luoguP4213 【模板】杜教篩（Sum）杜教篩

連接

luogu

思路

爲了作hdu來學杜教篩。
杜教篩模板題。
卡常數，我加了register竟然跑到不到800ms。
太深了。

代碼

// luogu-judger-enable-o2
#include <bits/stdc++.h>
#define ll long long
using namespace std;
const int _=5000030;
int vis[_],pri[_],cnt,N,limit,mu[_];
ll phi[_];
unordered_map<int,ll> ans_phi;
unordered_map<int,ll> ans_mu;
inline void Euler() {
    vis[1]=phi[1]=mu[1]=1;
    for(register int i=1;i<=limit;++i) {
        if(!vis[i]) pri[++cnt]=i,mu[i]=-1,phi[i]=i-1;
        for(register int j=1;j<=cnt&&i*pri[j]<=limit;++j) {
            vis[i*pri[j]]=1;
            if(i%pri[j]==0) {
                mu[i*pri[j]]=0;
                phi[i*pri[j]]=phi[i]*pri[j];
                break;
            } else {
                mu[i*pri[j]]=-mu[i];
                phi[i*pri[j]]=phi[i]*(pri[j]-1);
            }
        }
    }
    for(register int i=2;i<=limit;++i) mu[i]+=mu[i-1],phi[i]+=phi[i-1];
}
ll Solvephi(register int n) {
    if(n<=limit) return phi[n];
    if(ans_phi[n]) return ans_phi[n];
    register ll tmp=1LL*n*(n+1)/2;
    for(register int l=2,r;l<=n;l=r+1)
        r=n/(n/l),tmp-=Solvephi(n/l)*(r-l+1);
    return ans_phi[n]=tmp;
}
ll Solvemu(register int n) {
    if(n<=limit) return mu[n];  
    if(ans_mu[n]) return ans_mu[n];
    register ll tmp=1;
    for(register int l=2,r;l<=n;l=r+1)
        r=n/(n/l),tmp-=Solvemu(n/l)*(r-l+1);
    return ans_mu[n]=tmp;
}
int main() {
    int T;cin>>T;
    limit=5000000;
    Euler();
    while(T --> 0) {
        cin>>N;
        printf("%lld %lld\n",Solvephi(N),Solvemu(N));
    }
    return 0;
}