pollard rho



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poj2429,快速乘，不用TL。。。

#include<iostream>
#include<ctime>
#include<algorithm>
#include<cmath>
#include<cstdio>
using namespace std;
long long p,f[1000],ans;
long long f2[1000],q;
long long mod2(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;
}

long long pow_mod(long long a,long long b,long long m)
{
    long long exp=a%m, res=1;
    while(b>=1){
        if(b&1)
            res=mod2(res,exp,m);
        exp = mod2(exp,exp,m);
        b>>=1;
    }
    return res;
}
bool miller(long long k,long long d,long long n,long long a)
{
    if(n==2||n==a) return true;
    if(!(n&1)) return false;
    long long i,t=pow_mod(a,d,n);
    if(t==1) return true;
    for(i=0;i<k;i++)
    {
        if(t==n-1) return true;
        t=(t*t)%n;
    }
    return false;
}
bool judge(long long n)
{
    if(n<2) return false;
    long long k=0,d=n-1;
    while(!(d&1))
    {
        k++;
        d>>=1;
    }
    if(n<1373653)
    {
        if(miller(k,d,n,2)&&miller(k,d,n,3)) return true;
        return false;
    }
    if(n<9080191)
    {
        if(miller(k,d,n,31)&&miller(k,d,n,73)) return true;
        return false;
    }
    if(n<4759123141)
    {
        if(miller(k,d,n,2)&&miller(k,d,n,3)&&miller(k,d,n,5)&&miller(k,d,n,11)) return true;
        return false;
    }
    if(n<2152302898747)
    {
        if(miller(k,d,n,2)&&miller(k,d,n,3)&&miller(k,d,n,5)&&miller(k,d,n,7)&&miller(k,d,n,11)) return true;
        return false;
    }
    else
    {
        if(miller(k,d,n,2)&&miller(k,d,n,3)&&miller(k,d,n,5)&&miller(k,d,n,7)&&miller(k,d,n,11)&&miller(k,d,n,31)&&miller(k,d,n,61)&&miller(k,d,n,73)) return true;
        return false;
    }
}
long long gcd(long long a,long long b){
    long long c;
    while(b){
        c=b; b=a%b; a=c;
    }
    return a;
}
long long pollard_rho(long long n,long long k){
    srand(time(0));
    long long x=rand()%(n-1)+1;
    long long i=1,t=2,y=x,d;
    while(1){
        i++;
        x=(mod2(x,x,n)+k)%n;
        d=gcd(y-x,n);
        if(d>1 && d<n) return d;
        if(x==y) return n;
        if(t==i) y=x,t<<=1;
    }
}
void get_factor(long long n,long long k){
    if(judge(n)){
        f[p++]=n;
       return ;
    }
    long long h=n;
    while(h>=n)
        h=pollard_rho(h,k--);
    get_factor(h,k);
    get_factor(n/h,k);
}
void dfs(long long i,long long x,long long k){
    if(i>q) return ;
    if(x>ans && x<=k) ans=x;
    dfs(i+1,x,k);
    x*=f2[i];
    if(x>ans && x<=k) ans=x;
    dfs(i+1,x,k);
}
int main(int argc, char** argv) {
    long long m,n,k;
    while(scanf("%lld%lld",&m,&n)!=-1){
        if(m==n){
            printf("%lld %lld\n",m,n); continue;
        }
        k=n/m; p=0; q=0; ans=1;
        get_factor(k,180);
        sort(f,f+p);
        f2[0]=f[0];
        for(int i=0;i<p-1;i++)
            if(f[i]==f[i+1]) f2[q]*=f[i+1];
            else{
                q++; f2[q]=f[i+1];
            }
        long long tmp=(long long)sqrt(k*1.0);
        dfs(0,1,tmp);
        printf("%lld %lld\n",m*ans,k/ans*m);
    }
    return 0;
}