POJ2407Relatives --欧拉函数的简单运用

作者：ACShiryu

时间：2011-8-4

原题：http://poj.org/problem?id=2407

Relatives

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 7396		Accepted: 3402

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

题目大意就是给一个数n，求出不大于n且与n互素的数的个数，

这就是简单的欧拉函数的运用，关于欧拉函数的求法，网上一搜一大堆，这里省略。

提交一次就A了，不过测试数据不强，我的程序对于1输出的是1，而实际应该是0

参考代码：

#include<iostream>
#include<cstdlib>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
using namespace std;
int main()
{
    int n ;
    while ( scanf ( "%d", & n ) , n )
    {
        if ( n == 1 )
            printf ("0\n") ; 
        else
        {
            int i , j , m;
            m = sqrt ( n + 0.5 ) ;
            int ans = n ;
            for ( i = 2; i <= m ; i ++ )
                if ( n % i == 0)
                {
                    ans = ans / i * ( i - 1 ) ;
                    while ( n % i == 0 ) 
                        n /= i ;
                }
            if ( n > 1 )
                ans = ans / n * ( n - 1 ) ;
            
            printf ("%d\n",ans);
        }
    }
    return 0;
}