HDU 5645 DZY Loves Balls(概率)

DZY Loves Balls

Time Limit: 4000/2000 MS (Java/Others) Memory Limit: 262144/262144 K (Java/Others)
Total Submission(s): 661 Accepted Submission(s): 389

Problem Description

DZY loves playing balls.

He has n balls in a big box. On each ball there is an integer written.

One day he decides to pick two balls from the box. First he randomly picks a ball from the box, and names it A . Next, without putting A back into the box, he randomly picks another ball from the box, and names it B .

If the number written on A is strictly greater than the number on B , he will feel happy.

Now you are given the numbers on each ball. Please calculate the probability that he feels happy.

Input

First line contains t denoting the number of testcases.

t testcases follow. In each testcase, first line contains n , second line contains n space-separated positive integers ai , denoting the numbers on the balls.

( 1≤t≤300,2≤n≤300,1≤ai≤300 )

Output

For each testcase, output a real number with 6 decimal places.

Sample Input

   
   
   
   

    
    
    
    2
3
1 2 3
3
100 100 100
   
   
   
   

Sample Output

   
   
   
   

    
    
    
    0.500000
0.000000
   
   
   
   
   
   
   
   


   
   
   
   
   
   
   
   


   
   
   
   
   
   
   
   

    
    
    
    
/*
思路：对求号码进行排序 
取两次球第一次不放回，所有可能的情况为n*(n-1)，对于每一个球，枚举比他大的球的位置j，
n-j即为比第一次球大的数目a，a/(n*(n-1))，即为每一次的概率，累加即为结果 
*/
#include <iostream>
#include <algorithm>
#include <cstdio>
using namespace std;
const int N=300+5;
int a[N];
int main(){
	int t,i,j,n;
	double re;
	cin>>t;
	while(t--){
		cin>>n;
		re=0;
		for(i=0;i<n;i++)
		   cin>>a[i];
		sort(a,a+n);
		 for(i=0;i<n;i++){  //枚举每一个球 
		 	for(j=i+1;j<n;j++){   //找到比第一个球大的位置 
		 		if(a[i]<a[j]){
		 			break;
		 		}
		 	}
		 	re+=(double)(n-j)/(n*(n-1));
		 }
		 printf("%.6lf\n",re);
	}
	return 0;
}