HDU 1817Necklace of Beads(置换+Polya计数)

 1 #include <iostream>
 2 #include <algorithm>
 3 #include <cstring>
 4 #include <cstdio>
 5 #include <cmath>
 6 using namespace std;
 7 typedef long long LL;
 8 int n;
 9 LL Pow(LL a, LL b) // 手写long long
10 {
11     LL res = 1;
12     for (int i = 0; i < b; i++)
13         res *= a;
14     return res;
15 }
16 int gcd(int a, int b)
17 {
18     if (a == 0)
19         return b;
20     return gcd(b % a, a);
21 }
22 int main()
23 {
24     while (scanf("%d", &n) != EOF && n != -1)
25     {
26         if (n == 0)
27         {
28             printf("0\n");
29             continue;
30         }
31         LL ans = 0;
32         for (int i = 1; i <= n; i++)
33             ans += Pow(3, gcd(i, n));
34 
35         if (n & 1)
36         {
37             ans += n * Pow(3, (n + 1) / 2);
38         }
39         else
40         {
41             ans += n / 2 * Pow(3.0, n / 2 + 1);
42             ans += n / 2 * Pow(3.0, n / 2);
43             //ans += n / 2 * (pow(3.0, n / 2 + 1) + pow(3.0, n / 2));
44         }
45         printf("%I64d\n", ans / 2 / n);
46     }
47     return 0;
48 }