POJ 1286 Necklace of Beads(polya计数、burnside定理)

Description

Beads of red, blue or green colors are connected together into a circular necklace of n beads ( n < 24 ). If the repetitions that are produced by rotation around the center of the circular necklace or reflection to the axis of symmetry are all neglected, how many different forms of the necklace are there? 

Input

The input has several lines, and each line contains the input data n. 
-1 denotes the end of the input file. 

Output

The output should contain the output data: Number of different forms, in each line correspondent to the input data.

Sample Input

4
5
-1

Sample Output

21
39

使用三种颜色珠子串成 一个n颗珠子的项链，项链旋转和翻转相同的视为同样方案，问有多少不同方案数
#include <iostream>
using namespace std;
int gcd(int a,int b)
{
    return b==0?a:gcd(b,a%b);
}
long long power(long long p,long long n)
{
    long long ret=1;
    while(n)
    {
        if(n&1)ret=ret*p;
        p=p*p;
        n=n/2;
    }
    return ret;
}
int main()
{
    int n;
    while(cin>>n)
    {
        if(n==-1)break;
        else if(n==0)
            cout<<"0"<<endl;
        else
        {
            long long ans=0;
            for(int i=1; i<=n; i++)
                ans=ans+power(3,gcd(n,i));
            if(n&1)//是奇数，有n个包含(n/2+1)个循环节的循环群
                ans=ans+n*power(3,n/2+1);
            else
                ans=ans+(n/2)*(power(3,n/2+1)+power(3,n/2));
            ans=ans/(2*n);//别忘了除以置换群的总个数，这里由于既翻转又旋转所以是2*n
            cout<<ans<<endl;
        }
    }
    return 0;
}