hdu1812 Polya定理

一直知道有这么个定理，但一直没理解，今天看了看书，差不多知道怎么用了，但证明还是完全不用会。。。

用polya定理解题其实就是确定置换及其循环节。这题显然就是8个置换，四个旋转（其中一个为不动。。）和四个翻转，其循环节数分别为①n*n②(n*n+3)/4③(n*n+1)/2④同2⑤n+(n*n-n)/2⑥同5⑦奇数时n+(n*n-n)/2偶数时n*n/2⑧同7

import java.io.*;
import java.math.BigInteger;
import java.util.*;
public class Main {
    public static Scanner getFileScanner(boolean isOnlineJudge) {
        if(isOnlineJudge) {
            return new Scanner(System.in);
        }
        File myFile = new File("data.in");
        FileInputStream myFileStream = null;
        try {
            myFileStream = new FileInputStream(myFile);
        } catch (FileNotFoundException e) {
        }
        Scanner cin = new Scanner(myFileStream);
        return cin;
    }
    public static void main(String[] args) {
        Scanner cin = getFileScanner(true);
        int N, C;
        int[] ar = new int[8];
        while(cin.hasNextInt()) {
            N = cin.nextInt();
            C = cin.nextInt();
            ar[0] = N * N;
            ar[1] = (N * N + 3) / 4;
            ar[2] = (N * N + 1) / 2;
            ar[3] = ar[1];
            ar[4] = N + (N * N - N) / 2;
            ar[5] = ar[4];
            if(N % 2 == 1) {
                ar[6] = N + (N * N - N) / 2;
            }else {
                ar[6] = N * N / 2;
            }
            ar[7] = ar[6];
            BigInteger ans = BigInteger.ZERO;
            BigInteger BC = BigInteger.valueOf(C);
            for(int i = 0; i < 8; i++) {
                ans = ans.add(BC.pow(ar[i]));
            }
            ans = ans.divide(BigInteger.valueOf(8));
            System.out.println(ans);
        }
    }
}