BZOJ 3667 Pollard-rho &Miller-Rabin

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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\n",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\n",ans);        else puts("Prime");    }}

这里写图片描述

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