GCD Again
Time Limit: 1000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 2558 Accepted Submission(s): 1060
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
Sample Output
Author
lcy
Source
欧拉函数 :公式:f(x)=x*(1-1/p1)*(1-1/p2)*(1-1/p3)....*(1-1/pn) pi都是x的质因子
考查知识点:欧拉函数
//考查知识点:欧拉函数 。。。
#include<stdio.h>
int urler(int n)
{
int ans=n,i;
int temp=1;
for(i=2;i*i<=n;++i)//要是从2开始遍历到 n-1 容易tle 在此再次压缩
{
if(n%i==0)
{
ans-=ans/i;//欧拉函数公式 f(x)=n*(1-1/p1)*(i-i/p2)...(1-1/pn);
while(n%i==0)//
n/=i;
}
}
if(n>1)//上面压缩了 i的取值范围,此处n!=1说明此时的n也是原来n的一个质因子
ans-=ans/n;
return ans;
}
int main()
{
int n;
while(~scanf("%d",&n),n)
{
printf("%d\n",n-urler(n)-1);
}
return 0;
}
欧拉函数 hdu 1787
原文:http://blog.csdn.net/ice_alone/article/details/44675313