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Posted 2020-09-28 -凡-尘

Balls and Boxes

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 798    Accepted Submission(s): 527

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

题解：

转自：http://blog.csdn.net/qq978874169/article/details/52165136

 

 

#include<iostream>
#include<cmath>
#include<stdio.h>
using namespace std;
typedef long long int ll;
ll n,m;
ll fenzi,fenmu;
ll tmp;
ll gcd(ll a,ll b)
{
    return b==0?a:gcd(b,a%b);
}
int main()
{
    while(~scanf("%lld%lld",&n,&m)&&(n*m))
    {
        fenzi=n*(m-1);
        fenmu=m*m;
        tmp=gcd(fenzi,fenmu);
        fenzi/=tmp;
        fenmu/=tmp;
        printf("%lld/%lld\\n",fenzi,fenmu);
    }
    return 0;
}