代码用时:3h

比较裸的生成函数应用。理清容斥关系就好。

应为一个非常低级的错误（复数减法运算符重载出错），调了非常长的时间。

以后还是应该尽量自己写程序以免受别人程序干扰，FFT和复数运算模板要熟练。

#include<cmath>
#include<cstdio>
#include<algorithm>
#include<cstring>
#define rep(i,l,r) for (int i=l; i<=r; i++)
#define mem(a) memset(a,0,sizeof(a))
typedef long long ll;
using namespace std;

const int N=(1<<18)+100;
const double pi=acos(-1.);
int T,n,nn,m,q
,rev
;
ll s
;

struct C{
double x,y;
C (double a=0,double b=0):x(a),y(b){}
}a
;
C operator +(C a,C b){ return C(a.x+b.x,a.y+b.y); }
C operator -(C a,C b){ return C(a.x-b.x,a.y-b.y); }
C operator *(C a,C b){ return C(a.x*b.x-a.y*b.y,a.x*b.y+a.y*b.x); }

void DFT(C a[],int f){
for (int i=0;i<nn;i++)
if (i<rev[i]) swap(a[i],a[rev[i]]);
for (int i=1; i<nn; i<<=1){
C wn(cos(pi/i),f*sin(pi/i));
for (int p=i<<1,j=0; j<nn; j+=p){
C w(1,0);
for (int k=0; k<i; k++,w=w*wn){
C x=a[j+k],y=w*a[i+j+k]; a[j+k]=x+y; a[i+j+k]=x-y;
}
}
}
if (f==-1) rep(i,0,nn-1) a[i].x/=nn;
}

int main(){
freopen("hdu4609.in","r",stdin);
freopen("hdu4609.out","w",stdout);
scanf("%d",&T);
while (T--){
m=0; mem(a); mem(q); mem(s); mem(rev); scanf("%d",&n);
rep(i,1,n) scanf("%d",&q[i]),m=max(m,q[i]);
rep(i,1,n) a[q[i]].x++;
m<<=1; int L=0; for (nn=1; nn<=m; nn<<=1) L++;
rep(i,0,nn-1) rev[i]=(rev[i>>1]>>1)|((i&1)<<(L-1));
DFT(a,1); rep(i,0,nn-1) a[i]=a[i]*a[i]; DFT(a,-1);
rep(i,1,m) s[i]=(ll)(a[i].x+0.5);
rep(i,1,n) s[q[i]<<1]--;
rep(i,1,m) s[i]=s[i-1]+(s[i]>>1);
sort(q+1,q+n+1); ll ans=0,tot=1ll*n*(n-1)*(n-2)/6;
rep(i,1,n) ans+=1ll*s[m]-s[q[i]]-1ll*(n-i+1)*(n-1)+1ll*(n-i+1)*(n-i)/2;
printf("%.7lf\n",(double)ans/tot);
}
return 0;
}