BZOJ 4522 Pollard-rho+exgcd

思路:
N=P*Q
求出来P和Q 模拟就好…

//By SiriusRen
#include <cstdio>
#include <algorithm>
using namespace std;
typedef long long ll;
ll shai[10]={2,3,5,7,11,13,17,19,21,23};
ll mul(ll x,ll y,ll mod){
    x%=mod;ll res=0;
    while(y){
        if(y&1)res=(x+res)%mod;
        (x<<=1)%=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 x){
    if(x<=1)return 0;
    ll r=x-1;int s=0;
    while(!(r&1))r>>=1,s++;
    for(int i=0;i<10;i++){
        if(x==shai[i])return 1;
        if(!check(shai[i],x,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 P,Q,R,E,N,C,X,Y;
void pollard_rho(ll x){
    if(x==1)return;
    if(miller_rabin(x)){P=x;return;}
    ll p=x;
    while(p==x)p=prime_factor(x,rand()%(x-1));
    pollard_rho(p),pollard_rho(x/p);
}
ll exgcd(ll a,ll b,ll &x,ll &y){
    if(!b)x=1,y=0;
    else exgcd(b,a%b,y,x),y-=x*(a/b);
}
int main(){
    scanf("%lld%lld%lld",&E,&N,&C);
    pollard_rho(N),Q=N/P,R=(P-1)*(Q-1);
    exgcd(E,R,X,Y),X=(X+R)%R;
    printf("%lld %lld
",X,pow(C,X,N));
}

这里写图片描述

原文地址:https://www.cnblogs.com/SiriusRen/p/6532029.html