HDU5810 Balls and Boxes
来源:互联网 发布:淘宝买家手机号码采集 编辑:程序博客网 时间:2024/05/16 14:19
Balls and Boxes
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/65536 K (Java/Others)Total Submission(s): 797 Accepted Submission(s): 526
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
whereXi 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.
where
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.
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 12 20 0
Sample Output
0/11/2HintIn 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
—————————————————————————————————
题意:把n个球放到m个盒子里面,求上面这个式子的期望;
思路:打表找规律,发现答案=n*(m-1)/m*m 求gcd即可
证明:
E(V)=1/m*E(∑(xi-x)2)=E((x-n/m)2)=E(x2)-2*n/m*E(x)+n2/m2
E(x)=n/m;E(x2)=D(x)+[E(x)]2;变成二项分布了,D(x)=n*(m-1)/m2
所以带到上面的式子中就变成了E(v)=n*(m-1)/m2
#include <iostream>#include <cstdio>#include <cstring>#include <string>#include <algorithm>#include <cmath>#include <map>#include <cmath>#include <set>#include <stack>#include <queue>#include <vector>#include <bitset>#include <functional>using namespace std;#define LL long longconst int INF = 0x3f3f3f3f;LL n,m;LL gcd(LL x,LL y){ return x?gcd(y%x,x):y;}int main(){ while(~scanf("%lld%lld",&n,&m)&&(n+m)) { if(m==1) {printf("0/1\n");continue;} n=(m-1)*n; m=m*m; printf("%lld/%lld\n",n/gcd(n,m),m/gcd(n,m)); } return 0;}
阅读全文
0 0
- HDU5810 Balls and Boxes
- HDU5810-Balls and Boxes
- 【HDU5810】Balls and Boxes(数学题)
- hdu5810 Balls and Boxes(数学)
- hdu5810——Balls and Boxes(数学推导)
- HDU5810(2016多校第七场)——Balls and Boxes(组合数学,概率)
- Balls and Boxes
- Boxes and Balls
- Balls and Boxes CodeForces
- Boxes and Balls UVALive
- Boxes And Balls CodeForces
- Boxes and Balls UVALive
- UVALive 7500 Boxes and Balls
- HDU 5810 Balls and Boxes
- hdu 5810 Balls and Boxes
- UVALive-7500-Boxes and Balls
- hdu 5810 Balls and Boxes (数学)
- HDU 5810 Balls and Boxes(概率)
- 组合模式
- 重载Comparator
- IDEA快捷键
- 网站的SQL注入实战
- Apache Kylin无法启动,卡在 “Logging initialized using configuration..."
- HDU5810 Balls and Boxes
- c语言之指针和数组(一)
- thinkphp怎么显示当前服务器的地址_SERVER["SERVER_NAME"]
- jConsole, jVisualvm, btrace 使用体会
- HDU-1688 Sightseeing(最短路+次短路)
- 《图解HTTP》(一)之HTTP基础
- SpringTest框架JUnit单元测试用例获取ApplicationContext实例的方法
- SpringBoot学习(一)SpringBoot基础入门
- CodeForces 815E Karen and Neighborhood题解