「luogu1829」 [国家集训队]Crash的数字表格

Posted 2020-10-27 Cupcake

莫比乌斯反演推柿子，数论分块降复杂度，最后时间复杂度为O(n)。

 1 #include<bits/stdc++.h>
 2 #define ll long long
 3 using namespace std;
 4 const int N=1e7+10,mod=20101009;
 5 int n,m,mi;
 6 ll p[N],tot;
 7 ll u[N];
 8 bool isp[N];
 9 void getu(int lim){
10     u[1]=1;
11     for(int i=2;i<=lim;i++){
12         if(!isp[i]) u[i]=-1,p[++tot]=i;
13         for(int j=1;j<=tot&&1LL*i*p[j]<=lim;j++){
14             isp[p[j]*i]=1,u[i*p[j]]=-u[i];
15             if(!(i%p[j])){u[i*p[j]]=0;break;}
16         }
17     }
18     for(int i=2;i<=lim;i++) u[i]=((u[i]*i*i+u[i-1])%mod+mod)%mod;
19     return;
20 }
21 ll solve(int d){
22     ll x=n/d,y=m/d,l=1,r,lim=mi/d,res=0;
23     while(l<=lim){
24         r=min(x/(x/l),y/(y/l));
25         ll temp=((x/l+1)*(x/l)/2%mod)*((y/l+1)*(y/l)/2%mod)%mod;
26         res=((res+(u[r]-u[l-1])*temp)%mod+mod)%mod;
27         l=r+1;
28     }
29     return res;
30 }
31 int main(){
32     scanf("%d%d",&n,&m);
33     mi=min(n,m);
34     getu(mi);
35     ll ans=0;
36     int l=1,r;
37     while(l<=mi){
38         r=min(n/(n/l),m/(m/l));
39         ans=(ans+solve(l)*(l+r)*(r-l+1)/2+mod)%mod;
40         l=r+1;
41     }
42     printf("%lld",ans);
43     return 0;
44 }