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The Euler function(线性筛欧拉函数)
/*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 longusing namespace std;/**************************欧拉函数模板*****************************///筛选法打欧拉函数表 #define Max 3000010int euler[Max];void Init(){ euler[1]=1; for(int i=2;i<Max;i++) euler[i]=i; for(int i=2;i<Max;i++) if(euler[i]==i) for(int j=i;j<Max;j+=i) euler[j]=euler[j]/i*(i-1);//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=0; for(int i=a;i<=b;i++){ cur+=euler[i]; } printf("%lld\n",cur); } return 0;}
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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The Euler function(线性筛欧拉函数)
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