HDU5645 DZY Loves Balls 数学

DZY Loves Balls

Time Limit: 4000/2000 MS (Java/Others)    Memory Limit: 262144/262144 K (Java/Others)
Total Submission(s): 110    Accepted Submission(s): 80

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

 

题意：先后随机取2个，问后者比前者大的概率。

解：找出取出2个数相同的情况，所有情况减去这些的一半即满足的条件，除以C(N,2)即可。

AC代码：

//************************************************************************//
//*Author : Handsome How                                                 *//
//************************************************************************//
//#pragma comment(linker, "/STA    CK:1024000000,1024000000")
#pragma warning(disable:4996) 
#include <vector>
#include <map>
#include <set>
#include <deque>
#include <queue>
#include <stack>
#include <algorithm>
#include <sstream>
#include <iostream>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <cstring>
#include <ctime>                                                
#include <cassert>
#if defined(_MSC_VER) || __cplusplus > 199711L
#define aut(r,v) auto r = (v)
#else
#define aut(r,v) __typeof(v) r = (v)
#endif
#define each(it,o) for(aut(it, (o).begin()); it != (o).end(); ++ it)
#define fur(i,a,b) for(int i=(a);i<=(b);i++)
#define furr(i,a,b) for(int i=(a);i>=(b);i--)
#define cl(a) memset((a),0,sizeof(a))
using namespace std;
typedef long long LL;
//----------------------------------------------------
int numb[305];
int A(int n)
{
    int t;
    t = n*(n - 1);
    return t;
}

int main()
{
    //freopen("E:\\data.in", "r", stdin);
    ios :: sync_with_stdio(false);
    int T;
    scanf("%d", &T);
    while (T--)
    {
        cl(numb);
        int n;
        int t;
        scanf("%d", &n);
        fur(i, 1, n) {
            scanf("%d", &t);
            numb[t]++;
        }
        int fm = A(n);
        int fz = fm;
        fur(i, 1, 300)
            if (numb[i] > 1)
                fz = fz - A(numb[i]);
        double ans = 0.5*(double)fz / (double)fm;
        printf("%.6lf\n",ans);

    }
    return 0;
}