[BZOJ3529] [SDOI2014] 数表 - 莫比乌斯反演 - 树状数组

来源：互联网发布：工厂跟单软件编辑：程序博客网时间：2024/06/05 01:56

具体怎么反演的请看POPOQQQ大爷的莫比乌斯反演论文TATATAT

然后注意，当用到函数F(i)的时候再将函数筛入树状数组里。。

时间复杂度O(n log^2 n+q√n log n)

如果不自然溢出会慢很多TAT

<span style="font-size:18px;">#include "stdio.h"#include "iostream"#include "algorithm"#include "stdlib.h"#include "string.h"#include "memory.h"#include "math.h"#define rep(f,a,b) for(f=a;f<=b;f++)#define run(f,to) for(f=1;f<=to;f++)typedef long long ll;using namespace std;const int N=100005,Q=20005;inline int read(){int v=0; char ch=getchar();while(ch>'9'||ch<'0') ch=getchar();while(ch<='9'&&ch>='0') v=v*10+ch-'0',ch=getchar();return v;}struct Query{int n,m,a,f,id;bool operator <(const Query&q)const{return a<q.a;}} ask[Q];inline bool cmp(const Query&p,const Query&q){return p.id<q.id;}struct Ans{int f,id;bool operator <(const Ans&q)const{return f<q.f;}} save[N];    int mobius[N],pri[N],prl;bool flag[N]; int F[N];int val[N],sum[N],q;const int n=100000;void build(){mobius[1]=1; int i,j;rep(i,2,n){if(flag[i]^1){pri[++prl]=i;mobius[i]=-1;}for(j=1;i*pri[j]<=n;j++){flag[i*pri[j]]=true;if(i%pri[j]==0){mobius[i*pri[j]]=0;break;}mobius[i*pri[j]]=-mobius[i];}}rep(i,1,n){for (j=i;j<=n;j+=i){F[j]+=i;}}rep(i,1,n){save[i].f=F[i]&0x7fffffff;save[i].id=i;}sort(save+1,save+n+1);}void init(){int i; q=read(); rep(i,1,q){ask[i].n=read();ask[i].m=read();ask[i].a=read();ask[i].id=i;} sort(ask+1,ask+q+1);}inline int lowbit(int x){return x&-x;}inline int asksum(int l,int r){int ret=0;while(l<=r){ret+=val[r];for(r--;r-lowbit(r)>=l;r-=lowbit(r)){ret+=sum[r];}}return ret;}inline void add(int p,int value){val[p]+=value;for(int k=p;k<=n;k+=lowbit(k)){sum[k]+=value;}}void work(){int i,j=1,k;rep(i,1,q){while(ask[i].a>=save[j].f){for (k=1;k*save[j].id<=n;k++){add(k*save[j].id,save[j].f*mobius[k]);}j++;}int x=ask[i].n,y=ask[i].m,a=0;if(x>y) swap(x,y); int last;for (k=1;k<=x;k=last+1){last=min(x/(x/k),y/(y/k));ask[i].f+=(x/k)*(y/k)*asksum(k,last);}}sort(ask+1,ask+q+1,cmp);rep(i,1,q){printf("%d\n",ask[i].f&0x7fffffff);}}int main(){build(); init(); work();return 0;}</span><span style="font-size:24px;"></span>

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