POJ2407:Relatives(欧拉函数)

Relatives

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 9411		Accepted: 4453

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

Source

Waterloo local 2002.07.01

MYCode:
#include<iostream>
#include<cstring>
#include<cstdio>
#include<cmath>
using namespace std;
int euler(int x)
{
    int res=x;
    int i;
    for(i=2;i*i<=x;i++)
    {
        if(x%i==0)
        {
            res=res*1.0/i*(i-1);
            while(x%i==0)x/=i;
        }
    }
    if(x>1)res=res/x*(x-1);
    return res;
}
int main()
{
    int p;
    while(scanf("%d",&p))
    {
        if(p==0)
        break;
        int ans=euler(p);
        printf("%d\n",ans);
    }
}
//

欧拉函数模板题,可以使用素数表优化.