连通图计数模板【c++&Java】

题目：​​poj1737 Connected Graph​​​
问题：含有n个不同的点的连通图有多少种，即同构的图算是多个

ll f[maxn];       //含n个点的连通图个数
ll g[maxn];       //含n个点的不连通图个数
ll h[maxn];       //含n个点的图的个数 h[n] = 2^(n*(n-1)/2)
ll c[maxn][maxn]; //组合数
/*
f[n] = h[n]-g[n]
要想求f[n]，必须先求g[n]
求g[n]
g[n] = sum(k:1~n-1)(c[n-1][k-1]*f[k]*h[n-k])
初始值：f[1] = g[1] = 1;
c[m][n] = m!/(n!*(m-n)!)
*/
ll qpow(ll x,ll n)
{
    ll res = 1;
    while(n)
    {
        if(n&1)
            res = res*x%mod;
        x = x*x%mod;
        n >>= 1;
    }
    return res;
}
void init()
{
    for(ll i = 1;i<maxn;i++)
        h[i] = qpow(2,i*(i-1)/2);
    for(int i=0;i<maxn;i++)
    {
        for(int j=0;j<=i;j++)
        {
            if(i&&j)
                c[i][j] = (c[i-1][j]+c[i-1][j-1])%mod;
            else
                c[i][j] = 1;
        }
    }
    f[1] = g[1] = 1;
    for(int i=2;i<maxn;i++)
    {
        g[i] = 0;
        for(int k = 1;k<i;k++)
            g[i] = (g[i]+c[i-1][k-1]*f[k]%mod*h[i-k]%mod)%mod;
        f[i] = ((h[i]-g[i])%mod+mod)%mod;
    }
}

import java.util.*;
import java.math.*;
public class Main {
    static final int maxn = 105;
    static BigInteger[] f = new BigInteger[maxn];
    static BigInteger[] two = new BigInteger[maxn];
    static BigInteger[] g = new BigInteger[maxn];
    static BigInteger[] h = new BigInteger[maxn];
    static BigInteger[][] c = new BigInteger[maxn][maxn];
    static void init()
    {
        two[0] = BigInteger.ONE;
        for(int i=1;i<maxn;i++)
            two[i] = two[i-1].multiply(BigInteger.valueOf(2));
        for(int i=1;i<maxn;i++)
        {
            int a = i;
            int b = i-1;
            if(a%2==0)
                a/=2;
            else
                b/=2;
            h[i] = BigInteger.ONE;
            for(int j=0;j<a;j++)
                h[i] = h[i].multiply(two[b]);
        }
        for(int i=0;i<maxn;i++)
        {
            for(int j=0;j<=i;j++)
            {
                if(i==j || j==0)
                    c[i][j] = BigInteger.ONE;
                else
                    c[i][j] = c[i-1][j].add(c[i-1][j-1]);
            }
        }
        f[1] = g[1] = BigInteger.ONE;
        for(int i=2;i<maxn;i++)
        {
            g[i] = BigInteger.ZERO;
            for(int k = 1;k<i;k++)
                g[i] = g[i].add(c[i-1][k-1].multiply(f[k]).multiply(h[i-k]));
            f[i] = h[i].subtract(g[i]);
        }
    }
    public static void main(String[] args) {
        init();
        Scanner cin = new Scanner(System.in);
        int n = cin.nextInt();
        System.out.println(f[n]);
        cin.close();
    }
}