hdu 4609 3-idiots FFT

/*

hdu 4609 3-idiots FFT

http://www.cnblogs.com/kuangbin/archive/2013/07/24/3210565.html

*/

#pragma warning(disable : 4786)

#pragma comment(linker, "/STACK:102400000,102400000")

#include <iostream>

#include <string>

#include <cstring>

#include <cstdlib>

#include <cstdio>

#include <cmath>

#include <algorithm>

#include <functional>

#include <map>

#include <set>

#include <vector>

#include <stack>

#include <queue>//priority_queue

#include <bitset>

#include <complex>

#include <utility>

/*

**make_pair()

**/

using namespace std;

const double eps=1e-8;

const double PI=acos(-1.0);

const int inf=0x7fffffff;

template<typename T> inline T MIN(T a,T b){return a<b?a:b;}

template<typename T> inline T MAX(T a,T b){return a>b?a:b;}

template<typename T> inline T SQR(T a){return a*a;}

inline int dbcmp(double a){return a>eps?(1):(a<(-eps)?(-1):0);}



typedef __int64 LL;

int n;

const int size=400040;

int data[size/4];

LL num[size],sum[size];

complex<double> x1[size];







void change(complex<double> 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<double> y[],int len,int on)

{

    change(y,len);

    for(int h = 2;h <= len;h <<= 1)

    {

        complex<double> wn(cos(-on*2*PI/h),sin(-on*2*PI/h));

        for(int j = 0;j < len;j += h)

        {

            complex<double> w(1,0);

            for(int k = j;k < j+h/2;k++)

            {

                complex<double> u = y[k];

                complex<double> 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].real(y[i].real()/len);

}

int main() {

	// your code goes here

	int t,i;

	cin>>t;

	while(t--)

	{

		cin>>n;

		memset(num,0,sizeof(num));

		for(i=0;i<n;++i)

		{

			cin>>data[i];

			num[data[i]]++;

		}

		sort(data,data+n);

		int len1=data[n-1]+1;

		int len=1;

		while(len<2*len1) len<<=1;

		for(i=0;i<len1;++i)

		{

			x1[i]=complex<double>(num[i],0);

		}

		for(;i<len;++i)

		{

			x1[i]=complex<double>(0,0);

		}

		fft(x1,len,1);

		for(i=0;i<len;++i)

		{

			x1[i]=x1[i]*x1[i];

		}

		fft(x1,len,-1);



		for(i=0;i<len;++i)

		{

			num[i]=(LL)(x1[i].real()+0.5);

		}



		len=2*data[n-1];

		for(i=0;i<n;++i)

		{

			num[data[i]+data[i]]--;

		}

		for(i=1;i<=len;++i)

		{

			num[i]/=2;

		}

		sum[0]=0;

		for(i=1;i<=len;++i)

		{

			sum[i]=sum[i-1]+num[i];

		}

		LL cnt=0;

		for(i=0;i<n;++i)

		{

			cnt+=sum[len]-sum[data[i]];

			//减掉一个取大一个取小的情况，违背了data[i]是最长边的规则

			cnt-=(LL)(n-1-i)*i;

			//减掉一个取本身，一个取其他数的情况，否则data[i]就被取了两次

			cnt-=(LL)(n-1);

			//减掉取两个比他大的数的情况，违背了data[i]是最长边的规则

			cnt-=(LL)(n-1-i)*(n-2-i)/2;

		}

		LL tot = (LL)n*(n-1)*(n-2)/6;

		printf("%.7lf\n",(double)cnt/tot);

	}

	return 0;

}