PAT甲级 1015 Reversible Primes (20 分)

最新推荐文章于 2022-09-09 23:13:55 发布

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这篇博客介绍了一个编程问题，涉及判断一个正整数在给定基数下是否为可逆质数，即其反转数是否同样为质数。通过输入两个正整数N（小于10^5）和D（1到10），程序会检查N是否在基数D下为可逆质数，并输出Yes或No。示例中，73在十进制下是可逆质数，因为它的反转37也是质数。代码实现包括了质数判断函数和反转判断函数，用于解决这个问题。

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:

Sample Output:

Yes
Yes
No

#include <iostream>

using namespace std;
typedef long long LL;

bool isPrime(LL d) {
    if (d < 2) return false;
    for (LL i = 2; i * i <= d; ++i) {
        if (d % i == 0)
            return false;
    }
    return true;
}

bool get(LL a, LL b) {
    if (!isPrime(a))
        return false;
    LL res = 0;
    while (a) {
        res = res * b + a % b;
        a = a / b;
    }
    return isPrime(res);
}

int main() {
    LL a, b;
    while (cin >> a, a >= 0) {
        cin >> b;
        if (get(a, b))
            puts("Yes");
        else
            puts("No");
    }
    return 0;
}