poj1286

Polya计数原理第一题。基本应用。注释写得很清楚了，不再赘述。

/*************************************************************************
> File Name: poj1286.cpp
> Author: zhengnanlee 
> Mail: [email protected]  
> Created Time: 2013年09月19日 星期四 10时37分10秒
************************************************************************/

#include <iostream>
#include <math.h>

using namespace std;

#define LL long long

LL gcd(LL a, LL b)
{
    return b ? gcd(b, a % b) : a;
}

LL polya(LL n)
{
    LL ret = 0;
    for(LL i = 0; i < n; i++)
    ret += pow(3, gcd(i, n));//rotate the beeds...
    //flip them...
    if( n & 1 )//odd
    ret += n * pow(3, n / 2 + 1);//symmetric axis's num is n, and a cycle of (n + 1) / 2, with the length of 2, and 2 cycles with length of 1...
    else//even
    ret += n / 2 * pow(3, n / 2) + (n / 2) * pow(3, n / 2 + 1);//symmetric axis's num is n, categoried by the beeds, for n/2 axis which through the beed, they formed (n/2-1) cycles with the length of 2, and 2 cycles with the length of 1; for the n/2 axis which not through the beed, they formed (n/2) cycles with the length of 2.
    return ret / n / 2;//the average of them(according to Polya Theorem.)
}

int main()
{
    LL n;
    while(cin>> n && n != -1)
    {
        if (n <= 0) cout << 0 << endl;
        else cout << polya(n) << endl;
    }
    return 0;
}