《内蒙古自治区第十二届大学生程序设计竞赛试题_D: 正品的概率》

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解题思路，一个是 贝叶斯公式和 最大公约数的问题
（图是盗的:原连接_  https://blog.csdn.net/hy971216/article/details/78633375  ）

 1 import java.math.BigInteger;
 2 import java.util.Scanner;
 3 
 4 public class Main {
 5     
 6     public static BigInteger getPow(BigInteger a,BigInteger n){
 7         BigInteger res = new BigInteger("1");
 8         for(int i=1;i<=n.intValue();i++){
 9             res = res.multiply(a);
10         }
11         return res;
12     }
13     
14     public static void main(String[] args) {
15         
16         Scanner cin = new Scanner(System.in);
17         while(cin.hasNext()){
18             BigInteger m = new BigInteger(cin.next());
19             BigInteger n = new BigInteger(cin.next());
20             BigInteger k = new BigInteger(cin.next());
21             
22             BigInteger res = m.add(n.multiply(getPow(new BigInteger("2"), k)));
23             BigInteger gcd = res.gcd(m);
24             System.out.println(m.divide(gcd)+"/"+res.divide(gcd));
25         }
26         
27     }
28 
29 }