学步园

传送门:http://www.lydsy.com/JudgeOnline/problem.php?id=3529

其中

预处理sigma,u,在a固定的情况下就可以预处理F计算答案

考虑离线,按a升序排列询问

那么从 a->a‘ 的时候,对于满足

的d

用树状数组更新F的前缀和

Code:

#include<cstdio>
#include<iostream>
#include<algorithm>
#include<cctype>
using namespace std;
const int maxn=1e5+5;
int mx;
int d[maxn];
inline int lowbit(int x){return x&-x;}
int get(int x){
	int ans=0;
	while(x)ans+=d[x],x-=lowbit(x);
	return ans;
}
void updata(int x,int f){
	while(x<=mx)d[x]+=f,x+=lowbit(x);
}
struct qes{int n,m,a,id;bool operator<(const qes oth)const{return a<oth.a;}}Q[maxn];
int anss[maxn];
int getint(){
	int res=0;char c=getchar();
	while(!isdigit(c))c=getchar();
	while(isdigit(c))res=res*10+c-'0',c=getchar();
	return res;
}
bool notp[maxn];
int p[maxn],u[maxn];
pair<int,int> sig[maxn];
void init(int maxn){
	u[1]=1;
	for(int i=2;i<maxn;i++){
		if(!notp[i]){
			p[++p[0]]=i;u[i]=-1;
		}for(int j=1;i*p[j]<maxn&&j<=p[0];j++){
			notp[i*p[j]]=1;
			if(i%p[j]==0){
				u[i*p[j]]=0;break;
			}else u[i*p[j]]=-u[i];
		}
	}for(int i=1;i<maxn;i++)
	for(int j=i;j<maxn;j+=i)sig[j].first+=i;
	for(int i=1;i<maxn;i++)sig[i].second=i;
	sort(sig+1,sig+maxn);
}
int main(){
	int T=getint();
	for(int i=1;i<=T;i++){
		Q[i].n=getint();Q[i].m=getint();
		if(Q[i].n>Q[i].m)swap(Q[i].n,Q[i].m);
		Q[i].a=getint();Q[i].id=i;
		mx=max(mx,Q[i].n);
	}init(mx+1);
	sort(Q+1,Q+1+T);
	int lasta=1;
	for(int i=1;i<=T;i++){
		int newa=upper_bound(sig+1,sig+mx,make_pair(Q[i].a+1,-1))-sig-1;
		for(int j=lasta;j<=newa;j++)
		for(int k=sig[j].second;k<=mx;k+=sig[j].second)
			updata(k,sig[j].first*u[k/sig[j].second]);	
		for(int j=1,k;j<=Q[i].n;j=k+1){
			k=min(Q[i].n/(Q[i].n/j),Q[i].m/(Q[i].m/j));
			anss[Q[i].id]+=(get(k)-get(j-1))*(Q[i].n/j)*(Q[i].m/j);
		}lasta=newa+1;
	}for(int i=1;i<=T;i++)printf("%d\n",anss[i]&0x7fffffff);
	return 0;
}