poj 1811

模板题。

代码：

#include<ctime>
#include<iostream>
using namespace std;
long long factor[100],fac_top = -1;
//计算两个数的gcd
long long gcd(long long a,long long b)
{
	if(a==0)
		return b;
	long long c;
	while(b!=0)
	{
		c=b;
		b=a%b;
		a=c;
	}
	return a;
}
//ret = (a*b)%n (n<2^62)
long long muti_mod(long long a,long long b,long long n)
{
    long long  exp = a%n, res = 0;
    while(b)
	{
        if(b&1)
		{
            res += exp;
            if(res>n) res -= n;
        }
        exp <<= 1;
        if(exp>n) 
			exp -= n;
       
        b>>=1;
    }
    return res;
}
// ret = (a^b)%n
long long mod_exp(long long a,long long p,long long m)
{
    long long exp=a%m, res=1; //  
    while(p>1)
    {
        if(p&1)//
            res=muti_mod(res,exp,m);
        exp = muti_mod(exp,exp,m);
        p>>=1;
    }
    return muti_mod(res,exp,m);
}
//miller-rabin法测试素数, time 测试次数
bool miller_rabin(long long n, long long times)
{
    if(n==2)return 1;
    if(n<2||!(n&1))return 0;
   
    long long a, u=n-1, x, y;
    int t=0;
    while(u%2==0){
        t++;
        u/=2;
    }
    srand(time(0));
    for(int i=0;i<times;i++)
	{
        a = rand() % (n-1) + 1;
        x = mod_exp(a, u, n);
        for(int j=0;j<t;j++)
		{
            y = muti_mod(x, x, n);
            if ( y == 1 && x != 1 && x != n-1 )
                return false; //must not
            x = y;
        }
        if( y!=1) return false;
    }
    return true;
}

long long pollard_rho(long long n,int c)
{//找出一个因子
    long long x,y,d,i = 1,k = 2;
    srand(time(0));
    x = rand()%(n-1)+1;
    y = x;
    while(true) {
        i++;
         x = (muti_mod(x,x,n) + c) % n;
        d = gcd(y-x, n);
        if(1 < d && d < n)return d;
         if( y == x)       return n;
         if(i == k) {
            y = x;
             k <<= 1;
         }
    }
}
void findFactor(long long n,int k)
{//二分找出所有质因子，存入factor
    if(n==1)return;
    if(miller_rabin(n, 6))
	{
		factor[++fac_top] = n;
		return;
	}
	long long p = n;
	while(p >= n)
		p = pollard_rho(p,k--);//k值变化，防止死循环
	findFactor(p,k);
	findFactor(n/p,k);
}
int main()
{
    long long t,n,min;
    cin>>t;
    while(t--)
	{
        cin>>n;
        fac_top = min = -1;
        if(miller_rabin(n,10)) 
			cout<<"Prime"<<endl;
		else
		{
            findFactor(n,107);
            for(int i=0;i<=fac_top;i++){
               if(min<0||factor[i]<min)
                    min = factor[i];}
            cout<<min<<endl;
        }
    }
    return 0;
}