Balls and Boxes
题目连接：
http://acm.hdu.edu.cn/showproblem.php?pid=5810
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
题意
有n个球，m个盒子，问你n个球放在盒子里面的方差的期望是多少。
题解：
正解是数学，但是我们是打表找规律……
答案 n(m-1)/m^2
代码
#include<bits/stdc++.h>
using namespace std;
int main(){
long long n,m;
while(cin>>n>>m){
if(n==0&&m==0)break;
long long a=n*(m-1),b=m*m;
long long tmp = __gcd(a,b);
cout<<a/tmp<<"/"<<b/tmp<<endl;
}
}