1015 Reversible Primes （20 分)

1015 Reversible Primes （20 分)

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

作者: CHEN, Yue

单位: 浙江大学

时间限制: 400 ms

内存限制: 64 MB

代码长度限制: 16 KB

题目大意

给出一个数n以及进制d，要求判断n以及n在d进制翻转后是否都是素数。

分析

读取n，判断是否为素数。如是则转换为相应进制再翻转，转换为10进制判断是否为素数。

代码

#include <iostream>
#include <vector>
#include <algorithm>
#include <deque>
#include <map>
#include <cstring>
#include <cmath>

using namespace std;

string change(int n,int radix){
    if(radix==1)
        return NULL;
    int m=0;
    string ans="";
    while(n>=pow(radix,m))m++;
    for(int i=m-1;i>=0;i--){
        int base=pow(radix,i);
        int d=n/base;
        n-=d*base;
        ans+=to_string(d);
    }
    return ans;
}

int go_back(string s,int radix){
    int n=0;
    int l=s.length();
    for(int i=0;i<l;i++){
        int d=s[i]-'0';
        n+=d*pow(radix,l-i-1);
    }
    return n;
}

bool isprime(int n){
    if(n<=1)
        return false;
    int k=sqrt(n);
    for(int i=2;i<=k;i++){
        if(n%i==0)
            return false;
    }
    return  true;
}
int main() {
    std::ios::sync_with_stdio(false);
    int n,radix;
    while(cin>>n&&n>0){
        cin>>radix;
        if(isprime(n)){
        string s=change(n,radix);
        reverse(s.begin(),s.end());
        //cout<<s<<endl;
        int ans=go_back(s,radix);
        //cout<<ans<<endl;
        if(isprime(ans))
            cout<<"Yes"<<endl;
        else
            cout<<"No"<<endl;
        } else cout<<"No"<<endl;
    }
}