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)
2017-07-14 13:20
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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
[align=left]Problem Description[/align]
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.
[align=left]Input[/align]
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.
[align=left]Output[/align]
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.
[align=left]Sample Input[/align]
2 1
2 2
0 0
[align=left]Sample Output[/align]
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.
[align=left]Author[/align]
SYSU
[align=left]Source[/align]
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; }
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