poj2407解题报告

Relatives

Time Limit: 1000MS

Memory Limit: 65536K

Total Submissions: 6232

Accepted: 2786

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

7120

Sample Output

64

题目大意：给定一个数(小于1,000,000,000),求与他互质数的个数。。

思路：利用欧拉函数，将n素因子分解，带入欧拉函数求值。。

#include<iostream>#include<cmath>using namespace std;__int64 o(__int64 a,__int64 b){if(!a)return b;return o(b%a,a);}int main(){__int64 i,n,o1,o2,gys;while(scanf("%I64d",&n)&&n){if(n==1){cout<<'0'<<endl;continue;}o1=n;o2=1;for(i=2;i<=(int)sqrt((double)n);i++)if(n%i==0){o1*=(i-1);o2*=i;gys=o(o1,o2);o1/=gys;o2/=gys;while(n%i==0)n/=i;}if(n!=1){o1*=(n-1);o2*=n;gys=o(o1,o2);o1/=gys;o2/=gys;}printf("%I64d/n",o1);}return 0;}