bzoj 1002[FJOI2007]轮状病毒

题目链接：http://www.lydsy.com/JudgeOnline/problem.php?id=1002

题解：求给出图的生成树数目

关于生成树数目的计算：http://www.cnblogs.com/shjwudp/articles/4339068.html

这题有很坑，答案会爆longlong，用了java写的

/*
 * Problem: BZOJ 1002 
 * Author:  SHJWUDP
 * Created Time:  2015/4/15 星期三 19:24:14
 * File Name: Main.java
 * State: Accepted
 * Memo: Matrix-Tree
 */
import java.util.*;
import java.io.*;
import java.math.*;

public class Main {
    public static void main(String args[]) throws IOException {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);

        TaskA solver = new TaskA();
        solver.solve(in, out);
        out.close();
    }
}

class TaskA {
    public void solve(InputReader in, PrintWriter out) {
        int n=in.nextInt();
        if(n<=1) {
            out.print(1+"
");
            return ;
        }
        int[][] D=new int[n+1][n+1];
        int[][] A=new int[n+1][n+1];
        D[n][n]=n;
        for(int i=0; i<n; i++) D[i][i]=3;
        for(int i=0; i<n; i++) {
            A[i][n]=A[n][i]=1;
            int r=(i+1)%n;
            A[i][r]=A[r][i]=1;
        }

        BigInteger[][] C=new BigInteger[n+1][n+1];
        for(int i=0; i<=n; i++) {
            for(int j=0; j<=n; j++) {
                C[i][j]=BigInteger.valueOf(D[i][j]-A[i][j]);
            }
        }

        //计算C的m-1阶行列式 (m=n+1)
        BigInteger ans=BigInteger.ONE;
        for(int i=0; i<n; i++) {
            for(int j=i+1; j<n; j++) while(C[j][i]!=BigInteger.ZERO) {
                BigInteger t=C[i][i].divide(C[j][i]);
                for(int k=i; k<n; k++) {
                    C[i][k]=C[i][k].subtract(C[j][k].multiply(t));
                }
                for(int k=i; k<n; k++) {
                    BigInteger tmp=C[i][k];
                    C[i][k]=C[j][k];
                    C[j][k]=tmp;
                }
                ans=ans.negate();
            }
            ans=ans.multiply(C[i][i]);
        }
        if(ans.compareTo(BigInteger.ZERO)<0) ans=ans.negate();
        out.print(ans+"
");
    }
}

class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;

    public InputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream), 32768);
        tokenizer = null;
    }

    public String next() {
        while(tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }

    public BigInteger nextBigInt() {
        return new BigInteger(next());
    }
}