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  • POJ 2407 Relatives(欧拉函数入门题)

    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.

    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

    题意:输入个n,求(1,n-1)与n互质的个数有多少个
    思路:这明显就是欧拉函数模版题,就是求n的欧拉数
    #include<cstdio>
    #include<cstring>
    #include<cmath>
    #include<algorithm>
    using namespace std;
    typedef long long ll;
    ll phi(ll n)//求n的欧拉数
    {
        ll sum=n;
        for(int i=2;i*i<=n;i++)//O(根号n的复杂度)
        {
            if(n%i==0)
            {
                sum=sum-sum/i;
                do
                {
                    n/=i;
                }while(n%i==0);
            }
        }
        if(n>1) sum=sum-sum/n;
        return sum;
    }
    int main()
    {
        ll n;
        while(scanf("%lld",&n)!=EOF)
        {
            if(n==0)
            break;
            printf("%lld
    ",phi(n));
        }
    }
     
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  • 原文地址:https://www.cnblogs.com/Lis-/p/9387619.html
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