HDU 5810 Balls and Boxes （找规律）

Balls and Boxes

题目链接：

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 = \frac{\sum_{i=1}^{m}(X_{i}-\bar X)^{2}}{m}
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 first line is an integer T (T

Output

For each test case, output "Case #X: Y" in a line (without quotes), where X is the case number starting from 1, and Y is "Yes" if you can construct successfully or "No" if it's impossible to reach the requirements.
If Y is "Yes", output an integer M in a line, indicating the number of roads. Then M lines follow, each line contains two integers u and v (1

Sample Input

3
3
2 1 0
2
1 1
4
3 1 1 0

Sample Output

Case #1: Yes
2
1 2
2 3
Case #2: No
Case #3: Yes
4
1 2
1 3
2 4
3 4

Source

2016 Multi-University Training Contest 7


##题意：

把n个球等可能地投入m个盒子.
求方差的期望.


##题解：

推了几个数，然后眼神拟合出公式.....
ans = n*(m-1) / m^2 .

官方题解：


##代码：
``` cpp
#include
#include
#include
#include
#include
#include
#include
#include
#include
#define LL long long
#define eps 1e-8
#define maxn 1010
#define mod 100000007
#define inf 0x3f3f3f3f
#define mid(a,b) ((a+b)>>1)
#define IN freopen("in.txt","r",stdin);
using namespace std;

LL gcd(LL a,LL b) {

return b==0? a:gcd(b,a%b);

}

int main(int argc, char const *argv[])

{

//IN;

LL n,m;
while(scanf("%lld %lld", &n,&m) != EOF && (n||m))
{
    LL ans1 = n * (m - 1);
    LL ans2 = m * m;
    LL gcds = gcd(ans1, ans2);

    printf("%lld/%lld\n", ans1/gcds, ans2/gcds);
}

return 0;

}