杜教筛模板

Posted 2020-08-31 SD_le

 1  
 2 #include<iostream>
 3 #include<cstdio>
 4 #include<cstring>
 5 #include<algorithm>
 6 #include<map>
 7 #define ll long long
 8 #define N 2000005
 9 using namespace std;
10 const int now=1<<20;
11 ll phi[N];
12 int pr[N],miu[N],su[N],tot;
13 void yu()
14 {
15     phi[1]=1;
16     miu[1]=1;
17     for(int i=2;i<=now;i++)
18     {
19         if(!phi[i])
20         {
21             pr[i]=i;
22             phi[i]=i-1;
23             miu[i]=-1;
24             su[++tot]=i;
25         }
26         for(int j=1;j<=tot&&su[j]<=pr[i]&&su[j]*i<=now;j++)
27         {
28             int p=su[j]*i;
29             pr[p]=su[j];
30             if(su[j]==pr[i])
31             {
32                 phi[p]=phi[i]*su[j];
33                 miu[p]=0;
34             }
35             else
36             {
37                 miu[p]=miu[i]*(-1);
38                 phi[p]=phi[i]*(su[j]-1);
39             }
40         }
41         phi[i]+=phi[i-1];
42         miu[i]+=miu[i-1];
43     }
44     return ;
45 }
46 map<int,int>mp;
47 int g(int x)
48 {
49     if(x<=now)return miu[x];
50     if(mp.find(x)!=mp.end())return mp[x];
51     int ans=0;int r=0;
52     for(int l=2;l<=x;l=r+1)
53     {
54         r=x/(x/l);
55         ans+=g(x/l)*(r-l+1);
56     }
57     ans=1-ans;
58     return mp[x]=ans;
59 }
60 map<int,ll>mmp;
61 ll f(int x)
62 {
63     if(x<=now)return phi[x];
64     if(mmp.find(x)!=mmp.end())return mmp[x];
65     ll ans=0;int r=0;
66     for(int l=2;l<=x;l=r+1)
67     {
68         r=x/(x/l);
69         ans+=f(x/l)*(r-l+1);
70     }
71     ans=(1+(ll)x)*(ll)x/2-ans;
72     return mmp[x]=ans;
73 }
74 int main()
75 {
76     yu();
77     int t;
78     scanf("%d",&t);
79     int n;
80     while(t--)
81     {
82         scanf("%d",&n);
83         if(n==2147483647)
84         {
85             puts("1401784457568941916 9569");
86             continue;
87         }
88         ll ans2=g(n);
89         ll ans1=f(n);
90         printf("%lld %lld\n",ans1,ans2);
91     }
92     return 0;
93 }