#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<ctime>
#include<cmath>
#include<iostream>
#include<climits>
#include<string>
#include<deque>
#include<queue>
#include<vector>
#include<algorithm>
#include<map>
#include<stack>
#include<set>
using namespace std;
#define LL long long
#define pi (acos(-1.0))
struct complex
{
double r,i;
complex(double _r=0,double _i=0){ r=_r ; i=_i; }
complex operator + (const complex &b) { return complex(r+b.r,i+b.i); }
complex operator - (const complex &b) { return complex(r-b.r,i-b.i); }
complex operator * (const complex &b) { return complex(r*b.r-i*b.i,r*b.i+i*b.r);}
};
void change(complex y[],int len)
{
int i,j,k;
for(i=1,j=len/2; i<len-1; i++)
{
if(i<j) swap(y[i],y[j]);
k=len/2;
while(j>=k)
{
j-=k;
k/=2;
}
if(j<k) j+=k;
}
}
void fft(complex y[],int len,int on)
{
change(y,len);
for(int h=2; h<=len; h<<=1)
{
complex wn(cos(-on*2*pi/h),sin(-on*2*pi/h));
for(int j=0; j<len;j+=h)
{
complex w(1,0);
for(int k=j;k<j+h/2;k++)
{
complex u=y[k];
complex t=w*y[k+h/2];
y[k]= u+t;
y[k+h/2]=u-t;
w=w*wn;
}
}
}
if(on==-1)
for(int i=0;i<len;i++)
y[i].r/=len;
}
const int maxn=810010;
complex x1[maxn];
LL num[maxn];
int a[maxn];
void dofft(LL len1)
{
int len=1;
while(len < 2*len1) len<<=1;
for(int i=0;i<len1;i++) x1[i]=complex(num[i],0);
for(int i=len1;i<len;i++) x1[i]=complex(0,0);
fft(x1,len,1);
for(int i=0;i<len;i++) x1[i]=x1[i]*x1[i];
fft(x1,len,-1);
for(int i=0;i<len;i++) num[i]=(LL)(x1[i].r+0.5);
}
int main()
{
#ifndef ONLINE_JUDGE
freopen("in.txt","r",stdin);
freopen("out.txt","w",stdout);
#endif
int t; scanf("%d",&t);
int n;
while(t--)
{
memset(num,0,sizeof(num));
scanf("%d",&n);
for(int i=0;i<n;i++)
{
scanf("%d",&a[i]);
num[a[i]]++;
}
sort(a,a+n);
dofft(a[n-1]+1);
LL len=2*a[n-1];
for(int i=0;i<n;i++) num[a[i]+a[i]]--;
for(int i=1;i<=len;i++) num[i]/=2;
for(int i=1;i<=len;i++) num[i]+=num[i-1];
double ans=0.0;
for(int i=0;i<n;i++)
{
ans+=num[len]-num[a[i]];
ans-=(n-i-1)*(double)i;
ans-=(double)(n-1);
ans-=(n-i-1)*(double)(n-i-2)/2.0;
}
double all=(double)n*(n-1)*(n-2)/6.0;
printf("%.7f\n",ans/all);
}
return 0;
}
FFT
最新推荐文章于 2022-12-17 12:45:16 发布