【HDU - 2824】- The Euler functio 【欧拉筛】

最新推荐文章于 2021-03-07 15:07:35 发布

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本文介绍了一种基于欧拉函数的求和算法实现方法，该算法能够高效地计算从a到b范围内所有整数的欧拉函数之和。输入为两个整数a和b，输出为指定范围内的欧拉函数累加结果。

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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 < 3 000000 ) .
Output
Output the result of (a)+ (a+1)+….+ (b)
Sample Input
3 100
Sample Output
3042

#include<cstdio>
using namespace std ;
typedef long long LL ;

const int MAXN = 3000000 +10;
const int MAXM = 1e6;
const int mod  = 1e9+7 ;

LL e[MAXN]; // 不能再开一个数组sum,否则爆内存
void eular(){
    for(int i=0;i<MAXN;i++) e[i]=i;
    for(int i=2;i<MAXN;i++){
         if(e[i]==i)
         for(int j=i;j<MAXN;j+=i) e[j]=(LL)e[j]/i*(i-1);
        e[i]=e[i-1]+e[i];
    }
}

int main(){ 
    eular();
    int a,b;
    while(scanf("%d%d",&a,&b)!=EOF){
        printf("%lld\n",e[b]-e[a-1]);
    }
    return  0;
}