hdoj-【2824 The Euler function】

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于 2016-12-03 18:02:32 发布

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分类专栏：基础数学

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本文介绍了一个计算特定区间内所有整数欧拉函数之和的算法。通过预处理方式，优化了计算过程，使得在给定的限制条件下可以快速求解(a)到(b)间所有整数的欧拉函数总和。

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The Euler function

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 5923 Accepted Submission(s): 2501

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

#include<cstdio>
#include<cstring>
typedef long long LL;
LL num[3100000];
void Init()
{
	memset(num,0,sizeof(num)); 
	LL n,j;
	num[1]=1; 
	for(n=2;n<3000010;++n)
	{
		if(!num[n])
		{
			for(j=n;j<3000010;j+=n)
			{
				if(!num[j])
					num[j]=j;
				num[j]=num[j]*(n-1)/n; 
			} 
		}
	} 
} 
int main()
{
	Init();
	LL a,b;
	while(~scanf("%lld%lld",&a,&b))
	{
		LL sum=0;
		for(;a<=b;++a)
			 sum+=num[a];
		printf("%lld\n",sum); 
	} 
	return 0;
}