lightOJ 1317 Throwing Balls into the Baskets(期望) 解题报告
题目链接:http://acm.hust.edu.cn/vjudge/contest/view.action?cid=88890#problem/A
题目:
Description
You probably have played the game "Throwing Balls into the Basket". It is a simple game. You have to throw a ball into a basket from a certain distance. One day we (the AIUB ACMMER) were playing the game. But it was slightly different from the main game. In our game we were N people trying to throw balls into M identical Baskets. At each turn we all were selecting a basket and trying to throw a ball into it. After the game we saw exactly S balls were successful. Now you will be given the value of N and M. For each player probability of throwing a ball into any basket successfully is P. Assume that there are infinitely many balls and the probability of choosing a basket by any player is 1/M. If multiple people choose a common basket and throw their ball, you can assume that their balls will not conflict, and the probability remains same for getting inside a basket. You have to find the expected number of balls entered into the baskets after K turns.
Input
Input starts with an integer T (≤ 100), denoting the number of test cases.
Each case starts with a line containing three integers N (1 ≤ N ≤ 16), M (1 ≤ M ≤ 100) and K (0 ≤ K ≤ 100) and a real number P (0 ≤ P ≤ 1). P contains at most three places after the decimal point.
Output
For each case, print the case number and the expected number of balls. Errors less than 10-6 will be ignored.
Sample Input
2
1 1 1 0.5
1 1 2 0.5
Sample Output
Case 1: 0.5
Case 2: 1.000000
题目大意:
有n个人,m个篮筐,一共打了k轮,每轮每个人可以投一个球,每个球投进的概率都是p,求k轮后,投中的球的期望是多少?
分析:
因为每个人投进的概率都是相同的,所以期望也是相同的。因此只需要求出第一轮的期望就可以了,总期望=k*第一轮的期望。
代码:
1 #include<cstdio> 2 #include<iostream> 3 using namespace std; 4 5 int t,n,m,k; 6 double p,ans; 7 int a[20][20]; 8 9 void init() 10 { 11 a[1][1]=1; 12 a[1][0]=1; 13 for(int i=2;i<20;i++) 14 { 15 a[i][i]=1; 16 a[i][0]=1; 17 for(int j=1;j<i;j++) 18 a[i][j]=a[i-1][j]+a[i-1][j-1]; 19 } 20 } 21 22 double count(int j) 23 { 24 double b=1.0; 25 for(int i=0;i<j;i++) 26 b=b*p;//投中的期望 27 for(int i=0;i<n-j;i++) 28 b=b*(1.0-p);//没投中的期望 29 return b*j*a[n][j]; 30 } 31 32 int main() 33 { 34 int c=1; 35 scanf("%d",&t); 36 init(); 37 while(t--) 38 { 39 scanf("%d%d%d%lf",&n,&m,&k,&p); 40 ans=0.0;//小数 41 for(int i=0;i<=n;i++) 42 ans+=count(i);//第一轮的期望 43 printf("Case %d: %.7lf\n",c++,ans*k); 44 } 45 return 0; 46 }