(Parent reference for BST) Redefine TreeNode by adding a reference to a node’s parent, as shown below:

(Parent reference for BST) Redefine TreeNode by adding a reference to a node’s parent, as shown below:

Reimplement the insert and delete methods in the BST class to update the parent for each node in the tree. Add the following new method in BST:

/** Returns the node for the specified element. 
* Returns null if the element is not in the tree. */
private TreeNode<E> getNode(E element) 
/** Returns true if the node for the element is a leaf */
private boolean isLeaf(E element)
/** Returns the path of elements from the specified element 
 * to the root in an array list. */
public ArrayList<E> getPath(E e)

Write a test program that prompts the user to enter 10 integers, adds them to the tree, deletes the first integer from the tree, and displays the paths for all leaf nodes. Here is a sample run:

Enter 10 integers: 45 54 67 56 50 45 23 59 23 67

[50, 54, 23]

[59, 56, 67, 54, 23]