面试题玩数组

//题目

{"a1","b1","b2","a3","a2","b3"}
变成
{"a","a1","a2","a3","b","b1","b2","b3"}
且每当有新的元素添加时，如：a4、c1、f1、f2，将数组变成：
{"a","a1","a2","a3","a4","b","b1","b2","b3","c","c1","f","f1","f2"}
输出结果必须为list，初始输入为list，实现方法不限，请写出方案

import java.util.*;

public class G {

    private static Set<String> addCache = new HashSet<>();

    public static void main(String[] args) {
        List<String> list1 = new ArrayList<>();
        //添加进list
        list1.add("a1");
        list1.add("b1");
        list1.add("b2");
        list1.add("a3");
        list1.add("a2");
        list1.add("b3");
        System.out.println(list1);
        change(list1);
        System.err.println(list1);
        //添加新的数据
        list1.add("a4");
        list1.add("c1");
        list1.add("f1");
        list1.add("f2");
        change(list1);
        System.out.println(list1);
    }

    public static void change(List<String> list){
        list.removeAll(addCache);
        //添加首字母
        for (String s : list) {
            addCache.add(s.charAt(0)+"");
        }
        list.addAll(addCache);
        list.sort(null);
    }

}