Relatives
| Time Limit: 1000MS | Memory Limit: 65536K | |
| Total Submissions: 15566 | Accepted: 7900 |
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
题目大意
给定$n$，求出$\varphi \left( n\right)$
直接套公式。
$\varphi \left( n\right) =n\prod ^{k}_{i=1}\left( \dfrac {p_{i}-1}{p_{i}}\right)$
注意先除再乘，否则会爆精度
#include<iostream> #include<cstdio> #include<cmath> #include<cstring> #define LL long long using namespace std; int main() { LL N; while(cin>>N&&N!=0) { int limit=sqrt(N),ans=N; for(int i = 2; i <= limit ; ++i) { if(N%i==0) ans=ans/i*(i-1); while(N%i==0) N=N/i; } if(N>1) ans=ans/N*(N-1); printf("%d\n",ans); } return 0; }
