HDU 2824 The Euler function --------欧拉模板

The Euler function

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 2986    Accepted Submission(s): 1221

Problem 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

 

第一种打表的方法是，素数和欧拉，分开来打表。250ms

第二种打表只有一个，但是时间上更多。500ms

 

 #include<iostream>
 #include<cstdio>
 #include<cstdlib>
 #include<cstring>
 using namespace std;

 int prime[],len;
 int   opl[];
 bool s[];

 void Getprime() //打素数表
 {
     int i,j;
     len=;
     for(i=;i<=;i++)
     {
         if(s[i]==false)
         {
             prime[++len]=i;
             for(j=i*;j<=;j=j+i)
             s[j]=true;
         }
     }
 }

 void Euler() //欧拉打表。
 {
     int i,j;
     Getprime();
     for(i=;i<=;i++)
     opl[i]=i;
     opl[]=;
     for(i=;i<=len;i++)
     {
         for(j=prime[i];j<=;j=j+prime[i])
         opl[j]=opl[j]/prime[i]*(prime[i]-); //利用的定理

     }
 }

 int main()
 {
     int n,m,i;
     __int64 num;
     Euler();
     while(scanf("%d%d",&n,&m)>)
     {
         num=;
         for(i=n;i<=m;i++)
         num=num+opl[i];
         printf("%I64d\n",num);
     }
     return ;
 }

第二种方法。

 #include<iostream>
 #include<cstdio>
 #include<cstdlib>
 #include<cstring>
 using namespace std;

 int   opl[];
 bool s[];

 void Euler() //欧拉打表。
 {
     int i,j;
     for(i=;i<=;i++)
     opl[i]=i;
     opl[]=;

     for(i=;i<=;i++)
     if(s[i]==false)
     {
         for(j=i;j<=;j=j+i)
         {
             opl[j]=opl[j]/i*(i-);
             s[j]=true;
         }
     }
 }

 int main()
 {
     int n,m,i;
     __int64 num;
     Euler();
     while(scanf("%d%d",&n,&m)>)
     {
         num=;
         for(i=n;i<=m;i++)
         num=num+opl[i];
         printf("%I64d\n",num);
     }
     return ;
 }