HDU 4254 A Famous Game

HDU 4254 A Famous Game

J - 1010

Time Limit:1000MS     Memory Limit:32768KB     64bit IO Format:%I64d & %I64u

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Description

Mr. B and Mr. M like to play with balls. They have many balls colored in blue and red. Firstly, Mr. B randomly picks up N balls out of them and put them into a bag.  Mr. M knows that there are N+1 possible situations in which the number of red balls is ranged from 0 to N, and we assume the possibilities of the N+1 situations are  the same. But Mr. M does not know which situation occurs. Secondly, Mr. M picks up P balls out of the bag and examines them. There are Q red balls and P-Q blue  balls. The question is: if he picks up one more ball out of the bag, what is the possibility that this ball is red?

Input

Each test case contains only one line with three integers N, P and Q (2 <= N <= 100,000, 0 <= P <= N-1, 0 <= Q <= P).

Output

For each test case, display a single line containing the case number and the possibility of the next ball Mr. M picks out is red. The number should be rounded to four  decimal places.

Sample Input

3 0 0 4 2 1

Sample Output

Case 1: 0.5000 Case 2: 0.5000

Hint

For example as the sample test one, there are three balls in the bag. The possibilities of the four possible situations are all 0.25. If there are no red balls in the bag, the possibility of the next ball are red is 0. If there is one red ball in the bag, the possibility is 1/3. If there are two red balls, the possibility is 2/3. Finally if all balls are red, the possibility is 1. So the answer is 0*(1/4)+(1/3)*(1/4)+(2/3)*(1/4)+1*(1/4)=0.5.

#include#include#include#includeusing namespace std;int main(){ int n,kase=0,p,q; double y; while(scanf("%d%d%d",&n,&p,&q)!=EOF) { printf("Case %d: %.4lf\n",++kase, (q+1.0)/(p+2.0) ); } return 0;}

这题要用页贝斯公式，概率论的内容，该理论一定要好好学，找机会仔细做做

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