HDU 2824 The Euler function(欧拉函数）

The Euler function

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 8389    Accepted Submission(s): 3516

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

 

Source

2009 Multi-University Training Contest 1 - Host by TJU

 

Recommend

gaojie

 

求一个范围中欧拉函数的和，根据数据范围，用筛选法打表，复杂度O（nlogn)

 

代码如下：

#include <cstdio>
#include <iostream>
#include <algorithm>
using namespace std;
typedef long long LL;
const int N=3000010;
int prime[N],isprime[N];
int phi[N];
void get_phi()
{
    int i,j,cnt=0;
    for(i=2;i<N;i++){
        if(isprime[i]==0){
          prime[cnt++]=i;
          phi[i]=i-1;
        }
       for(j=0;j<cnt&&i*prime[j]<N;j++){
           
           isprime[i*prime[j]]=1;
           if(i%prime[j]==0)
           phi[i*prime[j]]=phi[i]*prime[j];
           else
           phi[i*prime[j]]=phi[i]*(prime[j]-1);
       }
    }
}
int main()
{
    ios::sync_with_stdio(false);
    int a,b;
    LL sum;
    get_phi();
    while(cin>>a>>b)
    {
     sum=0;
     for(int i=a;i<=b;i++)
     sum+=phi[i];
     cout<<sum<<endl;
    }
    return 0;
}