sgu282：Isomorphism(polya計數)

題目大意：
       給定一個n 階完全圖，可以把每條邊染成m 種顏色，問有多少種本質不同的圖。

分析：
       這是論文題，給個講的好點的鏈接吧：
      http://endlesscount.blog.163.com/blog/static/8211978720122154253812/

#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <climits>
#include <cmath>
#include <string>
#include <iostream>
#include <algorithm>
#include <set>
#include <map>
#include <list>
#include <queue>
#include <stack>
#define ONLINE_JUDGE
typedef long long LL;
typedef long double LD;
typedef double DB;
using namespace std;

const int MaxN = 69;
int Mod;

int n, m;
int inv[MaxN];
int L[MaxN];
int ans;
int Gcd[MaxN][MaxN];
int invl[MaxN];
int mi[MaxN*MaxN];

int PowerMod(int a, int b, int m)
{
    int re = 1, base = a;
    while(b)
    {
        if(b&1) re = (LL)re*base%m;
        base = (LL)base*base%m;
        b >>= 1;
    }
    return re;
}

#define Inv(a, b) (PowerMod(a, b-2, b))

int gcd(int a, int b)
{
    if(b) return gcd(b, a%b);
    else return a;
}

int calc(int m)
{
    int re = 1;
    for(int i = 1, l = 1; i <= m; ++i)
    {
        re = (LL)re*invl[L[i]]%Mod;
        if(i == m || L[i] != L[i+1])
        {
            re = (LL)re*inv[l]%Mod;
            l = 1;
        }
        else l++;
    }
    int num = 0;
    for(int i = 1; i <= m; ++i)
    {
        num += L[i]/2;
        for(int j = i+1; j <= m; ++j)
            num += Gcd[L[i]][L[j]];
    }
    re = (LL)re*mi[num]%Mod;
    return re;
}

void Dfs(int cnt, int sum)
{
    L[cnt] = n-sum;
    ans = (ans+calc(cnt))%Mod;
    for(int i = L[cnt-1]; i*2 <= n-sum; ++i)
    {
        L[cnt] = i;
        Dfs(cnt+1, sum+i);
    }
}

int main()
{
    #ifndef ONLINE_JUDGE
    freopen("sgu282.in", "r", stdin);
    freopen("sgu282.out", "w", stdout);
    #endif

    cin >> n >> m >> Mod;
    inv[0] = 1;
    for(int i = 1; i <= n; ++i)
    {
        inv[i] = (LL)inv[i-1]*Inv(i, Mod)%Mod;
        invl[i] = Inv(i, Mod);
    }
    mi[0] = 1;
    for(int i = 1; i <= n; ++i)
        for(int j = 1; j <= n; ++j)
            Gcd[i][j] = gcd(i, j), mi[(i-1)*n+j] = (LL)mi[(i-1)*n+j-1]*m%Mod;
    L[0] = 1;
    Dfs(1, 0);
    cout << ans << endl;

    #ifndef ONLINE_JUDGE
    fclose(stdin);
    fclose(stdout);
    #endif
    return 0;
}