hdu 5810 Balls and Boxes(2016 Multi-University Training Contest 7——数学题)

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=5810

Balls and Boxes

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)

Total Submission(s): 377    Accepted Submission(s): 274

Problem Description

Mr. Chopsticks is interested in random phenomena, and he conducts an experiment to study randomness. In the experiment, he throws n balls into m boxes in such a manner that each ball has equal probability of going to each boxes. After the experiment, he calculated the statistical variance V as

V=∑mi=1(Xi−X¯)2m

where  Xi is the number of balls in the ith box, and  X¯ is the average number of balls in a box.
Your task is to find out the expected value of V.

 

Input

The input contains multiple test cases. Each case contains two integers n and m (1 <= n, m <= 1000 000 000) in a line.
The input is terminated by n = m = 0.

 

Output

For each case, output the result as A/B in a line, where A/B should be an irreducible fraction. Let B=1 if the result is an integer.

 

Sample Input

2 1 2 2 0 0

 

Sample Output

0/1 1/2

Hint

In the second sample, there are four possible outcomes, two outcomes with V = 0 and two outcomes with V = 1.

 

Author

SYSU

 

Source

2016 Multi-University Training Contest 7

 

题目大意：给你n个球，放到m个盒子中，每个球放进每个盒子的概率一样。问你：方差V的期望是多少。

解题思路：推公式。

详见代码。

#include 
#include 
#include 

using namespace std;

#define ll long long

int main()
{
    ll n,m;
    while(~scanf("%lld%lld",&n,&m))
    {
        if (n==0&&m==0)
            break;
        ll a=m*m;
        ll b=(n*m)-n;
        ll g=__gcd(a,b);
        printf ("%lld/%lld\n",b/g,a/g);
    }
    return 0;
}