pku 2485 Highways 典型最小生成树_2485密码-优快云博客

本文介绍了一个典型的最小生成树问题解决方案，通过PRIM算法实现。该算法采用邻接矩阵存储图，并通过不断选择最短边的方式构造最小生成树，最终找到树中最长的边。

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题目连接

http://acm.pku.edu.cn/JudgeOnline/problem?id=2485

典型最小生成树

#include <stdio.h>

#define MAX_V 501
int arc[MAX_V][MAX_V];

int N;
struct CloseEdge{
int adjvex;
int lowcost;
}closedge[MAX_V];

int longest;

void MiniSpanTree_PRIM(int u){
longest = 0;
//初始化辅助数组
int i,j,k;
for(i = 0;i < N;i++)
  if(i != u){
   closedge[i].adjvex = u;
   closedge[i].lowcost = arc[u][i];
  }
//初始,U = {u}
closedge[u].lowcost = 0;
//选择其余N - 1个顶点
for(i = 0;i < N - 1;i++){
  //求出最小生成树的下一个节点,第k顶点
  int MaxCost = 1 << 20;
  for(j = 0; j < N;j++)
   if(closedge[j].lowcost != 0 && MaxCost > closedge[j].lowcost)
   {
    MaxCost = closedge[j].lowcost;
    k = j;
   }
  if(longest < closedge[k].lowcost)
   longest = closedge[k].lowcost;
  //k顶点加入到U集
  closedge[k].lowcost = 0;
  //新节点添加到树后,修改closedge数组
  for(j = 0;j < N;j++)
   if(closedge[j].lowcost > arc[k][j]){
    closedge[j].adjvex = k;
    closedge[j].lowcost = arc[k][j];
   }
}
}

int main(){
//FILE *fp = fopen("data.txt","r");
int test;
//fscanf(fp,"%d",&test);
scanf("%d",&test);
while(test--){
  //fscanf(fp,"%d",&N);
  scanf("%d",&N);
  for(int i = 0;i < N;i++)
   for(int j = 0;j < N;j++)
    //fscanf(fp,"%d",&arc[i][j]);
    scanf("%d",&arc[i][j]);
  MiniSpanTree_PRIM(0);
  printf("%d/n",longest);
}
return 0;
}