BZOJ 3944: Sum [杜教筛]

3944: Sum

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总结见学习笔记(现在还没写23333)

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
using namespace std;
typedef long long ll;
#define pii pair<ll, ll>
#define fir first
#define sec second
const int N=1664512, U=1664510;
inline ll read(){
	char c=getchar(); ll x=0,f=1;
	while(c<'0' || c>'9') {if(c=='-')f=-1; c=getchar();}
	while(c>='0' && c<='9') {x=x*10+c-'0'; c=getchar();}
	return x*f;
}
 
bool notp[N]; int p[N/10], mu[N]; ll phi[N];
void sieve(int n) {
	mu[1] = phi[1] = 1;
	for(int i=2; i<=n; i++) {
		if(!notp[i]) p[++p[0]] = i, mu[i] = -1, phi[i] = i-1;
		for(int j=1; j <= p[0] && i*p[j] <= n; j++) {
			int t = i*p[j];
			notp[t] = 1;
			if(i % p[j] == 0) {mu[t] = 0; phi[t] = phi[i]*p[j]; break;}
			mu[t] = -mu[i]; phi[t] = phi[i]*(p[j]-1);
		}
		mu[i] += mu[i-1]; phi[i] += phi[i-1];
	}
}
ll n;
pii nul(-1, -1);
namespace ha {
	const int p = 1001001;
	struct meow{int ne; pii val; ll r;} e[30000];
	int cnt=1, h[p];
	inline void insert(ll x, pii &val) {
		ll u = x % p;
		for(int i=h[u];i;i=e[i].ne) if(e[i].r == x) return;
		e[++cnt] = (meow){h[u], val, x}; h[u]=cnt;
	}
	inline pii quer(ll x) {
		ll u = x % p;
		for(int i=h[u];i;i=e[i].ne) if(e[i].r == x) return e[i].val;
		return nul;
	}
} using ha::insert; using ha::quer;
 
pii dj_sieve(ll n) {
	if(n <= U) return make_pair(mu[n], phi[n]);
	if(quer(n) != nul) return quer(n);
	pii ans(1, n*(n+1)/2); ll r;
	for(ll i=2; i<=n; i=r+1) {
		r = n/(n/i);
		pii t = dj_sieve(n/i);
		ans = make_pair(ans.fir - t.fir * (r-i+1), ans.sec - t.sec * (r-i+1));
	}
	insert(n, ans);
	return ans;
}
int main() {
	freopen("in", "r", stdin);
	sieve(U);
	int T=read();
	while(T--) {
		n=read(); if(n==0) {puts("0 0"); continue;}
		pii t = dj_sieve(n);
		printf("%lld %lld\n", t.sec, t.fir);
	}
}