Evaluating the Performance of Binary Search Tree The major advantage of binary search trees over other data structures is that the related sorting algorithms, search algorithms, insertion, and deletion can be very efficient when balanced. A binary search tree is an appropriate structure for many of the same applications discussed previously in conjunction with other collection structures, especially those providing sorted lists. The special advantage of using a binary search tree is that it facilitates searching while conferring the benefits of linking the elements. It provides the best features of both the sorted array-based list and the linked list. Similar to a sorted array-based list, it can be searched quickly, using a binary search. Similar to a linked list, it allows insertions and removals without having to move large amounts of data. Thus, a binary search tree is particularly well suited for applications in which processing time to insert, add and delete must be minimized. However, all aforementioned advantages are completed depend on how a tree was created. For example, in a balanced BST with N nodes, its minimum height is O(log n), it takes at maximum O(log n) comparisons to find a particular node. However, in the worst-case scenario, it takes up to O(n) comparisons to find a particular node. The following table summarizes the number of Nodes, height, and the number of comparisons to search a particular node in a balanced tree and the worst case. Example of Searching a Node in a Balanced Tree and the Worst Case Number of Nodes Height of the Tree Number of Comparisons Balanced Tree Worst Case Balanced Tree Worst Case 3 1 3 2 3 7 2 7 3 7 1024 9 1024 10 1024 4096 11 4096 12 4096 Your Tasks: For this assignment, you are required to design experiments to evaluate the relationship between BST tree height (h) and the number of comparisons to find a particular node in a tree.

Fix the code below so that there is a function that calculate the height of the triangle.   package recursion; import javax.swing.*;import java.awt.*; /** * Draw a Sierpinski Triangle of a given order on a JPanel. *  *  */public class SierpinskiPanel extends JPanel {     private static final int WIDTH = 810;    private static final int HEIGHT = 830;        private int order;     /**     * Construct a new SierpinskiPanel.     */    public SierpinskiPanel(int order) {                this.order = order;                this.setMinimumSize(new Dimension(WIDTH, HEIGHT));        this.setMaximumSize(new Dimension(WIDTH, HEIGHT));        this.setPreferredSize(new Dimension(WIDTH, HEIGHT));    }        public static double height(double size) {        double h = (size * Math.sqrt(3)) / 2.0;        return h;    }    /**     * Draw an inverted triangle at the specified location on this JPanel.     *      * @param x the x coordinate of the upper left corner of the triangle     * @param y the y…

class Queue {      private static int front, rear, capacity; private static int queue[];  Queue(int c) {  front = rear = 0;  capacity = c;  queue = new int[capacity]; }  static void queueEnqueue(int data) {   if (capacity == rear) {   System.out.printf("\nQueue is full\n");   return;  }     else {   queue[rear] = data;   rear++;  }  return; }  static void queueDequeue() {    if (front == rear) {   System.out.printf("\nQueue is empty\n");   return;  }   else {   for (int i = 0; i < rear - 1; i++) {    queue[i] = queue[i + 1];   }       if (rear < capacity)    queue[rear] = 0;       rear--;  }  return; }   static void queueDisplay() {  int i;  if (front == rear) {   System.out.printf("\nQueue is Empty\n");   return;  }     for (i = front; i < rear; i++) {   System.out.printf(" %d <-- ", queue[i]);  }  return; }   static void queueFront() {  if (front == rear) {   System.out.printf("\nQueue is Empty\n");   return;  }  System.out.printf("\nFront Element is: %d", queue[front]);…

Java programming language I have to create a remove method that removes the element at an index (ind) or space in an array and returns it. Thanks!   I have to write the remove method in the code below. i attached the part where i need to write it. public class ourArrayList<T>{ private Node<T> Head = null; private Node<T> Tail = null; private int size = 0; //default constructor public ourArrayList() { Head = Tail = null; size = 0; } public int size() { return size; } public boolean isEmpty() { return (size == 0); } //implement the method add, that adds to the back of the list public void add(T e) { //HW TODO and TEST //create a node and assign e to the data of that node. Node<T> N = new Node<T>();//N.mData is null and N.next is null as well N.setsData(e);   //chain the new node to the list   //check if the list is empty, then deal with the special case if(this.isEmpty()) { //head and tail refer to N this.Head = this.Tail = N; size++; //return we are done.…