poj Prime Test

最新推荐文章于 2021-03-06 19:37:01 发布

转载最新推荐文章于 2021-03-06 19:37:01 发布 · 123 阅读

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原文链接：http://www.cnblogs.com/one--world--one--dream/archive/2011/11/05/2237297.html

本文介绍了一种高效判断大整数是否为素数的方法，并实现了若非素数则找到其最小素因子的功能。通过Miller-Rabin素性检测算法与Pollard's Rho因数分解算法，可以在较短时间内完成对特定范围内整数的素性判断及因数分解。

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Prime Test

Time Limit: 6000MS		Memory Limit: 65536K
Total Submissions: 21644		Accepted: 4911
Case Time Limit: 4000MS

Description

Given a big integer number, you are required to find out whether it's a prime number.

Input

The first line contains the number of test cases T (1 <= T <= 20 ), then the following T lines each contains an integer number N (2 <= N < 2⁵⁴).

Output

For each test case, if N is a prime number, output a line containing the word "Prime", otherwise, output a line containing the smallest prime factor of N.

Sample Input

2
5
10

Sample Output

Prime
2

#include"stdio.h"
#include"time.h"
#include"iostream"
#include <cstdlib>
using namespace std;
int pri[]={2,3,5,7,11,13,17,19,23,29};
__int64 gcd(__int64 a,__int64 b)
{
   while(b)
   {
       __int64 c=a%b;
       a=b;
       b=c;
   }
   return a;
}
__int64 product_mod(__int64 a,__int64 b,__int64 n){
   __int64 tmp=0;
   while(b){
       if(b&1){
           tmp+=a;
           if(tmp>=n)
               tmp-=n;
       }
       a<<=1;
       if(a>=n)a-=n;
       b>>=1;
   }
   return tmp;
}
__int64 power_mod(__int64 a,__int64 m,__int64 n)
{
   __int64 tmp=1;
   a%=n;
   while(m)
   {
       if(m&1) tmp=product_mod(tmp,a,n);
       a=product_mod(a,a,n);
       m>>=1;
   }
   return tmp;
}
bool Miller_Rabin(__int64 n)
{
   if(n<2)
       return false;
   if(n==2)
       return true;
   if(!(n&1))
       return false;
   __int64 k=0,i,j,m,a;
   m=n-1;
   while(!(m&1)) m>>=1,k++;
   for(i=0;i<10;i++)
   {
       if(pri[i]>=n)
           return true;
       a=power_mod(pri[i],m,n);
       if(a==1) continue;
       for(j=0;j<k;j++)
       {
           if(a==n-1)
               break;
           a=product_mod(a,a,n);
       }
       if(j==k)
           return false;
   }
   return true;
}
__int64 pollard_rho(__int64 c,__int64 n)
{
   __int64 i,x,y,k,d;
   i=1;
   x=y=rand()%n;
   k=2;
   do{
       i++;
       d=gcd(n+y-x,n);
       if(d>1&&d<n)
           return d;
       if(i==k) y=x,k<<=1;
       x=(product_mod(x,x,n)+n-c)%n;
   }while(y!=x);
   return n;
}
__int64 rho(__int64 n)
{
   if(Miller_Rabin(n))
       return n;
   __int64 t=n;
   while(t>=n)
       t=pollard_rho(rand()%(n-1)+1,n);
   __int64 a=rho(t);
   __int64 b=rho(n/t);
   return a<b?a:b;
}
int main()
{
   int t;
   scanf("%d",&t);
   while(t--)
   {
       __int64 n;
       scanf("%I64d",&n);
       if(Miller_Rabin(n))
           printf("Prime\n");
       else {
           printf("%I64d\n",rho(n));
       }

   }
   return 0;
}

转载于:https://www.cnblogs.com/one--world--one--dream/archive/2011/11/05/2237297.html