POJ2407:Relatives(欧拉函数)
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Relatives
Time Limit: 1000MS Memory Limit: 65536KTotal Submissions: 9411 Accepted: 4453
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
Source
Waterloo local 2002.07.01
MYCode:
#include<iostream>
#include<cstring>
#include<cstdio>
#include<cmath>
using namespace std;
int euler(int x)
{
int res=x;
int i;
for(i=2;i*i<=x;i++)
{
if(x%i==0)
{
res=res*1.0/i*(i-1);
while(x%i==0)x/=i;
}
}
if(x>1)res=res/x*(x-1);
return res;
}
int main()
{
int p;
while(scanf("%d",&p))
{
if(p==0)
break;
int ans=euler(p);
printf("%d\n",ans);
}
}
//
#include<iostream>
#include<cstring>
#include<cstdio>
#include<cmath>
using namespace std;
int euler(int x)
{
int res=x;
int i;
for(i=2;i*i<=x;i++)
{
if(x%i==0)
{
res=res*1.0/i*(i-1);
while(x%i==0)x/=i;
}
}
if(x>1)res=res/x*(x-1);
return res;
}
int main()
{
int p;
while(scanf("%d",&p))
{
if(p==0)
break;
int ans=euler(p);
printf("%d\n",ans);
}
}
//
欧拉函数模板题,可以使用素数表优化.
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