Relatives 【poj-2407】【欧拉函数】

最新推荐文章于 2019-05-07 12:18:00 发布

原创最新推荐文章于 2019-05-07 12:18:00 发布 · 406 阅读

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本文介绍了一种通过算法计算小于给定正整数n并与n互质的正整数的数量的方法。该算法采用优化过的欧拉函数实现，适用于批量测试案例，并提供了样例输入输出以验证正确性。

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Relatives

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 14820		Accepted: 7447

Description

Given n, a positive integer, how many positive integers less than n are relatively prime to n? Two integers a and b are relatively prime if there are no integers x > 1, y > 0, z > 0 such that a = xy and b = xz.

Input

There are several test cases. For each test case, standard input contains a line with n <= 1,000,000,000. A line containing 0 follows the last case.

Output

For each test case there should be single line of output answering the question posed above.

Sample Input

7
12
0

Sample Output

6
4

代码如下：

#include<cstdio>
#include<cmath>
int Eular(int n)  
{  
    int ans=1;  
    for (int i=2;i<=sqrt((double)n);i++)  
    {  
        if (n%i==0)  
        {  
            n/=i;  
            ans*=(i-1); 
            while (n%i==0)   
            {  
                n/=i;  
                ans*=i;  
            }  
        }  
    }  
    if (n>1)   
        ans*=(n-1);  
    return ans;  
}  
int main()
{
	int m;
	
	while(scanf("%d",&m)&&m){
	
	
		printf("%d\n",Eular(m));
		
	}
	return 0;
}