【杭电oj】1787 - GCD Again（欧拉函数）

GCD Again

Time Limit: 1000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 2762    Accepted Submission(s): 1176

Problem Description

Do you have spent some time to think and try to solve those unsolved problem after one ACM contest?
No? Oh, you must do this when you want to become a "Big Cattle".
Now you will find that this problem is so familiar:
The greatest common divisor GCD (a, b) of two positive integers a and b, sometimes written (a, b), is the largest divisor common to a and b. For example, (1, 2) =1, (12, 18) =6. (a, b) can be easily found by the Euclidean algorithm. Now I am considering a little more difficult problem: 
Given an integer N, please count the number of the integers M (0<M<N) which satisfies (N,M)>1.
This is a simple version of problem “GCD” which you have done in a contest recently,so I name this problem “GCD Again”.If you cannot solve it still,please take a good think about your method of study.
Good Luck!

 

Input

Input contains multiple test cases. Each test case contains an integers N (1<N<100000000). A test case containing 0 terminates the input and this test case is not to be processed.

 

Output

For each integers N you should output the number of integers M in one line, and with one line of output for each line in input. 

 

Sample Input

   
   
   
   

    
    
    
    2
4
0
   
   
   
   

 

Sample Output

   
   
   
   

    
    
    
    0
1
   
   
   
   

 

Author

lcy

 

Source

2007省赛集训队练习赛（10）_以此感谢DOOMIII

这次做欧拉函数的题，忘了好多了，得加强记忆一下了。

代码如下：

#include <cstdio>
#include <cmath>
int Eular(int n)
{
	int ans=1;
	double t = (double)n;
	for (int i=2;i<=sqrt(t);i++)
	{
		if (n%i==0)
		{
			n/=i;
			ans*=(i-1);
			//若n有个因子是i的k次，根据欧拉公式有下面的代码
			while (n%i==0) 
			{
				n/=i;
				ans*=i;
			}
		}
	}
	if (n>1)		//若最后剩的数为大于5的素数，根据欧拉公式再算进去 
		ans*=(n-1);
	return ans;
}
int main()
{
	int n;
	int ans;
	while (~scanf ("%d",&n) && n)
	{
		ans = Eular (n);
		ans = n - 1 - ans;		//去除与其互质的数，剩下的就是GCD（N,M）> 1 的数了
		printf ("%d\n",ans); 
	}
	return 0;
}