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Necklace of Beads
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 Source |
MYCode:
#include<iostream>
#include<cstring>
#include<cstdio>
#include<cmath>
typedef long long ll;
using namespace std;
int gcd(int a,int b)
{
if(a%b==0)
return b;
return gcd(b,a%b);
}
int main()
{
int n;
while(scanf("%d",&n))
{
if(n==-1)
break;
if(n==0)//note
{
printf("0\n");
continue;
}
ll ans=0;
int i;
for(i=1;i<=n;i++)
{
ans+=(ll)(pow(3.0,gcd(n,i)));
}
if(n&1)
{
ans+=(ll)(n*pow(3.0,n/2+1));
}
else
{
ans+=(ll)(n/2*pow(3.0,n/2)+n/2*pow(3.0,n/2+1));
}
printf("%lld\n",ans/(2*n));
}
}
//
POLYA定理的应用
注意:
1特殊考虑n==0的情况,否则会runtime error
1结果要用long long.