POJ1286:Necklace of Beads(POLYA定理应用)

Necklace of Beads Time Limit: 1000MS Memory Limit: 10000K Total Submissions: 5410 Accepted: 2241 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 Xi'an 2002

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.