Reversible Primes (20)stoi应用

最新推荐文章于 2022-09-09 23:13:55 发布

原创最新推荐文章于 2022-09-09 23:13:55 发布 · 420 阅读

0 ·

CC 4.0 BY-SA版权

PAT 专栏收录该内容

12 篇文章

订阅专栏

本文介绍了一种算法，用于检测一个给定的正整数是否为可逆素数，即该数及其在指定进制下的反转数均为素数。通过示例说明了算法的工作原理，并提供了完整的C++实现代码。

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

int stoi (const string&  str, size_t* idx = 0, int base = 10);//将字符转化为整形
int stol (const string&  str, size_t* idx = 0, int base = 10);//将字符转化为long
int stoul (const string&  str, size_t* idx = 0, int base = 10);//将字符转化为unsigned long
int stoll (const string&  str, size_t* idx = 0, int base = 10);//将字符转化为long long
int stoull (const string&  str, size_t* idx = 0, int base = 10);//将字符转化为unsigned long long

str表示原始字符串，idx表示s中第一个非字符数值下标，默认为0，若字符中都是数字应该输入nullptr，base是转换所用基数默认为10

例如str=“110” 用stoi（str，nullptr，2）就转化为了整数6

题意：

给定一个数N，给定一个基数D若N为素数并且将N转化为D进制后反向N’，也为素数

例如23 2

23为素数，将23转化为2进制为10111，反向后为11101是29也为素数所以输出Yes

#include<iostream>
#include<string>
using namespace std;

bool isprime(int n)//判断素数
{
	if(n<2)
		return false;
	for(int i=2;i<=n/2;i++)
		if(n%i==0)
			return false;
	return true;
}
int reverse(int n,int radix)//按进制反向
{
	string s;
	while(n>0)//求反向radix进制数
	{
		s.push_back(n%radix+'0');
		n/=radix;
	}
	return stoi(s,nullptr,radix);
	
}
int main(){
	int n,radix;
	while(cin>>n&&n>= 0)
	{
		cin>>radix;
		if(isprime(n)&&isprime(reverse(n,radix)))
			cout<<"Yes"<<endl;
		else
			cout<<"No"<<endl;		
	}
	return 0;
}