DP：求出3点构成链的方案数 。然后总方案数减去它

Y

4
1 2
1 3
1 4

1
Hint
1. The only set is {2,3,4}.

2. Please use #pragma comment(linker, "/STACK:16777216")

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <vector>
#pragma comment(linker, "/STACK:16777216")

using namespace std;

typedef long long int LL;

const int maxn=100100;
vector<int> g[maxn];

int n;
LL ans,doubi[maxn],son[maxn];

void dfs(int u,int fa)
{
LL ndoubi=0,nson=0;
son[u]=1;
for(int i=0,sz=g[u].size();i<sz;i++)
{
int v=g[u][i];
if(v==fa) continue;
dfs(v,u);
son[u]+=son[v];
doubi[u]+=doubi[v]+son[v];

ans+=son[v]*nson;
ans+=son[v]*ndoubi;
ans+=doubi[v]*nson;
ans+=doubi[v];

nson+=son[v];
ndoubi+=doubi[v];
}
}

int main()
{
while(scanf("%d",&n)!=EOF)
{
ans=0;
memset(doubi,0,sizeof(doubi));
memset(son,0,sizeof(son));
for(int i=0;i<=n+10;i++)
g[i].clear();
for(int i=0;i<n-1;i++)
{
int a,b;
scanf("%d%d",&a,&b);
g[a].push_back(b);
g[b].push_back(a);
}
dfs(1,1);
cout<<1LL*n*(n-1)*(n-2)/6-ans<<endl;
}
return 0;
}