Tree の構造をString で表現するにはどうしたらいいのでしょうか？？

Question

今treeの構造をString で表現するメソッドを考えているのですが、どうしたらいいのかわかりません。 下のクラスの中のtoIndentedString()なのですが
どのようにString で表現しなくてはいけないのかは決まっていて、
food

meat vegetable
|
|
|
pork, chiken, beef
例えば、food が一番上で そのsubtreeがmeat とvegetable で、meat のsubtree がpork, chiken, beefであるとしたら、String で
food
meat
pork
chicken
beef
vegetable
このように subtreeはroot の次の段落で２空白空けてから表示されないといけません。recursive が使えると思うのですが、全く考えつきません。どうしたらいいのでしょうか？

package week10;

import java.util.*;

/**
 * Skeleton of the recursive implementation of a general tree.
 * 
 * @author Michael Albert
 * @param <T> The type of values stored in the tree.
 */
public class Tree<T> {
    
    private T rootValue;
    private List<Tree<T>> children;
    
    public Tree(T rootValue, List<Tree<T>> children) {
        this.rootValue = rootValue;
        this.children = children;
    }

    public Tree(T rootValue) {
        this(rootValue, new ArrayList<Tree<T>>());
    }

    /**
       Returns the number of nodes in the tree.
       @rerturn int the number of nodes in the tree
    */
    public int size() {
	int count =1;
	for (Tree<T> child: children){
	    count += child.size();
	}
	return count;

	
    }// end size
    
    public int maxDegree() {
	int max = children.size();
	for (Tree<T> child : children){
	    int n1 = child.maxDegree();
	    if (n1 > max){
		max = n1;

	    }
	}
	return max;
        // implement this method
	
        
    }
    /** Add a child as a new subtree below the root at the 
	end of the list of children.
     @param child*/
    public void add(Tree<T> child) {
	children.add(child);
        // implement this method
    }

    public Tree<T> find(T value) {
        if (rootValue.equals(value)) {
            return this;
        }
        for (Tree<T> child : children) {
            Tree<T> match = child.find(value);
            if (match != null) {
                return match;
            }
        }
        return null;
    }
    
    public List<T> postOrder() {
	List<T> list = new ArrayList<>();
	for (Tree<T> child: children){
	    list.addAll(child.postOrder());
	}
	list.add(rootValue);
	return list;
        // implement this method
    }
    
    public String toString() {
        if (children.isEmpty()) {
            return rootValue.toString();
        }
        return rootValue.toString() + ' ' + children.toString();
    }
    
    public String toIndentedString() {
	
        // implement this method
        return "Not implemented yet!";
    }

    /** A helper method for testing (used by main).  Searches tree for
     *  the given target and adds white space separated children to
     *  the tree matching target if there is one.
     *
     * @param target the root value to seach for.
     * @param children a white space separated list of children to add
     * to the tree whose value matches target.
     */
    private static void addChildren(String target, String children) {
        Tree<String> parent = tree.find(target);
        if (parent != null) {
            for (String child : children.split(" ")) {
                parent.add(new Tree<>(child));
            }
        }
    }

    /** A tree instance used for testing. */
    private static Tree<String> tree;

    /**
     * Entry point of the program (used for testing).
     *
     * @param args command line arguments are not used.
     */
    public static void main(String[] args) {
        System.out.println("Creating tree\n-------------");
        tree = new Tree<>("food");
        System.out.print(tree + "\nsize: " + tree.size());
        System.out.println(", max degree: " + tree.maxDegree());
        System.out.println("\nAdding children\n----------------");
        addChildren("food", "meat fruit vegetable");
        System.out.print(tree + "\nsize: " + tree.size());
        System.out.println(", max degree: " + tree.maxDegree());
        System.out.println("\nAdding deeper children\n----------------------");
        addChildren("meat", "chicken beef fish");
        addChildren("fish", "salmon cod tuna shark");
        addChildren("vegetable", "cabbage");
        System.out.print(tree + "\nsize: " + tree.size());
        System.out.println(", max degree: " + tree.maxDegree());
        System.out.println("\nPostorder\n---------");
        System.out.println(tree.postOrder());
        System.out.println("\nIndented string\n---------------");
        System.out.print(tree.toIndentedString());
    }

}

Answer 1

Treeの要素が、自分が今何層目に位置しているのかということがわかればいい。方法としては
0. 階層情報を要素ごとに持たせる
0. 文字列化する際に、頂上を0階層として、子要素を取り出す際に(自分の階層)+1を引数として渡して文字列化するようなメソッドを作ればいい。