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博客园首页新随笔联系管理订阅 随笔- 524 文章- 0 评论- 20 hdu-5810 Balls and Boxes(概率期望)

2024-10-25 15:43:01   210人阅读

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?Xˉ)2m

where Xi is the number of balls in the ith box, and Xˉ 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
 
技术分享

 

#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;
}

 

博客园首页新随笔联系管理订阅 随笔- 524 文章- 0 评论- 20 hdu-5810 Balls and Boxes(概率期望)


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