1.5 迴文質數

Prime Palindromes

The number 151 is a prime palindrome because it is both a prime number and a palindrome (it is the same number when read forward as backward). Write a program that finds all prime palindromes in the range of two supplied numbers a and b (5 <= a < b <= 100,000,000); both a and b are considered to be within the range .

PROGRAM NAME: pprime

INPUT FORMAT

Line 1:

Two integers, a and b

SAMPLE INPUT (file pprime.in)

5 500

OUTPUT FORMAT

The list of palindromic primes in numerical order, one per line.

SAMPLE OUTPUT (file pprime.out)

5

7

11

101

131

151

181

191

313

353

373

383

/*
ID: xdzhbin1
LANG: C++
TASK: pprime
*/

#include <vector>
#include <fstream>
#include <iostream>
#include <cmath>
using namespace std;

//把10000以下的質數放入向量中
void putprime(vector<long>& v)
{
	v.push_back(2);
	int i,j;
	bool isprime;
	for(i=3; i<10000; i++)
	{
		isprime = true;
		for (j=0; j<v.size(); j++)
		{
			if (i%v[j]==0)
			{
				isprime = false;
				break;
			}
		}
		if (isprime)
		{
			v.push_back(i);
		}
	}
}

//判斷數字num是否爲質數
bool isprime(long num, vector<long>& v)
{
	int i=0;
	while(v[i]*v[i]<=num)
	{
		if(num % v[i] == 0)	//依次去除質數列表中的每一項
			return false;
		i++;
	}
	return true;
}

//判斷是否爲迴文
bool ispal(long num)
{
	long src = num;
	long renum = 0;
	while (num!=0)
	{
		renum = renum *10 + num%10;
		num /= 10;
	}
	return src == renum;
}

//遞歸產生位數爲n的迴文數(n>=2)
void genpal(long num, int n, int index, vector<long>& v)
{
	if ((n+1)/2==index)//已填充的數字已經到要產生位數的一半，因爲產生的是迴文，鏡像另一半
	{
		int temp = (n%2==0 ? num : (num/10));
		int retemp = 0, bits = 0;
		while (temp!=0)
		{
			retemp = retemp*10 + temp%10;
			bits++;
			temp /= 10;
		}
		if (n/2!=bits) return; //有前導的0
		v.push_back(num*(int)pow(10,bits)+retemp);
		return;
	}
	int i;
	for (i=0; i<=9; i++)
	{
		num = num*10 + i;
		genpal(num,n,index+1,v);
		num /= 10;
	}
}


int main()
{
	ifstream in("pprime.in",ios::in);
	ofstream out("pprime.out",ios::out);
	
	int start,end;
	in>>start>>end;
	vector<long> vprime,vpal; //質數列表和迴文列表
	putprime(vprime);

	int i;
	for(i=1; i<9; i++)
	{
		vpal.push_back(i);	//把一位的迴文放入迴文列表中
	}
	for(i=2; i<9; i++)
	{
		genpal(0,i,0,vpal);//產生迴文數
	}
	for(i=0; i<vpal.size(); i++)
	{
		if (vpal[i]>=start&&vpal[i]<=end&&isprime(vpal[i],vprime))
		{
			out<<vpal[i]<<endl;
		}
	}

	/*for(i=start; i<=end; i+=2)
	{
		if(ispal(i)&&isprime(i,vprime))
			out<<i<<endl;
	}*/
	return 0;
}