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made several methods recursive, made independent of AbstractBinaryTree,

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made the thing work!
This commit is contained in:
gabe venberg 2021-04-27 02:15:46 -05:00
parent dd9c437269
commit b34a4b51aa
11 changed files with 428 additions and 527 deletions
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76
Lab110-VenbergGE/src/AbstractBinaryTree.java
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@ -1,76 +0,0 @@
import java.util.ArrayList;
import java.util.Iterator;
import java.util.List;
/*
* * Data Structures & Algorithms 6th Edition
* Goodrich, Tamassia, Goldwasser
* Code Fragments 8.7, 8.26, 8.22
*\
/**
* an abstract base class providing some functionality of the binarytree interface
* @author Gabriel Venberg
*/
public abstract class AbstractBinaryTree<E> extends AbstractTree<E> implements BinaryTree<E> {
public Position<E> sibling(Position<E> p){
Position<E> parent = parent(p);
//p is root.
if (parent == null){return null;}
//p is left child, right child might be null.
if (p==left(parent)){return right(parent);}
//p is right child, left child might be null.
else {return left(parent);}
}
/**returns the number of children of Position p*/
public int numChildren(Position<E> p){
int count=0;
if (left(p)!=null){count++;}
if(right(p)!=null){count++;}
return count;
}
/**returns an iterable collection of Positions representing p's children.*/
public Iterable<Position<E>> children(Position<E> p){
//max capacity of 2
List <Position<E>> snapshot=new ArrayList<>(2);
//needed to modify this, as the arraylist we made in class needed an index
if(left(p)!=null){snapshot.add(left(p));}
if(right(p)!=null){snapshot.add(right(p));}
// and our arraylist
return snapshot;
}
/**adds positions of the subtree rooted at Position p to the given snapshot*/
private void inorderSubtree(Position<E> p, List<Position<E>> snapshot){
if(left(p)!=null){inorderSubtree(left(p), snapshot);}
snapshot.add(p);
if(right(p)!=null){inorderSubtree(right(p), snapshot);}
}
/**returns an iterable collection of the positions of the tree, reported in inorder.*/
public Iterable<Position<E>> inorder(){
List<Position<E>> snapshot=new ArrayList<>();
//fill snapshot recursively
if(!isEmpty()){inorderSubtree(root(), snapshot);}
return snapshot;
}
/**Overrides positions to make inorder the default order for binary trees*/
public Iterable<Position<E>> positions(){
return inorder();
}
//nested ElementIterator class
/**this class adapts the iteration produced by positions() to returns elements*/
private class ElementIterator implements Iterator<E>{
Iterator<Position<E>> posIterator=positions().iterator();
public boolean hasNext(){return posIterator.hasNext();}
//return element
public E next(){return posIterator.next().getElement();}
public void remove(){posIterator.remove();}
}//end of nested ElementIterator class
/**returns an iterator if the elements stored in the tree*/
public Iterator<E> iterator(){return new ElementIterator();}
}

104
Lab110-VenbergGE/src/AbstractTree.java
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@ -1,104 +0,0 @@
import java.util.ArrayList;
import java.util.List;
/*
* * Data Structures & Algorithms 6th Edition
* Goodrich, Tamassia, Goldwasser
* Code Fragments 8.2-8.5, 8.19-21
*\
/*
* an abstract base class providing some functionality of the tree interface.
* @author Gabriel Venberg
*/
public abstract class AbstractTree<E> implements Tree<E> {
public boolean isInternal(Position<E> p) {return numChildren(p)>0;}
public boolean isExternal(Position<E> p){return numChildren(p)==0;}
public boolean isRoot(Position<E> p){return p == root();}
public boolean isEmpty(){return size()==0;}
/**returns the number of levels sperating position p from the root.*/
public int depth(Position<E> p){
if (isRoot(p)){return 0;}
else{return 1+depth(parent(p));}
}
/**returns the hight of the tree.*/
private int hightBad(){ //works, but quadratic worst case time.
int h=0;
for(Position<E> p : positions()){
//only consider leaf positions.
if(isExternal(p)){h=Math.max(h, depth(p));}
}
return h;
}
/**returns the hight of the subtree rooted at position p. should be O(n) time.*/
public int hight(Position<E> p){
//base case if p is external
int h=0;
for (Position<E> c : children(p)){
h=Math.max(h,1+hight(c));
}
return h;
}
//iterators
/**adds positions of the subtree rooted at position p to the given snapshot (for use in traversal)*/
private void preorderSubtree(Position<E> p, List<Position<E>> snapshot){
//for preorder, add position p before exploring subtrees.
snapshot.add(p);
for(Position<E> c:children(p)){
preorderSubtree(c, snapshot);
}
}
/**returns an iterable collection of positions in the tree, reported in preorder*/
public Iterable<Position<E>> preorder(){
List<Position<E>> snapshot=new ArrayList<>();
//fill the snapshot recursively
if(!isEmpty()){
preorderSubtree(root(), snapshot);
}
return snapshot;
}
/**adds positions of the subtree rooted at position p to the given snapshot (for use in traversal)*/
private void postorderSubtree(Position<E> p, List<Position<E>> snapshot){
//for postorder, add position p before exploring subtrees.
for(Position<E> c:children(p)){
postorderSubtree(c, snapshot);
}
snapshot.add(p);
}
/**returns an iterable collection of positions in the tree, reported in postorder*/
public Iterable<Position<E>> postorder(){
List<Position<E>> snapshot=new ArrayList<>();
//fill the snapshot recursively
if(!isEmpty()){
postorderSubtree(root(), snapshot);
}
return snapshot;
}
/**returns an iterable collection of positions in the tree in breadth first traversal*/
public Iterable<Position<E>> breadthFirst(){
List<Position<E>> snapshot=new ArrayList<>();
if(!isEmpty()){
Queue<Position<E>> fringe=new LinkedQueue<>();
fringe.enqueue(root());
while(!fringe.isEmpty()){
Position<E> p=fringe.dequeue();
snapshot.add(p);
for(Position<E> c:children(p)){
fringe.enqueue(c);
}
}
}
return snapshot;
}
/**default iterator*/
public Iterable<Position<E>> positions(){return preorder();}
}

55
Lab110-VenbergGE/src/ArrayStack.java Normal file
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@ -0,0 +1,55 @@
/*
* Data Structures & Algorithms 6th Edition
* Goodrich, Tamassia, Goldwasser
* Code Fragment 6.2
*
* An implementation of an ArrayStack class
* */
/**
*
* @author Gabriel Venberg
*/
public class ArrayStack<E> implements Stack<E> {
public static final int CAPACITY = 1000;//default capacity
private E[] data; //generic array used for storage.
private int t=-1; //index of the top element in the stack
//im swiching the authors comments to javadoc style, for ease of use.
/**
* constructs stack with default capacity
*/
public ArrayStack(){this(CAPACITY);}
/**
* constructs stack with given capacity
* @param capacity capacity to construct the stack with.
*/
public ArrayStack(int capacity){
data = (E[]) new Object[capacity];
}
public int size(){return (t+1);}
public boolean isEmpty(){return(t==-1);}
public void push(E e) throws IllegalStateException{
if(size()==data.length){throw new IllegalStateException("Stack is full");}
data[++t]=e; //increment t before storing a new item.
}
public E top(){
if(isEmpty()){return null;}
return data[t];
}
public E pop(){
if(isEmpty()){return null;}
E answer = data[t];
data[t] = null; //dereference to help with garbage collection.
t--;
return answer;
}
}

291
Lab110-VenbergGE/src/BinarySearchTree.java
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@ -1,17 +1,21 @@
import java.util.ArrayList;
/**
*
* @author Gabriel Venberg
*/
public class BinarySearchTree extends AbstractBinaryTree<Integer> {
public class BinarySearchTree {
//Represent a node of binary tree
private static class Node implements Position<Integer>{
private static class Node implements Position<Integer> {
private int data;
private Node left;
private Node right;
private Node parent;
public Node(int data){
public Node(int data) {
//Assign data to the new node, set left and right children to null
this.data = data;
this.left = null;
@ -19,59 +23,89 @@ public class BinarySearchTree extends AbstractBinaryTree<Integer> {
this.parent = null;
}
public Integer getElement(){return data;}
public Integer getElement() {
return data;
}
public Node getLeft(){return left;}
public Node getRight(){return right;}
public Node getParent(){return parent;}
public void setData(int newData){data=newData;}
public void setLeft(Node newLeft){left=newLeft;}
public void setRight(Node newRight){right=newRight;}
public void setParent(Node newParent){parent=newParent;}
public Node getLeft() {
return left;
}
public Node getRight() {
return right;
}
public Node getParent() {
return parent;
}
public void setData(int newData) {
data = newData;
}
public void setLeft(Node newLeft) {
left = newLeft;
}
public void setRight(Node newRight) {
right = newRight;
}
public void setParent(Node newParent) {
parent = newParent;
}
}
//Represent the root of binary tree
private Node root;
private int size = 0;
public BinarySearchTree(){
public BinarySearchTree() {
root = null;
}
public Position<Integer> root(){return root;}
public int size(){return size;}
public Position<Integer> root() {
return root;
}
public int size() {
return size;
}
//nonpublic utility
/**validates the position and returns it as a node*/
protected Node validate(Position<Integer> p) throws IllegalArgumentException{
if(!(p instanceof Node)){
/**
* validates the position and returns it as a node
*/
protected Node validate(Position<Integer> p) throws IllegalArgumentException {
if (!(p instanceof Node)) {
throw new IllegalArgumentException("not a valid position type");
}
//safe cast
Node node=(Node)p;
Node node = (Node) p;
//our convention for a defunct node. Wont this make the GC not clean it up? why not just set the parent to null and let the GC clean it up?
if(node.getParent()==node){
if (node.getParent() == node) {
throw new IllegalArgumentException("p is no longer in the tree");
}
return node;
}
//methods for getting info about specific nodes.
public Position<Integer> parent(Position<Integer> n){
Node node=validate(n);
public Position<Integer> parent(Position<Integer> n) {
Node node = validate(n);
return node.getParent();
}
public Position<Integer> left(Position<Integer> n){
public Position<Integer> left(Position<Integer> n) {
Node node = validate(n);
return node.getLeft();
}
public Position<Integer> right(Position<Integer> n){
public Position<Integer> right(Position<Integer> n) {
Node node = validate(n);
return node.getLeft();
}
//copy and modify to find method, use find to calculate depth of each node
//insert() will add new node to the binary search tree
public void insert(int data) {
//Create a new node
@ -79,32 +113,30 @@ public class BinarySearchTree extends AbstractBinaryTree<Integer> {
size++;
//Check whether tree is empty
if(root == null){
if (root == null) {
root = newNode;
return;
}
else {
} else {
//current node point to root of the tree
Node current = root, parent = null;
while(true) {
while (true) {
//parent keep track of the parent node of current node.
parent = current;
//If data is less than current's data, node will be inserted to the left of tree
if(data < current.data) {
if (data < current.data) {
current = current.getLeft();
if(current == null) {
if (current == null) {
parent.setLeft(newNode);
newNode.setParent(parent);
return;
}
}
//If data is greater than current's data, node will be inserted to the right of tree
} //If data is greater than current's data, node will be inserted to the right of tree
else {
current = current.getRight();
if(current == null) {
if (current == null) {
parent.setRight(newNode);
newNode.setParent(parent);
return;
@ -114,58 +146,93 @@ public class BinarySearchTree extends AbstractBinaryTree<Integer> {
}
}
//find() will take a key and return the depth of that key.
public int find(int data) throws IllegalStateException, IllegalArgumentException {
int depth = 0;
//chekc if tree is empty
if (root == null) {
throw new IllegalStateException("tree is empty");
} else {
Node current = root;
Node parent = null;
while (true) {
//advance our way along the tree
parent = current;
if(data < current.data) {
current = current.getLeft();
//if there is no left child, element does not exist.
if (current == null) {
throw new IllegalArgumentException("data does not exitst");
}
} else if(data > current.data) {
current = current.getRight();
if (current == null) {
throw new IllegalArgumentException("data does not exitst");
}
} //must otherwise be equal
else {
return depth;
}
depth++;
}
}
}
//gets the hight of the tree. should run in O(nlog(n)) time.
public int hight() throws IllegalStateException {
ArrayList<Integer> nodeList = nodeList(root);
int hight = 0;
for(int i=0; i<nodeList.size(); i++){
hight = Math.max(hight, find(nodeList.get(i)));
}
return hight;
}
//minNode() will find out the minimum node
public Position<Integer> minNode(Node root) {
if (root.left != null)
if (root.left != null) {
return minNode(root.left);
else
} else {
return root;
}
}
//deleteNode() will delete the given node from the binary search tree
public Position<Integer> deleteNode(Position<Integer> position, int value) {
size--;
Node node = validate(position);
if(node == null){
if (node == null) {
return null;
}
else {
} else {
//value is less than node's data then, search the value in left subtree
if(value < node.getElement())
//should be a safe cast...
node.setLeft((Node)deleteNode(node.getLeft(), value));
//value is greater than node's data then, search the value in right subtree
else if(value > node.getElement())
//should be a safe cast...
node.setRight((Node)deleteNode(node.getRight() , value));
//If value is equal to node's data that is, we have found the node to be deleted
if (value < node.getElement()) //should be a safe cast...
{
node.setLeft((Node) deleteNode(node.getLeft(), value));
} //value is greater than node's data then, search the value in right subtree
else if (value > node.getElement()) //should be a safe cast...
{
node.setRight((Node) deleteNode(node.getRight(), value));
} //If value is equal to node's data that is, we have found the node to be deleted
else {
//If node to be deleted has no child then, set the node to null
if(node.getLeft() == null && node.getRight() == null)
if (node.getLeft() == null && node.getRight() == null) {
node = null;
//If node to be deleted has only one right child
else if(node.getLeft() == null) {
node = node.getRight() ;
}
//If node to be deleted has only one left child
else if(node.getRight() == null) {
} //If node to be deleted has only one right child
else if (node.getLeft() == null) {
node = node.getRight();
} //If node to be deleted has only one left child
else if (node.getRight() == null) {
node = node.getLeft();
}
//If node to be deleted has two children node
} //If node to be deleted has two children node
else {
//then find the minimum node from right subtree
//should be a safe cast...
Node temp = (Node)minNode(node.getRight() );
Node temp = (Node) minNode(node.getRight());
//Exchange the data between node and temp
node.setData(temp.getElement());
//Delete the node duplicate node from right subtree
//should be a safe cast...
node.setRight((Node)deleteNode(node.getRight() , temp.getElement()));
node.setRight((Node) deleteNode(node.getRight(), temp.getElement()));
}
}
return node;
@ -173,21 +240,105 @@ public class BinarySearchTree extends AbstractBinaryTree<Integer> {
}
//inorder() will perform inorder traversal on binary search tree
//made iterative
public void inorderTraversal(Position<Integer> position) {
Node node = validate(position);
//Check whether tree is empty
if(root == null){
if (root == null) {
System.out.println("Tree is empty");
return;
} else {
ArrayStack<Node> nodeStack = new ArrayStack<>(size);
Node current = root;
while(current!=null||!nodeStack.isEmpty()){
//go down the left side as far as we can.
while(current!=null){
nodeStack.push(current);
current=current.getLeft();
}
else {
if(node.getLeft()!= null)
inorderTraversal((Position<Integer>)node.getLeft());
System.out.print(node.getElement() + " ");
if(node.getRight() != null)
inorderTraversal((Position<Integer>)node.getRight());
//then go up one and to the right
current = nodeStack.pop();
System.out.print(current.getElement());
current = current.getRight();
}
}
}
//turns out that if we visit the right node before the left one in a preorder, we get a reversed post order traversal.
public void postorderTraversal(Position<Integer> position) {
Node root = validate(position);
if (root == null) {
System.out.println("Tree is empty");
return;
} else {
ArrayStack<Node> nodeStack = new ArrayStack<>(size);
ArrayStack<Integer> returnStack = new ArrayStack<>(size);
nodeStack.push(root);
//do a modified preorder
while(!nodeStack.isEmpty()){
Node node = nodeStack.pop();
returnStack.push(node.getElement());
if (node.getRight() != null) {
nodeStack.push(node.getRight());
}
if (node.getLeft() != null) {
nodeStack.push(node.getLeft());
}
}
//print in reverse order
while(!returnStack.isEmpty()){
System.out.print(returnStack.pop());
}
}
}
//made iterative
public void preorderTraversal(Position<Integer> position) {
Node root = validate(position);
//Check whether tree is empty
if (root == null) {
System.out.println("Tree is empty");
return;
} else {
ArrayStack<Node> nodeStack = new ArrayStack<>(size);
nodeStack.push(root);
while (!nodeStack.isEmpty()) {
Node node = nodeStack.pop();
System.out.print(node.getElement());
if (node.getLeft() != null) {
nodeStack.push(node.getLeft());
}
if (node.getRight() != null) {
nodeStack.push(node.getRight());
}
}
}
}
//returns a list of entries from the external children of the node.
//made iterative
public ArrayList<Integer> nodeList(Position<Integer> position) throws IllegalStateException {
Node root = validate(position);
ArrayList<Integer> nodeList = new ArrayList<>();
//Check whether tree is empty
if (root == null) {
throw new IllegalStateException("tree is empty");
} else {
ArrayStack<Node> nodeStack = new ArrayStack<>(size);
nodeStack.push(root);
while (!nodeStack.isEmpty()) {
Node node = nodeStack.pop();
//only add if it is external.
if (node.getLeft() == null && node.getRight() == null) {
nodeList.add(node.getElement());
}
if (node.getLeft() != null) {
nodeStack.push(node.getLeft());
}
if (node.getRight() != null) {
nodeStack.push(node.getRight());
}
}
}
return nodeList;
}
}

18
Lab110-VenbergGE/src/BinaryTree.java
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@ -1,18 +0,0 @@
/*
* * Data Structures & Algorithms 6th Edition
* Goodrich, Tamassia, Goldwasser
* Code Fragments 8.6
*\
\**
*an interface for a binary tree, in which each node has at most two children.
* @author Gabriel Venberg
*/
public interface BinaryTree<E> extends Tree<E> {
/**returns the position of p's left child (or null if no child exists).*/
Position<E> left(Position<E> p) throws IllegalArgumentException;
/**returns the position of p's right child (or null if no child exists)*/
Position<E> right(Position<E> p) throws IllegalArgumentException;
/**returns the position of p's sibling (or null of no sibling exists).*/
Position <E> sibling(Position<E> p) throws IllegalArgumentException;
}

27
Lab110-VenbergGE/src/Client.java
View file

@ -27,7 +27,7 @@ public class Client {
//set up stuff needed for test.
final int BSTSize = 10;
final int BSTSize = 1000000;
long startTime;
long endTime;
String[][] data = new String[7][2];
@ -36,27 +36,34 @@ public class Client {
BinarySearchTree testTree = new BinarySearchTree();
startTime=System.nanoTime();
for(int i=0; i<BSTSize; i++){
System.out.println("test1,"+i);
testTree.insert(i);
}
data[0][1] = String.format("%,d", testTree.hight(testTree.root()));
System.out.println("test2");
data[0][1] = String.format("%,d", testTree.hight());
endTime=System.nanoTime();
data[0][0]=String.format("%,d", endTime-startTime);
testTree.inorderTraversal(testTree.root());
System.out.println();
testTree.preorderTraversal(testTree.root());
System.out.println();
testTree.postorderTraversal(testTree.root());
System.out.println();
//decending order test
testTree = new BinarySearchTree();
startTime=System.nanoTime();
for(int i=BSTSize-1; i>=0; i--){
System.out.println("test3,"+i);
testTree.insert(i);
}
data[1][1] = String.format("%,d", testTree.hight(testTree.root()));
System.out.println("test4,");
data[1][1] = String.format("%,d", testTree.hight());
endTime=System.nanoTime();
data[1][0]=String.format("%,d", endTime-startTime);
testTree.preorderTraversal(testTree.root());
System.out.println();
testTree.postorderTraversal(testTree.root());
System.out.println();
testTree.inorderTraversal(testTree.root());
System.out.println();
@ -73,15 +80,11 @@ public class Client {
startTime=System.nanoTime();
for(int j=0; j<uniqueNumbers.length; j++){
System.out.println("test5,"+i+","+j);
testTree.insert(uniqueNumbers[j]);
}
data[i+2][1]=String.format("%,d", testTree.hight(testTree.root()));
System.out.println("test6,"+i);
data[i+2][1]=String.format("%,d", testTree.hight());
endTime=System.nanoTime();
data[i+2][0]=String.format("%,d", endTime-startTime);
testTree.inorderTraversal(testTree.root());
System.out.println();
}
String[] colHeaders = {"Time taken", "Tree hight"};

21
Lab110-VenbergGE/src/LinkedQueue.java
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@ -1,21 +0,0 @@
/*
* Data Structures & Algorithms 6th Edition
* Goodrich, Tamassia, Goldwasser
* Code Fragment 6.11
*
* An implementation of the LinkedQueue class
* */
/**
*
* @author Gabriel Venberg
*/
public class LinkedQueue<E> implements Queue<E>{
private SinglyLinkedList<E> list = new SinglyLinkedList(); //an empty list
public LinkedQueue(){} //new queue relies on initaly empty list
public int size(){return list.size();}
public boolean isEmpty(){return list.isEmpty();}
public void enqueue(E element){list.addLast(element);}
public E first(){return list.first();}
public E dequeue(){return list.removeFirst();}
}

28
Lab110-VenbergGE/src/Queue.java
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@ -1,28 +0,0 @@
/**
* Data Structures & Algorithms 6th Edition
* Goodrich, Tamassia, Goldwasser
* Code Fragment 6.9
*
* An implementation of the Queue interface
* */
/**
*
* @author Gabriel Venberg
*/
public interface Queue<E> {
/** returns the number of elements in the queue*/
int size();
/** tests whether the queue is empty*/
boolean isEmpty();
/**inserts an element at the rear of the queue*/
void enqueue(E e);
/**returns, but does not remove, the first element of the queue (null if empty). */
E first();
/** removes and returns the first element of the queue (null if empty)*/
E dequeue();
}

78
Lab110-VenbergGE/src/SinglyLinkedList.java
View file

@ -1,78 +0,0 @@
/**
*SinglyLinkedListClass
* Code Fragments 3.14, 3.15
* from
* Data Structures & Algorithms, 6th edition
* by Michael T. Goodrich, Roberto Tamassia & Michael H. Goldwasser
* Wiley 2014
* Transcribed by
* @author Gabe Venberg
*/
public class SinglyLinkedList<E> {
private static class Node<E> {
private E element; //refrence to element stored at this node
private Node<E> next; //refrence to subsequent node of list
public Node(E e, Node<E> n){
element = e;
next = n;
}
public E getElement() {return element;}
public Node<E> getNext() {return next;}
public void setNext(Node<E> n) {next = n;}
}
//instance variables of SinglyLinkedList
private Node<E> head = null;//head node of list
private Node<E> tail = null;//last node of list
private int size = 0;//number of nodes in list
public SinglyLinkedList(){}//constructs an initaly empty list
//access methods
public int size() {return size;}
public boolean isEmpty() {return size == 0;}
public E first(){//returns but does not remove the first element
if (size == 0) {return null;} //special case
return head.getElement();
}
public E last(){//returns but does not remove last elemnt
if (size ==0) {return null;}//special case
return tail.getElement();
}
//update methods
public void addFirst(E e){//adds element e to the front of the list
head = new Node<>(e, head);//create and link a new node
if (size == 0) {tail = head;}//special case, head becomes tail also
size++;
}
public void addLast(E e){//adds element to end of list
Node<E> newest = new Node<>(e, null);//create and link a new node
if(size == 0){//special case, previously empty list
head = newest;
}
else{
tail.setNext(newest);//new node after existing tail
}
tail = newest;//new node becomes tail
size++;
}
public E removeFirst(){//removes and returns the first element
if(size == 0){return null;}//nothing to remove
E answer = head.getElement();
head = head.getNext();//will become null if list had only one node.
size--;
if(size==0){tail = null;}// special case as list is now empty
return answer;
}
}

46
Lab110-VenbergGE/src/Stack.java Normal file
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/**
* Data Structures & Algorithms 6th Edition
* Goodrich, Tamassia, Goldwasser
* Code Fragment 6.1
*
* An implementation of the stack interface
* */
/**
* A collection of objects that are inserted and removed according to a last-in
* first-out principle. Although similar in purpose, this interface differs from
* java.util.stack.
* @author Gabriel Venberg
*/
public interface Stack<E> {
/**
* returns the number of elements in the stack
* @return number of elements in the stack.
*/
int size();
/**
* tests whether the stack is empty.
* @return true if stack is empty, false otherwise.
*/
boolean isEmpty();
/**
* inserts an element at the top of the stack.
* @param e the element to be inserted.
*/
void push(E e);
/**
* returns, but does not remove, the top element of the stack.
* @return top element of the stack or null if empty.
*/
E top();
/**
* removes and returns the top element from the stack.
* @return element removed or null if empty.
*/
E pop();
}

29
Lab110-VenbergGE/src/Tree.java
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@ -1,29 +0,0 @@
import java.util.Iterator;
/*
* Data Structures & Algorithms 6th Edition
* Goodrich, Tamassia, Goldwasser
* Code Fragment 8.1
*
* An implementation of the tree interface
*/
/**
* An interface for a tree where nodes can have an arbitrary number of children.
* @author Gabriel Venberg
*/
public interface Tree<E> extends Iterable<E>{
Position <E> root();
Position<E> parent(Position<E> p) throws IllegalArgumentException;
Iterable<Position<E>> children(Position<E> p) throws IllegalArgumentException;
int numChildren(Position<E> p) throws IllegalArgumentException;
boolean isInternal(Position<E> p) throws IllegalArgumentException;
boolean isExternal(Position<E> p) throws IllegalArgumentException;
boolean isRoot(Position<E> p) throws IllegalArgumentException;
int size();
boolean isEmpty();
Iterator<E> iterator();
Iterable<Position<E>> positions();
}