adjvex;//当前点
int lowcost;//代价
}minside[max_vertex_num];

int locatevex(Graph g,vertex u)//定位
{
int i ;
for (i=0;i<g.vexnum ;++i)
if(strcmp(u,g.vexs[i])==0)
return i;
return -1;
}

void creategraph(Graph &g)
{
int i,j,k,w;
vertex va,vb;
printf("请无向图g的顶点数和边数（以空格为分隔）n");
//scanf("%d %d",&g.vexnum,&g.arcnum );
cin>>g.vexnum>>g.arcnum;
printf("请输入%d个顶点的值（<%d个字符）：n",g.vexnum,max_name);
for(i=0;i<g.vexnum ;++i)//构造顶点集
//scanf("%s",g.vexs[i]);
cin>>g.vexs[i];
for(i=0;i<g.vexnum;++i)
for(j=0;j<g.vexnum;++j)//初始化邻接矩阵
g.arcs[i][j]=100;
printf("请输入%d条边的顶点1 顶点2 权值（以空格作为间隔）：n",g.arcnum);
for(k=0;k<g.arcnum;++k)
{
//scanf("%s%s%d%*c",va,vb,&w);
cin>>va>>vb>>w;
i=locatevex(g,va);
j=locatevex(g,vb);
g.arcs[i][j]=g.arcs[j][i]=w;
}
}//对称

int minimum(minside sz,Graph g)
{
int i=0,min;
while(!sz[i].lowcost)
i++;
min=sz[i].lowcost;//将最小权值记在min中
k=i;//把与边关联的生成树外的定点序号记在k中
for(j=i+1;j<g.vexnum;j++)
if(sz[j].lowcost>0&&min>sz[j].lowcost )
{
min=sz[j].lowcost ;
k=j;
}
return k;
}

void minispantree_prim(Graph g,vertex u)
{
int i,k;
minside closedge ;
k=locatevex(g,u);
for(j=0;j<g.vexnum ;++j)
{
strcpy(closedge[j].adjvex,u);
closedge[j].lowcost = g.arcs[k][j];
}
closedge[k].lowcost =0;//将顶点vk加入生成树中
printf("最小代价生成树的各条边为：n");
for(i=1;i<g.vexnum ;++i)
{
k=minimum(closedge,g);
//printf("(%d-%d)n",closedge[k].adjvex,g.vexs[k]);//输出最小边及权值
cout<<closedge[k].adjvex<<"-"<<g.vexs[k]<<endl;
closedge[k].lowcost = 0;
for(j=0;j<g.vexnum ;++j)
if(g.arcs[k][j]>0&&g.arcs[k][j]<closedge[j].lowcost )
{
strcpy(closedge[j].adjvex,g.vexs[k]);
closedge[j].lowcost=g.arcs[k][j];
}
}
}//修改权值域

int main()
{
Graph g ;
creategraph(g);
minispantree_prim(g,g.vexs[0]);

return 0 ; }

（编辑：李大同）

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