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: [e-mail]  > 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 longLL 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;}