【Java】【高精度】【组合数】【递推】poj1737 Connected Graph

import java.util.*;
import java.io.*;
import java.math.*;

public class Main{
	static BigInteger[] g=new BigInteger[60];
	static BigInteger[] f=new BigInteger[60];
	static BigInteger[] pow_2=new BigInteger[2510];
	static long[][] C=new long[60][60];
	public static void main(String[] argc){
		C[0][0]=1l;
	    for(int i=1;i<=50;++i){
	        C[i][0]=C[i][i]=1l;
	        for(int j=1;j<i;++j){
	            C[i][j]=C[i-1][j]+C[i-1][j-1];
	        }
	    }
	    
	    pow_2[0]=BigInteger.ONE;
	    for(int i=1;i<=2500;++i){
	    	pow_2[i]=pow_2[i-1].multiply(BigInteger.valueOf(2l));
	    }
	    
		g[0]=BigInteger.ONE;
		for(int i=1;i<=50;++i){
			g[i]=BigInteger.ZERO;
			for(int k=1;k<i;++k){
				g[i]=g[i].add(((BigInteger.valueOf(C[i-1][k-1])).multiply(f[k])).multiply(pow_2[(i-k)*(i-k-1)/2]));
			}
			f[i]=pow_2[i*(i-1)/2].subtract(g[i]);
		}
		
		Scanner sc = new Scanner (new BufferedInputStream(System.in));
		while(true){
			int n=sc.nextInt();
			if(n==0){
				break;
			}
			System.out.println(f[n]);
		}
		sc.close();
    }
}