传送门

点分治常规题。练习模板

//OJ 2077
//by Cydiater
//2016.9.23
#include <iostream>
#include <cstdio>
#include <cstring>
#include <string>
#include <algorithm>
#include <queue>
#include <map>
#include <ctime>
#include <cmath>
#include <iomanip>
#include <cstdlib>
using namespace std;
#define ll long long
#define up(i,j,n)        for(int i=j;i<=n;i++)
#define down(i,j,n)        for(int i=j;i>=n;i--)
const int MAXN=1e6+5;
const int oo=0x3f3f3f3f;
inline int read(){
    char ch=getchar();int x=0,f=1;
    while(ch>'9'||ch<'0'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
    return x*f;
}
int LINK[MAXN],len=0,sum,max_siz[MAXN],root,siz[MAXN],dis[MAXN],head,tail,q[MAXN],cnt[3],ans=0;
bool vis[MAXN];
struct edge{
    int y,next,v;
}e[MAXN<<1];
int N;
namespace solution{
    inline void insert(int x,int y,int v){e[++len].next=LINK[x];LINK[x]=len;e[len].y=y;e[len].v=v;}
    inline int gcd(int a,int b){return b==0?a:gcd(b,a%b);}
    void init(){
        N=read();
        memset(vis,0,sizeof(vis));
        up(i,2,N){
            int x=read(),y=read(),v=read();
            insert(x,y,v);
            insert(y,x,v);
        }
    }
    void make_root(int node,int fa){
        max_siz[node]=0;siz[node]=1;
        for(int i=LINK[node];i;i=e[i].next)if(!vis[e[i].y]&&e[i].y!=fa){
            make_root(e[i].y,node);
            siz[node]+=siz[e[i].y];
            max_siz[node]=max(max_siz[node],siz[e[i].y]);
        }
        max_siz[node]=max(max_siz[node],sum-max_siz[node]);
        if(max_siz[node]<max_siz[root])root=node;
    }
    void get_deep(int node,int fa){
        q[++tail]=dis[node];
        for(int i=LINK[node];i;i=e[i].next)if(e[i].y!=fa&&!vis[e[i].y]){
            dis[e[i].y]=dis[node]+e[i].v;
            get_deep(e[i].y,node);
        }
    }
    int col(int node,int dist){
        dis[node]=dist;head=1;tail=0;
        get_deep(node,0);
        cnt[0]=cnt[1]=cnt[2]=0;
        up(i,head,tail)cnt[q[i]%3]++;
        return cnt[0]*cnt[0]+2*cnt[1]*cnt[2];
    }
    void work(int node){
        ans+=col(node,0);
        vis[node]=1;
        for(int i=LINK[node];i;i=e[i].next)if(!vis[e[i].y]){
            ans-=col(e[i].y,e[i].v);
            root=0;
            make_root(e[i].y,node);
            work(root);
        }
    }
    void slove(){
        sum=N;max_siz[0]=oo;root=0;
        make_root(1,0);
        work(root);
    }
    void output(){
        int d=gcd(ans,N*N);
        printf("%d/%d\n",ans/d,N*N/d);
    }
}
int main(){
    //freopen("input.in","r",stdin);
    using namespace solution;
    init();
    slove();
    output();
    return 0;
}