线性筛-三合一，强大O(n)

Posted 2020-09-03 Jason-Cow

校内CJOJ2395by Jesse Liu

筛法三合一 Euler、Möbius、Prime函数

基于数论的积性函数

gcd(a,b)=1  则  ƒ(ab)=ƒ(a)ƒ(b)

 

 1 #include <algorithm>
 2 #include <iostream>
 3 #include <cstring>
 4 #include <cstdlib>
 5 #include <cstdio>
 6 #include <vector>
 7 #include <cmath>
 8 #include <queue>
 9 #include <map>
10 #include <set>
11 using namespace std;
12 #define file(x) freopen(x".in","r",stdin),freopen(x".out","w",stdout)
13 inline void read(int &ans){
14   ans=0;char x=getchar();int f=0;
15   while(x<\'0\'||x>\'9\'){if(x==\'-\')f=1;x=getchar();}
16   while(x>=\'0\'&&x<=\'9\')ans=ans*10+x-\'0\',x=getchar();
17   if(f)ans=-ans;
18 }
19  
20 const int maxn=(int)1e7+10;
21 int phi[maxn],mu[maxn],p[maxn],flag[maxn],cnt;
22 void sieve(int n){
23   mu[1]=phi[1]=1;
24   for(int i=2;i<=n;i++){
25     if(!flag[i])p[++cnt]=i,mu[i]=-1,phi[i]=i-1;
26     for(int j=1;j<=cnt && i*p[j]<=n;j++){
27       flag[i*p[j]]=1;
28       if(i%p[j]==0){mu[i*p[j]]=0,phi[i*p[j]]=phi[i]*p[j];break;}
29       mu[i*p[j]]=-mu[i],phi[i*p[j]]=phi[i]*(p[j]-1);
30     }
31   }
32 }
33  
34 int main(){
35   sieve((int)1e7);
36   int T,op,n;
37   for(read(T);T--;){
38     read(op),read(n);
39     printf("%d\\n",op==1?p[n]:op==2?mu[n]:phi[n]);
40   }
41   return 0;
42 }

sieve

 

进一步学习的建议，Jesse Liu