POJ 2407 Relatives 【单个数的欧拉函数判断模板】

Relatives

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 16563		Accepted: 8410

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

题意：求输入数的欧拉函数

思路：直接套模板，单个欧拉函数的判断

代码 ：

#include<cstdio>
typedef long long ll;
using namespace std;

int euler(ll n)//单个数的欧拉函数判断模板
{
    ll ans=n;
    for(int i=2;i*i<=n;i++)
    {
        if(n%i==0)
        {
            ans=ans/i*(i-1);//等价于ans=ans-ans/i
            while(n%i==0)
                n=n/i;
        }
    }
    if(n>1) ans=ans/n*(n-1);
    return ans;
}
int main()
{
    ll n,t;
    while(scanf("%lld",&n))
    {
        if(n==0) break;
        ll temp=euler(n);
        printf("%lld\n",temp);
    }
   return 0;
}