HDU2824 The Euler function

Time Limit: 1000MS

Memory Limit: 32768KB

64bit IO Format: %I64d & %I64u

Description

The Euler function phi is an important kind of function in number theory, (n) represents the amount of the numbers which are smaller than n and coprime to n, and this function has a lot of beautiful characteristics. Here comes a very easy question: suppose you are given a, b, try to calculate (a)+ (a+1)+....+ (b)

 

Input

There are several test cases. Each line has two integers a, b (2<a<b<3000000).

 

Output

Output the result of (a)+ (a+1)+....+ (b)

 

Sample Input

3 100

 

Sample Output

3042

 

Source

2009 Multi-University Training Contest 1 - Host by TJU

算出300w个范围内的欧拉函数，然后求个前缀和。

然而这题内存限制好小，直接套惯用的模板会MLE。

已经没有什么优化的空间了，只好重构代码。

解1：MLE

 /*by SilverN*/
 #include<iostream>
 #include<algorithm>
 #include<cstring>
 #include<cstdio>
 #include<cmath>
 #define LL long long
 using namespace std;
 const int mxn=;
 LL phi[mxn],pr[mxn>>];
 int cnt=;
 int mark[mxn];
 int n;
 void euler(){
     phi[]=;
     for(int i=;i<=mxn;i++){
         if(!mark[i])
             pr[++cnt]=mark[i]=i,phi[i]=i-;
         for(int j=;j<=cnt && pr[j]*i<mxn;j++){
             mark[i*pr[j]]=pr[j];
             if(mark[i]==pr[j]){
                 phi[pr[j]*i]=phi[i]*pr[j];
                 break;
             }
             else phi[i*pr[j]]=phi[i]*(pr[j]-);
         }
     }
     return;
 }
 int main(){
     int s,t;
     euler();
     int i;
     for(i=;i<=mxn;i++)phi[i]+=phi[i-];
     while(scanf("%d%d",&s,&t)!=EOF)printf("%I64d\n",phi[t]-phi[s-]);
     return ;
 }

解2：AC

 #include <cstdio>
 long long n=,phi[],p[],top=;
 bool ma[];
 void init()
 {
      phi[]=;
      for (int i=;i<=n;++i)
      {
          if (!ma[i]) ma[i]=true,p[++top]=i,phi[i]=i-;
          for (int j=;j<=top&&i*p[j]<=n;++j)
          {
              ma[i*p[j]]=true;
              if (i%p[j]==){phi[i*p[j]]=phi[i]*p[j];break;}
              else phi[i*p[j]]=(p[j]-)*phi[i];
          }
      }
 }
 int main()
 {
     int l,r; init();
     for (int i=;i<=n;++i) phi[i]+=phi[i-];
     while (~scanf("%d%d",&l,&r)) printf("%lld\n",phi[r]-phi[l-]);
 }