1015. Reversible Primes (20)

A reversible prime in any number system is a prime whose "reverse" in that number system is also a prime. For example in the decimal system 73 is a reversible prime because its reverse 37 is also a prime.

Now given any two positive integers N (< 10⁵) and D (1 < D <= 10), you are supposed to tell if N is a reversible prime with radix D.

Input Specification:

The input file consists of several test cases. Each case occupies a line which contains two integers N and D. The input is finished by a negative N.

Output Specification:

For each test case, print in one line "Yes" if N is a reversible prime with radix D, or "No" if not.

Sample Input:

73 10
23 2
23 10
-2

Sample Output:

Yes
Yes
No

 

思路：先說一下題目的意思，判斷該十進制數N在D進制下的反轉再轉爲十進制是不是質數，好比sample中的23在二進制的反轉就是11101(原本是10111)，再轉爲10進制就是29，是質數。

因此咱們要作的就是先把N轉爲D進製表示，反轉，再轉回十進制進行判斷。

 1 import java.math.BigInteger;
 2 import java.util.*;
 3 
 4 public class Main {
 5 
 6     private static int revInRadixD(int num, int D) {
 7         StringBuilder rev = new StringBuilder();
 8         int shang = num;
 9         while (shang != 0) {
10             rev.append(shang % D);
11             shang /= D;
12 
13         }
14         int result = 0;
15         int len = rev.length();
16         for (int i = 0; i < len; i++) {
17             result += (rev.charAt(i) - '0') * Math.pow(D, len - 1 - i);
18         }
19         return result;
20     }
21 
22     private static boolean isPrime(int num) {
23         if (num < 2) return false;
24         for (int i = 2; i <= Math.sqrt(num); i++) {
25             if (num % i == 0) {
26                 return false;
27             }
28         }
29         return true;
30     }
31 
32     public static void main(String[] args) {
33         Scanner in = new Scanner(System.in);
34         while (in.hasNext()) {
35             int N = in.nextInt();
36             if (N < 0) return;
37             int D = in.nextInt();
38             boolean isPrime = isPrime(N) && isPrime(revInRadixD(N, D));
39             System.out.println(isPrime ? "Yes" : "No");
40         }
41 
42     }
43 }