P2634 [国家集训队]聪聪可可(题解)(点分治)

图论——点分治
洛谷题目

#include<iostream>
#include<cstdlib>
#include<cstdio>
#include<cmath>
#include<cstring>
#include<iomanip>
#include<algorithm>
#include<ctime>
#include<queue>
#include<stack>
#include<vector>
#define rg register
#define il inline
#define lst long long
#define ldb long double
#define N 20050
using namespace std;
const int Inf=1e9;
int n,cnt,ans;
int Max,tot,root;
struct EDGE{
    int to,nxt,v;
}ljl[N<<1];
int hd[N];
int size[N],vis[N];
int dis[N],hh[3];
il int read()
{
    rg int s=0,m=0;rg char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')m=1;ch=getchar();}
    while(ch>='0'&&ch<='9')s=(s<<3)+(s<<1)+(ch^48),ch=getchar();
    return m?-s:s;
}
il void add(rg int p,rg int q,rg int o)
{
    ljl[++cnt]=(EDGE){q,hd[p],o},hd[p]=cnt;
}
void get_root(rg int now,rg int fm)
{
    size[now]=1;rg int num=0;
    for(rg int i=hd[now];i;i=ljl[i].nxt)
    {
        rg int qw=ljl[i].to;
        if(qw==fm||vis[qw])continue;
        get_root(qw,now);
        size[now]+=size[qw];
        num=max(num,size[qw]);
    }
    num=max(num,tot-size[now]);
    if(Max>num)Max=num,root=now;
}
void get_dis(rg int now,rg int fm)
{
    hh[dis[now]%3]++;
    for(rg int i=hd[now];i;i=ljl[i].nxt)
    {
        rg int qw=ljl[i].to;
        if(qw==fm||vis[qw])continue;
        dis[qw]=dis[now]+ljl[i].v;
        get_dis(qw,now);
    }
}
il int Query(rg int now,rg int base)
{
    rg int res=0;
    hh[0]=hh[1]=hh[2]=0;
    dis[now]=base;
    get_dis(now,0);
    res+=hh[0]*hh[0]+(hh[1]*hh[2]<<1);
    return res;
}
void divide(rg int now,rg int fm)
{
    ans+=Query(now,0),vis[now]=1;
    rg int all=tot;
    for(rg int i=hd[now];i;i=ljl[i].nxt)
    {
        rg int qw=ljl[i].to;
        if(qw==fm||vis[qw])continue;
        ans-=Query(qw,ljl[i].v);
        tot=size[now]>size[qw]?size[qw]:all-size[qw];
        root=0,Max=Inf;
        get_root(qw,0);
        divide(root,0);
    }
}
il int gcd(rg int x,rg int y)
{
    return y?gcd(y,x%y):x;
}
int main()
{
    n=read();
    for(rg int i=1;i<n;++i)
    {
        rg int p=read(),q=read(),o=read();
        add(p,q,o),add(q,p,o);
    }
    Max=Inf,tot=n;
    get_root(1,0),divide(root,0);
    rg int GCD=gcd(ans,n*n);
    printf("%d/%d\n",ans/GCD,n*n/GCD);
    return 0;
}