HDU 2824(欧拉函数)

最新推荐文章于 2019-09-03 23:02:13 发布

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#欧拉函数

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本文介绍了一个计算欧拉函数φ(n)的程序实现方法，并通过一个简单的样例输入输出展示了如何求解从a到b范围内所有整数的欧拉函数之和。

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The Euler function

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)

链接：2824

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

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代码：

#include<iostream>
using namespace std;
bool flag[3000005];
int phi[3000005]={0,1},p[3000005]={0},cnt=0;
int main()
{
for(int i=0;i<=3000004;i++)flag[i]=1;
for(int i=2;i<3000000;i++)
{
if(flag[i])
{
p[cnt++]=i;
phi[i]=i-1;
}
for(int j=0;j<cnt;j++)
{
if(i*p[j]>3000000)break;
flag[i*p[j]]=0;
if(i%p[j]==0)
{
phi[i*p[j]]=p[j]*phi[i];
break;
}
else phi[i*p[j]]=(p[j]-1)*phi[i];
}
}
int i,x,y;
while(cin>>x>>y)
{
long long ans=0;
for(i=x;i<=y;i++)ans+=phi[i];
cout<<ans<<endl;
}
return 0;
}