[ACM] POJ 1286 Necklace of Beads (Polya计数，直接套公式）

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

Output

Sample Input

4
5
-1

Sample Output

21
39

Source

和http://blog.csdn.net/sr_19930829/article/details/38108871几乎是一模一样的。考虑n=0的情况，要不然runtime error- - ！ 

代码：

#include <iostream>
#define LL long long
using namespace std;

int gcd(int a,int b)
{
    return b==0?a:gcd(b,a%b);
}

LL power(LL p,LL n)
{
    LL sum=1;
    while(n)
    {
        if(n&1)
            sum*=p;
        p*=p;
        n/=2;

    }
    return sum;
}

int main()
{
    int n;
    while(cin>>n&&n!=-1)
    {
        if(n==0)//考虑n等于0的情况。。
        {
            cout<<0<<endl;
            continue;
        }
        LL ans=0;
        for(int i=1;i<=n;i++)
            ans+=power(3,gcd(i,n));
        if(n&1)
            ans+=n*power(3,n/2+1);
        else
            ans+=(power(3,n/2+1)+power(3,n/2))*(n/2);
        ans/=n*2;
        cout<<ans<<endl;
    }
    return 0;
}

[ACM] POJ 1286 Necklace of Beads (Polya计数，直接套公式）,布布扣,bubuko.com

[ACM] POJ 1286 Necklace of Beads (Polya计数，直接套公式）

原文：http://blog.csdn.net/sr_19930829/article/details/38109823