【BZOJ-3667】Rabin_Miller算法 随机化判素数

#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cstring>
#include<ctime>
#include<cstdlib>
using namespace std;
long long read()
{
    long long x=0,f=1; char ch=getchar();
    while (ch<‘0‘ || ch>‘9‘) {if (ch==‘-‘) f=-1; ch=getchar();}
    while (ch>=‘0‘ && ch<=‘9‘) {x=x*10+ch-‘0‘; ch=getchar();}
    return x*f;
}
long long X,maxz;
long long gcd(long long a,long long b)
{
    if (b==0) return a;
    return gcd(b,a%b);
}
//long long mul(long long a,long long b,long long p)
//{
//    if (b==0) return 0; if (b==1) return a%p;
//    long long re;
//    re=mul(a,b>>1,p);
//    if ((b&1)==1) return (re+re+a)%p;
//             else return (re+re)%p;
//}
long long mul(long long a,long long b,long long p)
{
    long long tmp=(a*b-(long long)((long double)a/p*b+1e-8)*p);
    return tmp<0?tmp+p:tmp;
}
long long quick_pow(long long a,long long b,long long p)
{
    long long ans=1; a%=p;
    for (long long i=b; i; i>>=1,a=mul(a,a,p))
        if (i&1) ans=mul(ans,a,p);
    return ans;
}
bool check(long long a,long long n,long long r,long long s)
{
    long long ans=quick_pow(a,r,n),p=ans;
    for(int i=1; i<=s; i++)
    {
        ans=mul(ans,ans,n);
        if(ans==1&&p!=1&&p!=n-1)return 1;
        p=ans;
    }
    if(ans!=1)return 1;else return 0;
}
bool Robin_Miller(long long x)
{
    if(x<=1) return 0;
    if(x==2) return 1;
    if(x%2==0) return 0;
    long long r=x-1,s=0;
    while(r%2==0) r/=2,s++;
    for(int i=0; i<20; i++)
        if(check(rand()%(x-1)+1,x,r,s))
            return 0;
    return 1;
}
long long Rho(long long x,long long t)
{
    long long k=2,a=rand()%x,b=a,p=1;
    for(long long i=1; p==1; i++)
    {
        a=(mul(a,a,x)+t)%x;
        p=b>a?b-a:a-b;
        p=gcd(x,p);
        if(i==k) b=a,k+=k;
    }
    return p;
}
void work(long long x)
{
    if(x==1) return;
    if(Robin_Miller(x)){maxz=max(x,maxz);return;}
    long long t=x;
    while(t==x) t=Rho(x,rand()%(x-1)+1);
    work(t); work(x/t);
}
int main()
{
    int n;n=read();
    while (n--)
        {
            X=read(); maxz=0;
            work(X);
            if (maxz==X) puts("Prime");
                else printf("%lld\n",maxz);
        }
    return 0;
}