P2634 聪明可可

题面

https://www.luogu.org/problem/P2634

题解

#include<cstdio>
#include<iostream>
#include<vector>
using namespace std;
vector<int> to[20500],len[20500];
int n;
int dp[20500][3];
long long tot,ans;
// len[x][i]+j+dis=0 dis=-j-len[x][i]
// x+len
void dfs(int x,int ff) {
  int i,l=to[x].size();
  dp[x][0]=1; dp[x][1]=0; dp[x][2]=0;
  for (i=0;i<l;i++) if (to[x][i]!=ff) {
    dfs(to[x][i],x);
    ans+=dp[to[x][i]][(6-len[x][i])%3]*1LL*dp[x][0];
    ans+=dp[to[x][i]][(5-len[x][i])%3]*1LL*dp[x][1];
    ans+=dp[to[x][i]][(4-len[x][i])%3]*1LL*dp[x][2];
    dp[x][len[x][i]]+=dp[to[x][i]][0];
    dp[x][(1+len[x][i])%3]+=dp[to[x][i]][1];
    dp[x][(2+len[x][i])%3]+=dp[to[x][i]][2];
  }
}

long long gcd(long long x,long long y) {
  if (!y) return x; else return gcd(y,x%y);
}
int main(){
  int i,u,v,l;
  scanf("%d",&n);
  tot=n*n;
  for (i=1;i<n;i++) {
    scanf("%d %d %d",&u,&v,&l);
    l%=3;
    to[u].push_back(v); len[u].push_back(l);
    to[v].push_back(u); len[v].push_back(l);
  }
  dfs(1,-1);
  ans=ans*2+n;
  long long d=gcd(ans,tot);
  cout<<ans/d<<'/'<<tot/d<<endl;
}