SGU 102. Coprimes

Question：

For given integer N (1<=N<=104) find amount of positive numbers not greater than N that coprime with N. Let us call two positive integers (say, A and B, for example) coprime if (and only if) their greatest common divisor is 1. (i.e. A and B are coprime iff
gcd(A,B) = 1).

Input

Input file contains integer N.

Output

Write answer in output file.

Sample Input

9

Sample Output

6

代码

#include <iostream>
#include <cstdlib>

using namespace std;

int main(int argc, char *argv[])
{
int n, count = 1;
cin >> n;
for (int i = 2; i < n; i ++)
{
int a = n, b = i, r;
while (1)				//欧几里德算法（辗转相除法）求最大公约数
{
r = a % b;
if (r == 0)
{
if (b == 1) count ++;
break;
}
a = b;
b = r;
}
}

cout << count << endl;
return EXIT_SUCCESS;
}

Mark：

1.这里使用了欧几里德算法来求最大公约数；用欧拉函数直接求结果，可能会更快。

2.开始时，把count初值设为0，然后从1开始判断，这样使得1的结果为0，不符合题目中的定义；后来把count设置为1，然后从2开始判断，AC了。

   原来的方法也可以，但是应该把 i < n 改为 i <= n 。