P2634 [国家集训队]聪聪可可

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;

const int N=2e4+5;
const int INF=0x7fffffff;

inline int read()
{
    char c=getchar();int num=0;
    for(;!isdigit(c);c=getchar());
    for(;isdigit(c);c=getchar())
        num=num*10+c-'0';
    return num;
}

inline int gcd(int a,int b)
{
    int c;
    while(b)
    {
        c=a,a=b,b=c%b;
    }
    return a;
}

int n,ans;
int head[N],num_edge;
struct Edge
{
    int v,w,nxt;
}edge[N<<1];

void add_edge(int u,int v,int w)
{
    edge[++num_edge].v=v;
    edge[num_edge].w=w;
    edge[num_edge].nxt=head[u];
    head[u]=num_edge;
}

bool vis[N];
int Siz,root;
int siz[N],mxson[N];
void getroot(int u,int fa)
{
    siz[u]=1,mxson[u]=0;
    for(int i=head[u],v;i;i=edge[i].nxt)
    {
        v=edge[i].v;
        if(v==fa||vis[v])
            continue;
        getroot(v,u);
        siz[u]+=siz[v];
        if(mxson[u]<siz[v])
            mxson[u]=siz[v];
    }
    mxson[u]=max(mxson[u],Siz-mxson[u]);
    if(mxson[u]<mxson[root])
        root=u;
}

int dis[N],cnt[N];
void getdis(int u,int fa)
{
    ++cnt[dis[u]];
    for(int i=head[u],v;i;i=edge[i].nxt)
    {
        v=edge[i].v;
        if(vis[v]||v==fa)
            continue;
        dis[v]=dis[u]+edge[i].w,
        dis[v]%=3;
        getdis(v,u);
    }
}

int solve(int u,int dist)
{
    cnt[0]=cnt[1]=cnt[2]=0;
    dis[u]=dist%3;
    getdis(u,0);
    return cnt[1]*cnt[2]*2+cnt[0]*cnt[0];
}

void divide(int u)
{
    ans+=solve(u,0);
    vis[u]=1;
    for(int i=head[u],v;i;i=edge[i].nxt)
    {
        v=edge[i].v;
        if(vis[v])
            continue;
        ans-=solve(v,edge[i].w);
        root=0,Siz=siz[v];
        getroot(v,0);
        divide(root);
    }
}

int main()
{
    n=read();
    for(int i=1,u,v,w;i<n;++i)
    {
        u=read(),v=read(),w=read();
        add_edge(u,v,w);
        add_edge(v,u,w);
    }
    mxson[0]=INF,Siz=n;
    getroot(1,0);
    divide(root);
    int a=n*n;
    if(a==ans)
        puts("1");
    else
    {
        int g=gcd(ans,a);
        printf("%d/%d",ans/g,a/g);
    }
    return 0;
}