Problem E: Relatives

code

6 年前

时间： 1ms 内存：128M

描述：

Problem E: Relatives

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.

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.

For each test case there should be single line of output answering the question posed above.

输入：

输出：

示例输入：

7
12
0

示例输出：

6
4

提示：

参考答案（内存最优[748]）：

#include <stdio.h>

main(){
   int n,i,sum;
   while (1 == scanf("%d",&n) && n) {
      sum = n;
      for (i=2;i*i <= n;i++) {
         if (n%i == 0) {
            sum -= sum/i;
         }
         while (n%i == 0) n /= i;
      }
      if (n > 1) sum -= sum/n;
      printf("%d\n",sum);
   }
}

参考答案（时间最优[0]）：

#include <stdio.h>

main(){
   int n,i,sum;
   while (1 == scanf("%d",&n) && n) {
      sum = n;
      for (i=2;i*i <= n;i++) {
         if (n%i == 0) {
            sum -= sum/i;
         }
         while (n%i == 0) n /= i;
      }
      if (n > 1) sum -= sum/n;
      printf("%d\n",sum);
   }
}

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