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7-1 Sexy Primes (20分)

Sexy primes are pairs of primes of the form (p, p+6), so-named since "sex" is the Latin word for "six". (Quoted from http://mathworld.wolfram.com/SexyPrimes.html)

Now given an integer, you are supposed to tell if it is a sexy prime.

Input Specification:

Each input file contains one test case. Each case gives a positive integer $N (≤10​^8​​)$.

Output Specification:

For each case, print in a line Yes if N is a sexy prime, then print in the next line the other sexy prime paired with N (if the answer is not unique, output the smaller number). Or if N is not a sexy prime, print No instead, then print in the next line the smallest sexy prime which is larger than N.

Sample Input 1:

47

Sample Output 1:

Yes
41

Sample Input 2:

21

Sample Output 2:

No
23

题目限制

时间限制内存限制
400 ms64 MB

image.png

题目大意:

一个数x是“sexy prime”指的是x是质数且x-6或x+6也是质数。给出一个数,判断这个数是不是“sexy prime”,如果是的话输出与这个数配对的另一个“sexy prime”,如果有多个就输出小的那个(也就是x-6),如果不是就输出最小的比这个数大的“sexy prime”。

算法思路:

使用isPrime函数判断一个数N是否为素数,然后对于输入的数字N,首先判断N和N-6是否为素数,如果是,输出Yes和N-6,否则判断N和N+6是否为素数,如果是,输出Yes和N+6,如果都不是,说明N不是sexy prime,输出No,然后从N+1开始遍历每一个数字i,判断i和i-6是否为素数,如果是输出i并结束程序,否则判断i和i+6是否为素数,如果是输出i并结束程序。

isPrime函数
bool isPrime(int N){
    if(N<=1) return false;
    int sqrtn = (int)sqrt(N*1.0);
    for (int i = 2; i <= sqrtn; ++i) {
        if(N%i==0) return false;
    }
    return true;
}

提交结果:

image.png

AC代码:

#include<cstdio>
#include <cmath>

using namespace std;

bool isPrime(int N){
    if(N<=1) return false;
    int sqrtn = (int)sqrt(N*1.0);
    for (int i = 2; i <= sqrtn; ++i) {
        if(N%i==0) return false;
    }
    return true;
}

int main(){
    int N;
    scanf("%d",&N);
    if(isPrime(N)&&isPrime(N-6)){
        // N是sexy prime,找到仅次于N的sexy prime
        printf("Yes\n%d",N-6);
    } else if(isPrime(N)&&isPrime(N+6)){
        printf("Yes\n%d",N+6);
    } else {
        // N不是sexy prime,找到仅大于N的sexy prime
        printf("No\n");
        for (int i = N+1; ; ++i) {
            if(isPrime(i)&&isPrime(i-6)){
                printf("%d",i);
                break;
            }
            if(isPrime(i)&&isPrime(i+6)){
                printf("%d",i);
                break;
            }
        }
    }
    return 0;
}


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