HDU4081 Qin Shi Huang's National Road System

先求最小生成树

再遍历每一对顶点，如果该顶点之间的边属于最小生成树，则剪掉这对顶点在最小生成树里的最长路径

否则直接剪掉连接这对顶点的边~

用prim算法求最小生成树最长路径的模板~

#include<cstdio>
#include<cstring>
#include<algorithm>
#include<vector>
#include<cmath>
using namespace std;
const int maxn=1014;
const int inf=1e9;
double g[maxn][maxn],d[maxn],w[maxn];
int visit[maxn],N,S,P,pre[maxn];
double len[maxn][maxn];//表示点i,j在最小生成树上的最长路径 
double c[maxn][maxn];
void init () {
    for (int i=0;i<maxn;i++)
    for (int j=0;j<maxn;j++)
    g[i][j]=inf,c[i][j]=0,len[i][j]=0;
}
double prim (int s) {
    fill (d,d+maxn,inf);
    fill (visit,visit+maxn,0);
    for (int i=1;i<=N;i++) pre[i]=i;
    d[s]=0;
    double ans=0;
    for (int i=1;i<=N;i++) {
        int u=-1,min=inf;
        for (int j=1;j<=N;j++)
        if (!visit[j]&&d[j]<min) {
            u=j;
            min=d[j];
        }
        if (u==-1) return -1;
        visit[u]=1;
        ans+=d[u];
        if (pre[u]!=u) c[u][pre[u]]=c[pre[u]][u]=1;
        for (int v=1;v<=N;v++)
        if (!visit[v]&&g[u][v]!=inf&&g[u][v]<d[v]) {
            d[v]=g[u][v];
            pre[v]=u;
        } 
        for (int v=1;v<=N;v++)
        if (visit[v]&&u!=v) len[u][v]=len[v][u]=max(len[pre[u]][v],d[u]); 
    }
    return ans;
}
struct node {
    double x,y;
}Node[maxn];
int main () {
    int T;
    scanf ("%d",&T);
    while (T--) {
        scanf("%d",&N);
        for (int i=1;i<=N;i++) scanf ("%lf %lf %lf",&Node[i].x,&Node[i].y,&w[i]);
        init ();
        for (int i=1;i<=N;i++)
        for (int j=i+1;j<=N;j++)
        g[i][j]=g[j][i]=sqrt((Node[i].x-Node[j].x)*(Node[i].x-Node[j].x)+(Node[i].y-Node[j].y)*(Node[i].y-Node[j].y));
        double mst=prim(1);
        double Max=0;
        for (int i=1;i<=N;i++)
        for (int j=i+1;j<=N;j++) 
        if (!c[i][j]) Max=max(Max,(w[i]+w[j])/(mst-len[i][j]));
        else Max=max(Max,(w[i]+w[j])/(mst-g[i][j]));
        printf ("%.2f\n",Max);
    } 
    return 0;
}