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ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#606059 | #998. 素数分解 | Yoshinow2001 | AC ✓ | 9131ms | 3856kb | C++23 | 2.5kb | 2024-10-02 21:52:04 | 2024-10-02 21:52:10 |
Judging History
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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Test #1:
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Test #29:
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