BZOJ 3667 Pollard-rho &Miller-Rabin

论O(1)快速乘和O(logn)快速乘的差距….

//By SiriusRen
#include <cstdio>
#include <algorithm>
using namespace std;
typedef long long ll;
ll shai[10]={2,3,5,7,11,13,17,19,23,29};
ll mul(ll a,ll b,ll p){
    ll d=((long double)a/p*b+1e-8);
    ll res=a*b-d*p;
    res=res<0?res+p:res;
    return res;
}
ll pow(ll x,ll y,ll mod){
    x%=mod;ll res=1;
    while(y){
        if(y&1)res=mul(res,x,mod);
        x=mul(x,x,mod),y>>=1;
    }return res;
}
bool check(ll a,ll n,ll r,int s){
    ll x=pow(a,r,n),pre=x;
    for(int i=1;i<=s;i++){
        x=mul(x,x,n);
        if(x==1&&pre!=1&&pre!=n-1)return 0;
        pre=x;
    }return x==1;
}
bool miller_rabin(ll n){
    if(n<=1)return 0;
    ll r=n-1,s=0;
    while(!(r&1))r>>=1,s++;
    for(int i=0;i<10;i++){
        if(shai[i]==n)return 1;
        if(!check(shai[i],n,r,s))return 0;
    }return 1;
}
ll gcd(ll x,ll y){return y?gcd(y,x%y):x;}
ll prime_factor(ll n,ll c){
    ll k=2,x=rand()%n,y=x,p=1;
    for(int i=1;p==1;i++){
        x=(mul(x,x,n)+c)%n;
        p=gcd(abs(x-y),n);
        if(i==k)y=x,k<<=1;
    }return p;
}
ll ans,xx;int cases;
void pollard_rho(ll n){
    if(n==1)return;
    if(miller_rabin(n)){ans=max(ans,n);return;}
    ll p=n;
    while(p==n)p=prime_factor(n,rand()%(n-1));
    pollard_rho(p),pollard_rho(n/p);
}
int main(){
    scanf("%d",&cases);
    while(cases--){
        ans=0,scanf("%lld",&xx),pollard_rho(xx);
        if(ans!=xx)printf("%lld
",ans);
        else puts("Prime");
    }
}


//By SiriusRen
#include <cstdio>
#include <algorithm>
using namespace std;
typedef unsigned long long ll;
ll shai[10]={2,3,5,7,11,13,17,19,23,29};
ll mul(ll x,ll y,ll mod){
    x%=mod;ll res=0;
    while(y){
        if(y&1)res=(res+x)%mod;
        x=(x+x)%mod;
        y>>=1;
    }return res;
}
ll pow(ll x,ll y,ll mod){
    x%=mod;ll res=1;
    while(y){
        if(y&1)res=mul(res,x,mod);
        x=mul(x,x,mod),y>>=1;
    }return res;
}
bool check(ll a,ll n,ll r,int s){
    ll x=pow(a,r,n),pre=x;
    for(int i=1;i<=s;i++){
        x=mul(x,x,n);
        if(x==1&&pre!=1&&pre!=n-1)return 0;
        pre=x;
    }return x==1;
}
bool miller_rabin(ll n){
    if(n<=1)return 0;
    ll r=n-1,s=0;
    while(!(r&1))r>>=1,s++;
    for(int i=0;i<10;i++){
        if(shai[i]==n)return 1;
        if(!check(shai[i],n,r,s))return 0;
    }return 1;
}
ll gcd(ll x,ll y){return y?gcd(y,x%y):x;}
ll prime_factor(ll n,ll c){
    ll k=2,x=rand()%n,y=x,p=1;
    for(int i=1;p==1;i++){
        x=(mul(x,x,n)+c)%n;
        p=gcd(abs((long long)x-(long long)y),(long long)n);
        if(i==k)y=x,k<<=1;
    }return p;
}
ll ans,xx;int cases;
void pollard_rho(ll n){
    if(n==1)return;
    if(miller_rabin(n)){ans=max(ans,n);return;}
    ll p=n;
    while(p==n)p=prime_factor(n,rand()%(n-1));
    pollard_rho(p),pollard_rho(n/p);
}
int main(){
    scanf("%d",&cases);
    while(cases--){
        ans=0,scanf("%llu",&xx),pollard_rho(xx);
        if(ans!=xx)printf("%llu
",ans);
        else puts("Prime");
    }
}