G - The Euler function(hdu 2824)

原题链接

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
题意分析：求a到b之间所有的欧拉函数值的和
相当于一个模版题，先筛出1-maxn的所有欧拉函数的值即可，文末有线性的欧拉筛，更快

 

#include <iostream>
#include <stdio.h>
#include <algorithm>
#include <string.h>
#include <vector>
#include <math.h>
#include <map>
#include <queue>
#include <set>
using namespace std;
typedef long long ll;
const int maxn=3e6+7;
const int mod=1e9+7;
ll p[maxn];
//o(nloglogn)的筛法
void get_Phi()
{
    for(int i=2;i<=maxn;i++)p[i]=0;
        p[1]=1;
    for(int i=2;i<=maxn;i++)
        if(!p[i]){
            for(int j=i;j<=maxn;j+=i){
                if(!p[j])p[j]=j;
            p[j]=p[j]/i*(i-1);
           }
        }
}
int main()
{
    //freopen("in.txt","r",stdin);
    get_Phi();
    int a,b;
    while(scanf("%d%d",&a,&b)!=-1)
    {
        ll ans=0;
        for(int i=a;i<=b;i++)
            ans+=p[i];
        printf("%lld\n",ans );
    }
    //printf("%lld\n",ans );
    return 0;
}

//线性筛
const int N=3e6+7;
int prime[N],isprime[N];//记录素数的
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];
                break;
            }else
                phi[i*prime[j]]=phi[i]*(prime[j]-1);
        }
    }
}