P4718 【模板】Pollard-Rho算法

不知道为什么原来的板子一直T。
所以换了个板子。
讲真，觉得原来的板子没问题啊啊啊啊。

#include<iostream>
#include<cstdio>
#include<cstring>
#include<string>
#include<algorithm>
#include<cstdlib>
#include<ctime>
#define ll long long
using namespace std;
const int s=8;
ll maxx=0;

ll mult_mod(ll a,ll b,ll p)
{
    a%=p,b%=p;
    ll c=(long double)a*b/p;
    ll ans=a*b-c*p;
    if(ans<0) ans+=p;
    else if(ans>=p) ans-=p;
    return ans;
}


ll pow_mod(ll a,ll n,ll p)
{
    ll ans=1;
    a%=p;
    while(n)
    {
        if(n&1) ans=mult_mod(ans,a,p);
        a=mult_mod(a,a,p);
        n>>=1;
    }
    return ans;
}

bool check(ll a,ll n, ll x,ll t)
{
    ll ret = pow_mod(a,x,n);
    ll last=ret;
    for(int i=1;i<=t;i++)
    {
        ret=mult_mod(ret,ret,n);
        if(ret==1&&last!=1&&last!=n-1) return true;
        last=ret;
    }
    if(ret!=1) return true;
    else return false;
}

bool Miller_Rabin(ll n)
{
    if(n<2) return false;
    if(n==2) return true;
    if((n&1)==0) return false;

    ll x=n-1;
    ll t=0;
    while((x&1)==0)
    {
        x>>=1;
        t++;
    }

    srand(time(NULL));

    for(int i=0;i<s;i++)
    {
        ll a=rand()%(n-1)+1;
        if(check(a,n,x,t))
            return false;
    }
    return true;
}

ll gcd(ll a,ll b)
{
    ll t;
    while(b)
    {
        t=a;
        a=b;
        b=t%b;
    }
    if(a>=0) return a;
    else return -a;
}

ll Pollard_rho(ll x)
{

    ll s=0,t=0,c=rand()%(x-1)+1;
    ll step=0,goal=1;
    ll val=1;
    for(goal=1;;goal<<=1,s=t,val=1)
    {
        for(step=1;step<=goal;++step)
        {
            t=(mult_mod(t,t,x)+c)%x;
            val=mult_mod(val,abs(t-s),x);
            if((step%127)==0)
            {
                ll d=gcd(val,x);
                if(d>1)
                    return d;
            }
        }
        ll d=gcd(val,x);
        if(d>1)
            return d;
    }
}

void findfac(ll n)
{
    if(n==1) return ;
    if(n<=maxx) return ;
    if(Miller_Rabin(n))
    {
        maxx=max(maxx,n);
        return ;
    }

    ll p=n;
    while(p>=n) p=Pollard_rho(n);
    while(n%p==0)n/=p;
    findfac(n);
    findfac(p);
}

int main(void)
{
    int t;
    cin>>t;
    while(t--)
    {
        ll n;
        scanf("%lld",&n);
        maxx=0;
        findfac(n);
        if(maxx==n) printf("Prime\n");
        else printf("%lld\n",maxx);
    }
    return 0;
}

两个差不多，一个的t上来就随机化了。

#include<iostream>
#include<cstdio>
#include<cstring>
#include<string>
#include<algorithm>
#include<cstdlib>
#include<ctime>
#define ll long long
using namespace std;
const int s=8;
ll maxx=0;

ll mult_mod(ll a,ll b,ll p)
{
    a%=p,b%=p;
    ll c=(long double)a*b/p;
    ll ans=a*b-c*p;
    if(ans<0) ans+=p;
    else if(ans>=p) ans-=p;
    return ans;
}


ll pow_mod(ll a,ll n,ll p)
{
    ll ans=1;
    a%=p;
    while(n)
    {
        if(n&1) ans=mult_mod(ans,a,p);
        a=mult_mod(a,a,p);
        n>>=1;
    }
    return ans;
}

bool check(ll a,ll n, ll x,ll t)
{
    ll ret = pow_mod(a,x,n);
    ll last=ret;
    for(int i=1;i<=t;i++)
    {
        ret=mult_mod(ret,ret,n);
        if(ret==1&&last!=1&&last!=n-1) return true;
        last=ret;
    }
    if(ret!=1) return true;
    else return false;
}

bool Miller_Rabin(ll n)
{
    if(n<2) return false;
    if(n==2) return true;
    if((n&1)==0) return false;

    ll x=n-1;
    ll t=0;
    while((x&1)==0)
    {
        x>>=1;
        t++;
    }

    srand(time(NULL));

    for(int i=0;i<s;i++)
    {
        ll a=rand()%(n-1)+1;
        if(check(a,n,x,t))
            return false;
    }
    return true;
}

ll gcd(ll a,ll b)
{
    ll t;
    while(b)
    {
        t=a;
        a=b;
        b=t%b;
    }
    if(a>=0) return a;
    else return -a;
}

ll Pollard_rho(ll x)
{

    ll s=0,t=rand(),c=rand()%(x-1)+1;
    ll step=0,goal=1;
    ll val=1;
    for(goal=1;;goal<<=1,s=t,val=1)
    {
        for(step=1;step<=goal;++step)
        {
            t=(mult_mod(t,t,x)+c)%x;
            val=mult_mod(val,abs(t-s),x);
            if((step%127)==0)
            {
                ll d=gcd(val,x);
                if(d>1)
                    return d;
            }
        }
        ll d=gcd(val,x);
        if(d>1)
            return d;
    }
}

void findfac(ll n)
{
    if(n==1) return ;
    if(n<=maxx) return ;
    if(Miller_Rabin(n))
    {
        maxx=max(maxx,n);
        return ;
    }

    ll p=n;
    while(p>=n) p=Pollard_rho(n);
    while(n%p==0)n/=p;
    findfac(n);
    findfac(p);
}

int main(void)
{
    int t;
    cin>>t;
    while(t--)
    {
        ll n;
        scanf("%lld",&n);
        maxx=0;
        findfac(n);
        if(maxx==n) printf("Prime\n");
        else printf("%lld\n",maxx);
    }
    return 0;
}

不剪枝也比原来快啊。。。为啥。。。

#include<iostream>
#include<cstdio>
#include<cstring>
#include<string>
#include<algorithm>
#include<cstdlib>
#include<ctime>
#define ll long long
using namespace std;
const int s=8;
ll maxx=0;

ll mult_mod(ll a,ll b,ll p)
{
    a%=p,b%=p;
    ll c=(long double)a*b/p;
    ll ans=a*b-c*p;
    if(ans<0) ans+=p;
    else if(ans>=p) ans-=p;
    return ans;
}


ll pow_mod(ll a,ll n,ll p)
{
    ll ans=1;
    a%=p;
    while(n)
    {
        if(n&1) ans=mult_mod(ans,a,p);
        a=mult_mod(a,a,p);
        n>>=1;
    }
    return ans;
}

bool check(ll a,ll n, ll x,ll t)
{
    ll ret = pow_mod(a,x,n);
    ll last=ret;
    for(int i=1;i<=t;i++)
    {
        ret=mult_mod(ret,ret,n);
        if(ret==1&&last!=1&&last!=n-1) return true;
        last=ret;
    }
    if(ret!=1) return true;
    else return false;
}

bool Miller_Rabin(ll n)
{
    if(n<2) return false;
    if(n==2) return true;
    if((n&1)==0) return false;

    ll x=n-1;
    ll t=0;
    while((x&1)==0)
    {
        x>>=1;
        t++;
    }

    srand(time(NULL));

    for(int i=0;i<s;i++)
    {
        ll a=rand()%(n-1)+1;
        if(check(a,n,x,t))
            return false;
    }
    return true;
}

ll gcd(ll a,ll b)
{
    ll t;
    while(b)
    {
        t=a;
        a=b;
        b=t%b;
    }
    if(a>=0) return a;
    else return -a;
}

ll Pollard_rho(ll x)
{

    ll s=0,t=0,c=rand()%(x-1)+1;
    ll step=0,goal=1;
    ll val=1;
    for(goal=1;;goal<<=1,s=t,val=1)
    {
        for(step=1;step<=goal;++step)
        {
            t=(mult_mod(t,t,x)+c)%x;
            val=mult_mod(val,abs(t-s),x);
            if((step%127)==0)
            {
                ll d=gcd(val,x);
                if(d>1)
                    return d;
            }
        }
        ll d=gcd(val,x);
        if(d>1)
            return d;
    }
}
ll fac[200],tot=0;

void findfac(ll n)
{
    if(n==1) return ;
    //if(n<=maxx) return ;
    if(Miller_Rabin(n))
    {
        fac[++tot]=n;
        return ;
    }

    ll p=n;
    while(p>=n) p=Pollard_rho(n);
    while(n%p==0)n/=p;
    findfac(n);
    findfac(p);
}

int main(void)
{
    int t;
    cin>>t;
    while(t--)
    {
        ll n;
        scanf("%lld",&n);
        if(Miller_Rabin(n))
        {
            printf("Prime\n");
            continue;
        }

        maxx=0;
        tot=0;
        findfac(n);
        for(int i=1;i<=tot;i++)
            maxx=max(maxx,fac[i]);
        printf("%lld\n",maxx);
    }
    return 0;
}