We are asked to write the following recursive methods in given...

We are asked to write the following recursive methods in given class bellow :

1. boolean isFull (): that returns the true if the binary tree is full, false otherwise.
A full binary tree is defined as a binary tree in which all nodes have either zero or two
child nodes.

2. int getItemLevel (E data): returns the level of the item data, and 0 if the item does not
exist in the tree.
3. void printItemsAtLevel (int level): prints the nodes at the level given as a parameter.

Given the class BinaryTree:

public class BinaryTree <E> {
    protected static class Node<E> {
        
        public E data;
        
        public Node<E> left;
        
        public Node<E> right;

      
        public Node(E data) {
            this.data = data;
            left = null;
            right = null;
        }

      
        @Override
        public String toString() {
            return data.toString();
        }
    }

    
   
    protected BinaryTree(Node<E> root) {
        this.root = root;
    }

   
    public BinaryTree(E data, BinaryTree<E> leftTree, BinaryTree<E> rightTree) {
        root = new Node<>(data);
        if (leftTree != null) {
            root.left = leftTree.root;
        } else {
            root.left = null;
        }
        if (rightTree != null) {
            root.right = rightTree.root;
        } else {
            root.right = null;
        }
    }

    
    public BinaryTree<E> getLeftSubtree() {
        if (root != null && root.left != null) {
            return new BinaryTree<>(root.left);
        } else {
            return null;
        }
    }

    
    public BinaryTree<E> getRightSubtree() {
        if (root != null && root.right != null) {
            return new BinaryTree<>(root.right);
        } else {
            return null;
        }
    }

    
    public E getData() {
        if (root != null) {
            return root.data;
        } else {
            return null;
        }
    }

 
    public boolean isLeaf() {

        return (root == null || (root.left == null && root.right == null));
    }

    @Override
    public String toString() {
        StringBuilder sb = new StringBuilder();
        toString(root, 1, sb);
        return sb.toString();
    }

    private void toString(Node<E> root, int level, StringBuilder sb) {
        for (int i = 1; i < level; i++)
            sb.append(" ");
        if (root == null)
            sb.append("null\n");
        else {
            sb.append(root.data+"\n");
            toString(root.left, level + 1, sb);
            toString(root.right, level + 1, sb);
        }

    }

  
    public static BinaryTree<String> readBinaryTree(Scanner scan) {
        // Read a line and trim leading and trailing spaces.
        String data = scan.nextLine().trim();
        if (data.equals("null")) {
            return new BinaryTree<>();
        } else {
            BinaryTree<String> leftTree = readBinaryTree(scan);
            BinaryTree<String> rightTree = readBinaryTree(scan);
            return new BinaryTree<>(data, leftTree, rightTree);
        }
    }

}