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  • 欧拉函数线性筛(模板)

      1 #define IOS ios_base::sync_with_stdio(0); cin.tie(0);
      2 #include <cstdio>//sprintf islower isupper
      3 #include <cstdlib>//malloc  exit strcat itoa system("cls")
      4 #include <iostream>//pair
      5 #include <fstream>//freopen("C:\Users\13606\Desktop\Input.txt","r",stdin);
      6 #include <bitset>
      7 //#include <map>
      8 //#include<unordered_map>
      9 #include <vector>
     10 #include <stack>
     11 #include <set>
     12 #include <string.h>//strstr substr strcat
     13 #include <string>
     14 #include <time.h>// srand(((unsigned)time(NULL))); Seed n=rand()%10 - 0~9;
     15 #include <cmath>
     16 #include <deque>
     17 #include <queue>//priority_queue<int, vector<int>, greater<int> > q;//less
     18 #include <vector>//emplace_back
     19 //#include <math.h>
     20 #include <cassert>
     21 #include <iomanip>
     22 //#include <windows.h>//reverse(a,a+len);// ~ ! ~ ! floor
     23 #include <algorithm>//sort + unique : sz=unique(b+1,b+n+1)-(b+1);+nth_element(first, nth, last, compare)
     24 using namespace std;//next_permutation(a+1,a+1+n);//prev_permutation
     25 //******************
     26 clock_t __START,__END;
     27 double __TOTALTIME;
     28 void _MS(){__START=clock();}
     29 void _ME(){__END=clock();__TOTALTIME=(double)(__END-__START)/CLOCKS_PER_SEC;cout<<"Time: "<<__TOTALTIME<<" s"<<endl;}
     30 //***********************
     31 #define rint register int
     32 #define fo(a,b,c) for(rint a=b;a<=c;++a)
     33 #define fr(a,b,c) for(rint a=b;a>=c;--a)
     34 #define mem(a,b) memset(a,b,sizeof(a))
     35 #define pr printf
     36 #define sc scanf
     37 #define ls rt<<1
     38 #define rs rt<<1|1
     39 typedef pair<int,int> PII;
     40 typedef vector<int> VI;
     41 typedef long long ll;
     42 const double E=2.718281828;
     43 const double PI=acos(-1.0);
     44 const ll INF=(1LL<<60);
     45 const int inf=(1<<30);
     46 const double ESP=1e-9;
     47 const int mod=(int)1e9+7;
     48 const int N=(int)3e6+10;
     49 
     50 int prime[N];
     51 ll phi[N];
     52 bool unprime[N];
     53 
     54 ///O(NloglogN),推荐
     55 void phi_table()
     56 {
     57     int i, j;
     58     for (i = 2; i < N; ++i)
     59         if (!phi[i])
     60             for (j = i; j < N; j += i)
     61             {
     62                 if (!phi[j]) phi[j] = j;
     63                 phi[j] -= phi[j] / i; ///简化后的代码
     64             }
     65 }
     66 
     67 ///O(N)
     68 void linear_phi_table2()
     69 {
     70     int i, j, k = 0;
     71     for (i = 2; i < N; i++)
     72     {
     73         if (!unprime[i]) ///若i为素数,phi(i)=i-1
     74         {
     75             prime[k++] = i;
     76             phi[i] = i - 1;
     77         }
     78         for (j = 0; j < k && prime[j] * i < N; j++)
     79         {
     80             unprime[prime[j] * i] = true;
     81             if (i % prime[j]) ///若i和p互素,则phi(i*p) = phi(i) * phi(p) = phi(i) * (p-1)
     82                 phi[prime[j] * i] = phi[i] * (prime[j] - 1);
     83             else
     84             {
     85                 ///此时有i=kp,则
     86                 ///phi(p*kp) = phi(k*p^2) = p*phi(kp)
     87                 phi[prime[j] * i] = phi[i] * prime[j];
     88                 break;
     89             }
     90         }
     91     }
     92 }
     93 
     94 int main()
     95 {
     96     int a,b;
     97     linear_phi_table2();
     98     for(int i=2;i<=3000010;++i)
     99         phi[i]+=phi[i-1];
    100     while(~sc("%d%d",&a,&b))
    101     {
    102         pr("%lld
    ",phi[b]-phi[a-1]);
    103     }
    104     return 0;
    105 }
    106 
    107 /**************************************************************************************/
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  • 原文地址:https://www.cnblogs.com/--HPY-7m/p/11915602.html
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