有一道离散数学的题，帮帮我。

分别用t(R) = R∪R2∪…∪Rn 和Warkshallde 算法实现求关系的闭包。（输入、输出采用文件的方式）
例如：
输入：文件input.txt，下面给出一个input.txt文件的格式样例。
A={a,b,c,d}
R={,,,}
输出：计算结果写入文件output.txt。如上input.txt文件对应的output.txt如下。
算法一：
t(R)={,,,,,,,,}
执行时间：
算法二：
t(R)={,,,,,,,,}
执行时间：
谢谢了

package relations;

public class Main {
public static void main(String args[]){
long time1_star = System.currentTimeMillis();

    System.out.println("--- R1∪R2∪R3∪....Rn --- ");
    new Relations();
    System.out.println();
    long time1_end = System.currentTimeMillis();
    System.out.println("耗时:"+String.valueOf(time1_end-time1_star)+"毫秒");

    long time2_star = System.currentTimeMillis();
    System.out.println("--- Warkshallde --- ");
    new Warkshallde();
    System.out.println();
    long time2_end = System.currentTimeMillis();
    System.out.println("耗时:"+String.valueOf(time2_end-time2_star)+"毫秒");

}

}

package relations;

public class BiList{
private Object[] data=new Object[3];
private int index=0;
private void expand(){
Object[] data2=new Object[data.length*2];
System.arraycopy(data,0,data2,0,data.length);
data=data2;
}
public void add(Object o){
if (data.length==index) expand();
data[index]=o;
index++;
}
public void add(int pos,Object o){
if (data.length==index) expand();
for(int i=index;i>pos;i--){
data[i]=data[i-1];
}
data[pos]=o;
index++;
}
public Object remove(int pos){
Object o=data[pos];
index--;
for(int i=pos;i<index;i++){
data[i]=data[i+1];
}
return o;
}
public int size(){
return index;
}
public Object get(int pos){
return data[pos];
}
public void clear(){
index=0;
}
public boolean isEmpty(){
return index==0;
}
public Object[] toArray(){
return data;
}
}

package relations;

public class Binary {
private String one;
private String two;
public Binary(){}
public Binary(String one,String two){
this.one = one;
this.two = two;
}
public String getOne() {
return one;
}
public void setOne(String one) {
this.one = one;
}
public String getTwo() {
return two;
}
public void setTwo(String two) {
this.two = two;
}

}

package relations;

import java.io.BufferedReader;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;

public class Relations {
private static BiList A = new BiList();
private static BiList R = new BiList();
private static int n=0;

public Relations(){
    BiList<Binary> copy = new BiList<Binary>();
    readInput();
    for(int i=0 ; i<R.size(); i++){
        Binary b=(Binary)R.get(i);
        copy.add(new Binary(b.getOne(),b.getTwo()));
    }
    System.out.print("t(R)={");
    operate(copy);
    System.out.print("}");
}

public static void initA(String s,int line){
    if(line==1){
        String type=s.replace(" ","").replace("{", "").replace("}","");
        String[] a = type.substring(2,type.length()).split(",");
        for(String a1:a){
            A.add(new Binary(a1,a1));
        }
        n=A.size();
        /*
        System.out.print("A={");
        for(int i=0 ; i<A.size(); i++){
            Binary b=(Binary)A.get(i);
            System.out.print("<"+b.getOne()+","+b.getTwo()+">");
        }
        System.out.println("}");
        */
    }
}

public static void initR(String s,int line){
    if(line==2){
        String type=s.replace(" ","").replace("}", "").replace("<", "").replace(",", "");
        String[] a = type.substring(3,type.length()).split(">");

        for(String a1:a){
            R.add(new Binary(a1.substring(0,1),a1.substring(1,2)));
        }

        System.out.print("R={");
        for(int i=0 ; i<R.size(); i++){
            Binary b=(Binary)R.get(i);
            System.out.print("<"+b.getOne()+","+b.getTwo()+">");
        }
        System.out.println("}");
    }
}

private static BiList<Binary> operate(BiList<Binary> list){
    BiList<Binary> type1 = new BiList<Binary>();
    if(n==0){
        for(int i=0; i<R.size(); i++){
            Binary r=(Binary)R.get(i);
            list.add(new Binary(r.getOne(),r.getTwo()));
        }
        print(list);
        return list;
    }

    for(int i=0; i<list.size(); i++){
        Binary r=(Binary)list.get(i);
        type1.add(new Binary(r.getOne(),r.getTwo()));
    }
    list.clear();
    for(int i=0; i<R.size();i++){
        for(int j=0; j<type1.size(); j++){
            Binary r=(Binary)R.get(i);
            Binary r1=(Binary)type1.get(j);
            if(r.getTwo().equals(r1.getOne())){
                list.add(new Binary(r.getOne(),r1.getTwo()));
            }
        }
    }
    print(list);
    for(int i=0; i<list.size();i++){
        for(int j=0; j<list.size(); j++){
            Binary r=(Binary)list.get(i);
            Binary r1=(Binary)list.get(j);
            if(r.getOne().endsWith(r1.getOne())&&r.getTwo().equals(r1.getTwo())){
                list.remove(j);
            }
        }
    }
    for(int i=0; i<list.size();i++){
        for(int j=0; j<list.size(); j++){
            Binary r=(Binary)list.get(i);
            Binary r1=(Binary)list.get(j);
            if(r.getOne().endsWith(r1.getOne())&&r.getTwo().equals(r1.getTwo())){
                list.remove(j);
            }
        }
    }
    n--;
    return operate(list);
}


public static void print(BiList<?> li){

    for(int i=0 ; i<li.size(); i++){
        Binary b=(Binary)li.get(i);
        System.out.print("<"+b.getOne()+","+b.getTwo()+">");
    }

}


public static void readInput(){
    try{
        BufferedReader br = new BufferedReader(
                new FileReader("d:\\input.txt"));
        String line="";
        int i=0;
        while((line=br.readLine()) !=null){
            i++;
            initA(line,i);
            initR(line,i);
        }
        } catch(FileNotFoundException e){
            e.printStackTrace();
        } catch (IOException e) {
            e.printStackTrace();
        }
}

public static void main(String args[]){
    new Relations();
}

}

package relations;

public class Util {
public static int praseToDigit(String s){
if(s.equals("a")){
return 1-1;
}
if(s.equals("b")){
return 2-1;
}
if(s.equals("c")){
return 3-1;
}
if(s.equals("d")){
return 4-1;
}
if(s.equals("e")){
return 5-1;
}
return -1;
}
public static String praseToABC(int i){
if(i==0){
return "a";
}
if(i==1){
return "b";
}
if(i==2){
return "c";
}
if(i==3){
return "d";
}
if(i==4){
return "e";
}
return null;
}
}

package relations;

import java.io.BufferedReader;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;

public class Warkshallde {
private static BiList A = new BiList();
private static BiList R = new BiList();
private static int[][] matrix;
public Warkshallde(){
readInput();
matrixOperation();
System.out.print("t(R)={");
for(int i=0; i for(int j=0; j if(matrix[i][j]==1){
System.out.print("");
}
}
}
System.out.print("}");
}

public static void initA(String s,int line){
    if(line==1) {
        String type=s.replace(" ","").replace("{", "").replace("}","");
        String[] a = type.substring(2,type.length()).split(",");
        for(String a1:a){
            A.add(new Binary(a1,a1));
        }
        matrix = new int[A.size()][A.size()];
    }
}

public static void initR(String s,int line){
    if(line==2){
    String type=s.replace(" ","").replace("}", "").replace("<", "").replace(",", "");
        String[] a = type.substring(3,type.length()).split(">");
        for(String a1:a){
            R.add(new Binary(a1.substring(0,1),a1.substring(1,2)));
            int row = Util.praseToDigit(a1.substring(0,1));
            int col = Util.praseToDigit(a1.substring(1,2));
            matrix[row][col]=1;
        }
    }
}

public static void print(BiList<?> list){
    System.out.print("A={");
    for(int i=0 ; i<list.size(); i++){
        Binary b=(Binary)list.get(i);
        System.out.print("<"+b.getOne()+","+b.getTwo()+">");
    }
    System.out.println("}");
}

public static void matrixOperation(){
    for(int i=0; i<matrix.length-1;i++){
        for(int j=0; j<matrix[i].length-1; j++){
            if(matrix[j][i]==1){
                operate(i,j);   
            }
        }
    }
    for(int i1=0; i1<matrix.length;i1++){
        for(int j=0; j<matrix[i1].length; j++){
            System.out.print(matrix[i1][j]+" ");
        }
        System.out.println();
    }
}

public static void operate(int index,int add ){
    int i=matrix.length-1;
    while(i>=0){
        if(matrix[index][i]==matrix[add][i]&& matrix[index][i]==0){
            matrix[add][i]=0;
        }
        matrix[add][i]=1;
        i--;
    }
}

public static void readInput(){
    try{
        BufferedReader br = new BufferedReader(
                new FileReader("d:\\input.txt"));
        String line="";
        int i=0;
        while((line=br.readLine()) !=null){
            i++;
            initA(line,i);
            initR(line,i);
        }
        } catch(FileNotFoundException e){
            e.printStackTrace();
        } catch (IOException e) {
            e.printStackTrace();
        }
}


public static void main(String args[]){
    new Warkshallde();
}

}

Warkshallde 算法实现求关系的闭包
请参见：http://mrcio-s.iteye.com/blog/534036

没空写注释，抱歉了。程序很简单看下能明白，有计算两个算法的时间对比。