Extend program BinarySearchTree.java by adding the following operations to the BinarySearchTree class: a. Find the height of the BST. b. Find node with the largest key. c. Find the average of the key values of the nodes. d. Print the nodes in the tree in pre-order, in-order, and post-order. (decided by the user after run) e. Create the same BST shown in question 2. Run your program for the BST shown in question 1 to its final state and output the height, the largest key, and average of the keys. import java.util.*; public class BinarySearchTree1 { public Node root; public BinarySearchTree1() { root = null; } public Node getroot() { return root; } public Node Search(int KEY) { Node x = root; while (x != null && x.item != KEY) { if (KEY < x.item) { x = x.Left; } else { x = x.Right; } } return x; // x.item == key or x == null } public Node SearchRec(Node root, int key) { if (root == null) return null; if ( root.item == key ) return root; if (root.item > key) return SearchRec(root.Left, key); else return SearchRec(root.Right, key); } public void Insert(int newItem) { Node parent = null; Node newNode = new Node(newItem); Node current = root; while (current != null) { parent = current; if (newNode.item < current.item) { current = current.Left; } else { current = current.Right; } } if (root == null) { root = newNode; } else { if (newNode.item < parent.item) { parent.Left = newNode; } else { parent.Right = newNode; } } } public boolean Delete(int key) { Node parent = null; Node curr = root; while (curr != null && curr.item != key) { parent = curr; if (key < curr.item) { curr = curr.Left; } else { curr = curr.Right; } } if (curr == null) { return false; } if (curr.Left == null && curr.Right == null) { if (curr != root) { if (parent.Left == curr) { parent.Left = null; } else { parent.Right = null; } } else { root = null; } } else if (curr.Left != null && curr.Right != null) { Node successor = getSuccessor(curr.Right); int val = successor.item; Delete(successor.item); curr.item = val; } else { Node child = (curr.Left != null)? curr.Left: curr.Right; if (curr != root) { if (curr == parent.Left) { parent.Left = child; } else { parent.Right = child; } } else { root = child; } } return true; } public Node getSuccessor(Node curr) { while (curr.Left != null) { curr = curr.Left; } return curr; } public void InOrder(Node theRoot) { if (!(theRoot == null)) { InOrder(theRoot.Left); theRoot.DisplayNode(); InOrder(theRoot.Right); } } }
Extend program BinarySearchTree.java by adding the following operations to the BinarySearchTree class:
a. Find the height of the BST.
b. Find node with the largest key.
c. Find the average of the key values of the nodes.
d. Print the nodes in the tree in pre-order, in-order, and post-order. (decided by the user after run)
e. Create the same BST shown in question 2. Run your program for the BST shown in question 1 to
its final state and output the height, the largest key, and average of the keys.
import java.util.*;
public class BinarySearchTree1
{
public Node root;
public BinarySearchTree1()
{
root = null;
}
public Node getroot()
{
return root;
}
public Node Search(int KEY)
{
Node x = root;
while (x != null && x.item != KEY)
{
if (KEY < x.item)
{
x = x.Left;
}
else
{
x = x.Right;
}
}
return x; // x.item == key or x == null
}
public Node SearchRec(Node root, int key)
{
if (root == null)
return null;
if ( root.item == key )
return root;
if (root.item > key)
return SearchRec(root.Left, key);
else
return SearchRec(root.Right, key);
}
public void Insert(int newItem)
{
Node parent = null;
Node newNode = new Node(newItem);
Node current = root;
while (current != null)
{
parent = current;
if (newNode.item < current.item)
{
current = current.Left;
}
else
{
current = current.Right;
}
}
if (root == null)
{
root = newNode;
}
else
{
if (newNode.item < parent.item)
{
parent.Left = newNode;
}
else
{
parent.Right = newNode;
}
}
}
public boolean Delete(int key)
{
Node parent = null;
Node curr = root;
while (curr != null && curr.item != key)
{
parent = curr;
if (key < curr.item)
{
curr = curr.Left;
}
else
{
curr = curr.Right;
}
}
if (curr == null) {
return false;
}
if (curr.Left == null && curr.Right == null)
{
if (curr != root)
{
if (parent.Left == curr) {
parent.Left = null;
}
else {
parent.Right = null;
}
}
else {
root = null;
}
}
else if (curr.Left != null && curr.Right != null)
{
Node successor = getSuccessor(curr.Right);
int val = successor.item;
Delete(successor.item);
curr.item = val;
}
else {
Node child = (curr.Left != null)? curr.Left: curr.Right;
if (curr != root)
{
if (curr == parent.Left) {
parent.Left = child;
}
else {
parent.Right = child;
}
}
else {
root = child;
}
}
return true;
}
public Node getSuccessor(Node curr)
{
while (curr.Left != null) {
curr = curr.Left;
}
return curr;
}
public void InOrder(Node theRoot)
{
if (!(theRoot == null))
{
InOrder(theRoot.Left);
theRoot.DisplayNode();
InOrder(theRoot.Right);
}
}
}
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