public class BinaryNode {
private Pixel p;
private BinaryNode childleft,childright,nodeparent;
//constructor
public BinaryNode(Pixel value, BinaryNode left, BinaryNode right, BinaryNode parent){
p = value;
childleft = left;
childright = right;
nodeparent = parent;
}
//constructor for leaf
public BinaryNode(){
p = null;
childleft = childright = nodeparent = null;
}
//return parent
public BinaryNode getParent(){
return nodeparent;

}
//set parent
public void setParent(BinaryNode parent){
nodeparent = parent;
}
//set left
public void setLeft(BinaryNode left){
childleft = left;
}
//set right
public void setRight(BinaryNode right){
childright = right;
}
// set data
public void setData(Pixel p1 ){
p = p1;
}
//check if it is leaf
public boolean isLeaf(){
if (p == null && childleft == null && childright == null){
return true;
}
else{
return false;
}

}
//get the data
public Pixel getData(){
return p;
}
//get the left child
public BinaryNode getLeft(){
return childleft;
}
// get the right child
public BinaryNode getRight(){
return childright;
}

}
// binary search tree class
public class BinarySearchTree implements BinarySearchTreeADT{
BinaryNode root ; //each tree must have a root

//constructor of binary search tree
public BinarySearchTree(){
root = new BinaryNode();
}
//return the root of the tree
public BinaryNode getRoot(){
return root;
}
//get the pixel with same location k
public Pixel get(BinaryNode r, Location k)
{
return getNode(r,k).getData();
}
// insert the pixel to the tree
public void put(BinaryNode r, Pixel data) throws DuplicatedKeyException{
//get the position where the pixel should be inserted
BinaryNode p = getNode(r,data.getLocation());
// if this node is not null, return duplicatedkeyexception
if (!p.isLeaf()){
throw new DuplicatedKeyException();
}
//store the pixel with store function
else{
store(p,data);
}
}

private void store(BinaryNode p, Pixel data) {
//set pixel into the node, and set parent of each child equal to this node
p.setData(data);
BinaryNode left = new BinaryNode();
BinaryNode right = new BinaryNode();
p.setLeft(left);
p.setRight(right);
left.setParent(p);
right.setParent(p);

}
// helper function for finding the right position
private BinaryNode getNode(BinaryNode r, Location key){
//if r is a leaf, return r
if (r.isLeaf()){
return r;
}
else{
// if location is equal to this internal node return r
if (r.getData().getLocation().compareTo(key) == 0){
return r;
}
// if location is greater than this node, go to right
else if (r.getData().getLocation().compareTo(key) == 1){
return getNode(r.getLeft(),key);
}
//other wise go left
else {
return getNode(r.getRight(),key);
}
}
}
// helper function for finding the smallest node.
private BinaryNode getSmallest(BinaryNode r){

BinaryNode p = r;
while (!p.isLeaf()){
p = p.getLeft();
}
return p.getParent();
}

//remove the pixel with same location
public void remove(BinaryNode r, Location key) throws InexistentKeyException {
BinaryNode temp = getNode(r,key);// find the right ndoe
if (temp.isLeaf()){
// if there no such pixel , throw this exception.
throw new InexistentKeyException();
}

else{
//at least one of child is leaf
if (temp.getLeft().isLeaf() || temp.getRight().isLeaf()){
//left child is leaf
if(temp.getLeft().isLeaf()){

BinaryNode right = temp.getRight();
BinaryNode parent = temp.getParent();
//if this node is root, we need set a new root(non-leaf child)
if (parent == null){
this.root = right;
right.setParent(null);
}
//otherwise , the parent points to its non-leaf child
else{
if(parent.getRight().equals(temp)){
parent.setRight(right);
right.setParent(parent);
}
else{
parent.setLeft(right);
right.setParent(parent);
}
}
}
//when right child is a leaf,
else{
BinaryNode left = temp.getLeft();
BinaryNode parent = temp.getParent();
//if the node is root, we need set a new root(non-leaf child)
if (parent == null){
this.root = left ;
left.setParent(null);
}
else{
//otherwise , the parent points to its non-leaf child
if(parent.getRight().equals(temp)){
parent.setRight(left);
left.setParent(parent);
}
else{
parent.setLeft(left);
left.setParent(parent);
}
}}}

else{
//when the node is internal, find the smallest of its right sub tree and replace it
BinaryNode small = getSmallest(temp.getRight());
//replace the data with smallest node of subtree data;
temp.setData(small.getData());
BinaryNode smallparent = small.getParent();
//set its parent points to smallest ndoe 's right;
if(smallparent.getLeft().equals(small)){
smallparent.setLeft(small.getRight());
}
else{
smallparent.setRight(small.getRight());
}
small.getRight().setParent(smallparent);
}

}

}
//helper function of finding smallest node
private BinaryNode smallestNode(BinaryNode r){
if (r.isLeaf()){
return null;
}
else{
BinaryNode p = r;
while (!p.isLeaf()){
p = p.getLeft();
}
return p.getParent();

}
}
//helper function of finding largest node
private BinaryNode largestNode(BinaryNode r){
//if the leaf , return null;
if(r.isLeaf()){
return null;
}
// else return the most right leaf's parent;
else{
BinaryNode p = r;
while(!p.isLeaf()){
p = p.getRight();
}
return p.getParent();
}
}
//successor method
public Pixel successor(BinaryNode r, Location key) {
// TODO Auto-generated method stub
//if r is leaf return null
if (r.isLeaf()){
return null;
}
else{
// else find the the node who is least larger than current node
BinaryNode p = getNode(r,key);
if (!p.isLeaf()&&!p.getRight().isLeaf()){
//if right child is not leaf, find the smallest of its right sub tree
return smallestNode(p.getRight()).getData();
}
else{
// otherwise, go through its parents
BinaryNode parent = p.getParent();
//check the closet parent that the right child is temp
while(parent != null && parent.getRight()==p)
{
p = parent;
parent = parent.getParent();
}
if(parent!= null){
return parent.getData();
}
else{
return null;
}
}
}

}

//predecessor function
public Pixel predecessor(BinaryNode r, Location key) {
// TODO Auto-generated method stub
//if r is a leaf return null
if(r.isLeaf()){
return null;
}
else{
//find the the node who is least smaller than current node
BinaryNode temp = getNode(r,key);
//if right child is not leaf, find the largest of its left sub tree
if (!temp.isLeaf() && !temp.getLeft().isLeaf()){
return largestNode(temp.getLeft()).getData();
}
else{
// other wise go through its parents
BinaryNode p = temp.getParent();
//check the closet parent that the left child is temp
while ( p!= null && p.getLeft()==(temp)){
temp = p;
p = p.getParent();
}
if(p == null){

return null;
}
else{
return p.getData();
}
}
}

}
// find the smallest pixel
public Pixel smallest(BinaryNode r) throws EmptyTreeException {
// TODO Auto-generated method stub
if (r.isLeaf())
throw new EmptyTreeException();
else{
//return the most left node's parent's pixel
BinaryNode p = r;
while (!p.isLeaf()){
p = p.getLeft();
}
return p.getParent().getData();
}
}
//find the largest pixel.
public Pixel largest(BinaryNode r) throws EmptyTreeException {
// TODO Auto-generated method stub
if (this.getRoot().isLeaf())
throw new EmptyTreeException();
else{
//return the most right node's parent's pixel
BinaryNode p = r;
while (!p.isLeaf()){
p = p.getRight();
}
return p.getParent().getData();
}
}

}
/*
* Returns the Pixel with the smallest key larger than the given one (note
* that the tree does not need to store a node with the given key). Returns
* null if the given key has no successor.
*/
public Pixel successor(BinaryNode r, Location key);

/*
* Returns the Pixel with the largest key smaller than the given one (note
* that the tree does not need to store a node with the given key). Returns
* null if the given key has no predecessor.
*/
public Pixel predecessor(BinaryNode r, Location key);

/*
* Returns the Pixel with the smallest key. Throws an EmptyTreeException if
* the tree is empty.
*/
public Pixel smallest(BinaryNode r) throws EmptyTreeException;

/*
* Returns the Pixel with the largest key. Throws an EmptyTreeException if
* the tree is empty.
*/
public Pixel largest(BinaryNode r) throws EmptyTreeException;
}
import java.awt.Color;
import java.awt.Graphics;

import javax.swing.JComponent;

public class Board extends JComponent {

static final long serialVersionUID = 1;

public Board() {
}

public void paint(Graphics display) {
display.setColor(Color.lightGray);
}
}

Answer the following questions: 1) List of prime numbers Recall:...