POJ 1286 Necklace of Beads(项链的珠子)

Posted 2020-08-09 丿球痞D小七

Necklace of Beads

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 7874		Accepted: 3290

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

/*Polya原理*/
#include <cstdio>
#include <iostream>
using namespace std;
long long aaaa(long long a,long long b)
{
    long long res=1,tmp=a;
    while(b) 
    {
        if (b&1) 
            res*=tmp;
        tmp*=tmp;
        b>>=1;
    }
    return res;
}
int gcd(int a,int b) 
{
    return b==0?a:gcd(b,a%b);
}
int main()
{
    int n;
    while ( ~scanf("%d", &n) && n != -1) 
    {
        long long a = 0, b = 0;
        for (int i=0;i<n;i++) 
        {
            a+=aaaa(3,gcd(i,n));
        } 
        if (n&1) 
            b=(long long)n*aaaa(3,(n+1)/2);
        else 
            b=(long long)n/2*(aaaa(3,n/2+1)+aaaa(3,n/2));
        if (n==0) 
            printf("0\n");
        else 
            printf("%lld\n",(a+b)/2/n);
    }
    return 0;
}