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=3000002;
LL phi[mxn],pr[mxn>>1];
int cnt=0;
int mark[mxn];
int n;
void euler(){
    phi[1]=1;
    for(int i=2;i<=mxn;i++){
        if(!mark[i])
            pr[++cnt]=mark[i]=i,phi[i]=i-1;
        for(int j=1;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]-1);
        }
    }
    return;
}
int main(){
    int s,t;
    euler();
    int i;
    for(i=1;i<=mxn;i++)phi[i]+=phi[i-1];
    while(scanf("%d%d",&s,&t)!=EOF)printf("%I64d\n",phi[t]-phi[s-1]);
    return 0;
}

 

解2：AC

#include <cstdio>
long long n=3000000,phi[3000001],p[1500001],top=0;
bool ma[3000001];
void init()
{
     phi[1]=1;
     for (int i=2;i<=n;++i)
     {
         if (!ma[i]) ma[i]=true,p[++top]=i,phi[i]=i-1;
         for (int j=1;j<=top&&i*p[j]<=n;++j)
         {
             ma[i*p[j]]=true;
             if (i%p[j]==0){phi[i*p[j]]=phi[i]*p[j];break;}
             else phi[i*p[j]]=(p[j]-1)*phi[i];
         }
     }
}
int main()
{
    int l,r; init();
    for (int i=1;i<=n;++i) phi[i]+=phi[i-1];
    while (~scanf("%d%d",&l,&r)) printf("%lld\n",phi[r]-phi[l-1]);
}