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QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#606059#998. 素数分解Yoshinow2001AC ✓9131ms3856kbC++232.5kb2024-10-02 21:52:042024-10-02 21:52:10

Judging History

This is the latest submission verdict.

  • [2024-10-02 21:52:10]
  • Judged
  • Verdict: AC
  • Time: 9131ms
  • Memory: 3856kb
  • [2024-10-02 21:52:04]
  • Submitted

answer

#include<bits/stdc++.h>
#define rep(i,a,b) for(int i=(a);i<=(b);i++)
// #define endl '\n'
#define fastio ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0)
using namespace std;
typedef __int128 ll;


ll get(){
    string s;
    cin>>s;
    __int128 r=0;
    auto len=s.length();
    for(int i=0;i<len;i++)r=r*10+s[i]-'0';
    return r;
};
string ptr(__int128 x){
    if(x==0)return "0";
    string s;
    while(x){
        s+=(char)(x%10+'0');
        x/=10;
    }
    reverse(s.begin(),s.end());
    return s;
};
std::mt19937_64 rng {std::chrono::steady_clock::now().time_since_epoch().count()};//全局初始化

ll mul(ll a,ll b,ll mod){
	ll ans = 0;
	a %= mod,b %= mod;
	for (;b;a = a * 10000000 % mod,b /= 10000000) ans = (ans + a * (b % 10000000)) % mod;
	return ans;
}
ll ksm(ll a,ll b,ll p){
    ll ret=1;
    for(;b;b>>=1,a=mul(a,a,p))if(b&1)ret=mul(ret,a,p);
    return ret;
}
bool Miller_Rabin(const ll & p){
    if(p<3||(p&1)==0)return p==2;
    ll s,a,k=0,t=p-1;
    while(!(t&1)){t>>=1;k++;}
    // cout<<"check ml"<<endl;
    for(int tc=1;tc<=20;tc++){
        a=rng()%(p-2)+2;//[2,p-1]
        s=ksm(a,t,p);
        if(s==1||s==p-1)continue;
        for(int i=0;i<k-1;i++){
            s=mul(s,s,p);
            if(s==p-1)break;
        }
        if(s!=p-1)return false;
    }
    return true;
}
vector<ll> decom;
ll Pollard_Rho(const ll & x){
    // cout<<"pr on "<<ptr(x)<<endl;
    auto f=[&](ll x,ll c,ll MOD){return (mul(x,x,MOD)+c)%MOD;};
    auto abs=[&](ll x){return x>0?x:-x;};
    ll c=rng()%(x-2)+1;
    ll s=f(0,c,x),t=f(s,c,x);
    constexpr int STEP=128;
    while(s!=t){
        ll prod=1;
        for(int _=0;_<STEP;_++){
            ll val=abs(s-t);
            prod=mul(prod,val,x);
            s=f(s,c,x);t=f(f(t,c,x),c,x);
            if(prod==0){
                ll d=__gcd(val,x);
                if(1<d&&d<x)return d;
            }
        }
        ll d=__gcd(prod,x);
        if(1<d&&d<x)return d;
        s=f(s,c,x);t=f(f(t,c,x),c,x);
    }
    // assert(false);
    return x;
}
void solve(ll x){
    if(x<2)return;
    if(Miller_Rabin(x)){
        // cout<<"prime :"<<ptr(x)<<endl;
        decom.push_back(x);
        return;
    }
    ll p=x;
    // cout<<"pr"<<endl;
    while(p==x)p=Pollard_Rho(x);
    while(x%p==0)x/=p;
    solve(x);solve(p);
}
int main(){
    fastio;
    ll n=get();
    solve(n);
    if(decom[0]>decom[1])swap(decom[0],decom[1]);
    cout<<ptr(decom[0])<<' '<<ptr(decom[1]);
    return 0;
}

Details

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