The Euler function(线性筛欧拉函数)

时间:2021-01-23 16:49:18
/*
题意:(n)表示小于n与n互质的数有多少个,给你两个数a,b让你计算a+(a+1)+(a+2)+......+b; 初步思路:暴力搞一下,打表 #放弃:打了十几分钟没打完 #改进:欧拉函数:具体证明看po主的博客 ^0^ #超时:这里直接用欧拉函数暴力搞还是不可以的,用到线性筛欧拉函数,这里总和爆int,要用long long */
#include<bits/stdc++.h>
#define ll long long
using namespace std;
/**************************欧拉函数模板*****************************/
//筛选法打欧拉函数表
#define Max 3000010
int euler[Max];
void Init(){
euler[]=;
for(int i=;i<Max;i++)
euler[i]=i;
for(int i=;i<Max;i++)
if(euler[i]==i)
for(int j=i;j<Max;j+=i)
euler[j]=euler[j]/i*(i-);//先进行除法是为了防止中间数据的溢出
}
/**************************欧拉函数模板*****************************/
int a,b;
int main(){
// freopen("in.txt","r",stdin);
Init();
while(scanf("%d%d",&a,&b)!=EOF){
ll cur=;
for(int i=a;i<=b;i++){
cur+=euler[i];
}
printf("%lld\n",cur);
}
return ;
}

The Euler function

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 224 Accepted Submission(s): 124
 
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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