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Lab 110, not hight count is funky (can be impossibly low) and seems to be incredibly unperformant. Im going to sleep on it.

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gabe venberg 2021-04-26 00:35:14 -05:00
parent 29c576c988
commit dd9c437269
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2
.gitignore vendored
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@ -47,3 +47,5 @@ hs_err_pid*
/Lab108-VenbergGE/build/
/Lab108-VenbergGE/dist/
/Lab109/build/
/Lab110-VenbergGE/nbproject/private/
/Lab110-VenbergGE/build/

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Lab110-VenbergGE/src/ASCIITable.java Normal file
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/*
* Copyright (C) 2021 Gabriel Venberg
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
/**
* utility library for nicely formatted ascii tables.
* @author Gabriel Venberg
*/
public class ASCIITable {
/**
* generates an ASCII table based on a 2d data array. the top level array is an array of rows.
* @param data 2d array containing data to put in table
* @param padding how much padding to put on each side of entries
* @param tableHeader string to put in the table header (may cause problems if extremely long)
* @param columnHeaders array of strings to put at the top of each column.
* @return
*/
public static String render(Object data[][], int padding, String tableHeader, String[] columnHeaders) throws IllegalArgumentException {
int cols = calcNoCols(data);
if(cols!=columnHeaders.length){throw new IllegalArgumentException("must have equal number of column headers as columns!");}
int[] colWidths = calcColumnWidth(cols, data, columnHeaders);
//colWidths does not count padding or the | chars betwwen tables.
int width = sumOfArray(colWidths)+padding*cols*2+(cols-1);
String horizontalSpacer = assembleHorizontalSpacers(colWidths, padding, cols);
/*ok, so each cell will have the colwidth for the data, then padding for padding,
* then a | at the end. (plus 1 at the begginning of the table.
there will be 2 rows for each row of data (horizontal sep) plus a horizontal sep
at the end.
*/
String string = horizontalSpacer+'\n';
//print table header
string=string+tableHeader(tableHeader, width)+"\n";
string = string+horizontalSpacer+"\n";
//print coumn headers
string=string+columnHeaderString(colWidths, padding, columnHeaders)+'\n';
//got everything set up, build the table row by row.
for(int i=0; i<data.length; i++){
string = string+horizontalSpacer+"\n";
string = string+dataString(colWidths, padding, data[i])+'\n';
}
string = string+horizontalSpacer;
return string;
}
private static String tableHeader(String header, int width){
String string="|";
int halfPadding=(width-header.length())/2;
//front padding
for(int i=0; i<halfPadding; i++){string=string+" ";}
//if the total padding we need is odd, put it in front of the header
if((width-header.length())%2==1){string=string+" ";}
string=string+header;
//rear padding
for(int i=0; i<halfPadding; i++){string=string+" ";}
string=string+"|";
return string;
}
/**
* calcs the sum of all elements in an int array
* @param array array to be summed
* @return sum of array
*/
private static int sumOfArray(int[] array){
int sum=0;
for(int i=0; i<array.length; i++){
sum += array[i];
}
return sum;
}
/**
* calculates the maximum number of entries the rows in the data set have
* @param data 2D array of data
* @return needed number of rows in the final table.
*/
private static int calcNoCols(Object data[][]){
int rows = 0;
for(int i=0; i<data.length; i++){
rows = Math.max(rows, data[i].length);
}
return rows;
}
/**
* calculates the needed column widths for a data array without padding
* @param data the array of data
* @return an array of integers representing the needed width of each column
*/
private static int[] calcColumnWidth(int cols, Object data[][], String[] headers){
int[] maxWidths = new int[cols];
for(int i=0; i<cols; i++){
maxWidths[i]=headers[i].length();
for(int j=0; j<data.length; j++){
maxWidths[i]=Math.max(maxWidths[i], data[j][i].toString().length());
}
}
return maxWidths;
}
/**
* gives the horizontal spacer needed for the table
* @param colWidth width of each column;
* @param padding padding on each side of data.
* @param noOfCols number of columns;
* @return a string suitable to use as the horizontal spacer for the table.
*/
private static String assembleHorizontalSpacers(int[] colWidth, int padding, int noOfCols){
String string = "+";
for(int i=0; i<noOfCols; i++){
for(int j=0; j<colWidth[i]+2*padding; j++){
string = string+'-';
}
string = string+'+';
}
return string;
}
/**
* takes a single row of the data array and returns a row. Make sure your colWidth is accurate.
* @param colWidth width of each column
* @param padding min padding to have around each entry
* @param data 1D array of data to print
* @return a string containing the data
*/
private static String dataString(int[] colWidth, int padding, Object data[]){
String string ="|";
//for each entry in the row
for(int i=0; i<data.length; i++){
//only calc this once.
int length=data[i].toString().length();
// front padding. Also, I wish java had string multiplication.
for(int p=0; p<padding+(colWidth[i]-length); p++){string = string+" ";}
string = string+data[i].toString();
//rear padding
for(int p=0; p<padding; p++){string = string+" ";}
string = string+"|";
}
return string;
}
/**
* takes an array of strings (column headers) and outputs a single row of the column, center justified.
* @param colWidth width of each column
* @param padding min padding around each entry
* @param columnHeaders 1d array of strings containing col headers
* @return
*/
private static String columnHeaderString(int[] colWidth, int padding, String columnHeaders[]){
String string="|";
for(int i=0; i<columnHeaders.length; i++){
//calc this once.
int length=columnHeaders[i].length();
int sidePadding=(colWidth[i]-length+padding*2)/2;
//front padding
for(int p=0; p<sidePadding; p++){string=string+" ";}
//if we need an odd number of total padding, add the spare on the front
if((colWidth[i]-length)%2==1){string=string+" ";}
string=string+columnHeaders[i];
//rear padding
for(int p=0; p<sidePadding; p++){string=string+" ";}
string=string+"|";
}
return string;
}
}

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Lab110-VenbergGE/src/AbstractBinaryTree.java Normal file
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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();}
}

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Lab110-VenbergGE/src/AbstractTree.java Normal file
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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();}
}

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Lab110-VenbergGE/src/BinarySearchTree.java Normal file
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/**
*
* @author Gabriel Venberg
*/
public class BinarySearchTree extends AbstractBinaryTree<Integer> {
//Represent a node of binary tree
private static class Node implements Position<Integer>{
private int data;
private Node left;
private Node right;
private Node parent;
public Node(int data){
//Assign data to the new node, set left and right children to null
this.data = data;
this.left = null;
this.right = null;
this.parent = null;
}
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;}
}
//Represent the root of binary tree
private Node root;
private int size = 0;
public BinarySearchTree(){
root = null;
}
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)){
throw new IllegalArgumentException("not a valid position type");
}
//safe cast
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){
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);
return node.getParent();
}
public Position<Integer> left(Position<Integer> n){
Node node = validate(n);
return node.getLeft();
}
public Position<Integer> right(Position<Integer> n){
Node node = validate(n);
return node.getLeft();
}
//insert() will add new node to the binary search tree
public void insert(int data) {
//Create a new node
Node newNode = new Node(data);
size++;
//Check whether tree is empty
if(root == null){
root = newNode;
return;
}
else {
//current node point to root of the tree
Node current = root, parent = null;
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) {
current = current.getLeft();
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
else {
current = current.getRight();
if(current == null) {
parent.setRight(newNode);
newNode.setParent(parent);
return;
}
}
}
}
}
//minNode() will find out the minimum node
public Position<Integer> minNode(Node root) {
if (root.left != null)
return minNode(root.left);
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){
return null;
}
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
else {
//If node to be deleted has no child then, set the node to 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) {
node = node.getLeft();
}
//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() );
//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()));
}
}
return node;
}
}
//inorder() will perform inorder traversal on binary search tree
public void inorderTraversal(Position<Integer> position) {
Node node = validate(position);
//Check whether tree is empty
if(root == null){
System.out.println("Tree is empty");
return;
}
else {
if(node.getLeft()!= null)
inorderTraversal((Position<Integer>)node.getLeft());
System.out.print(node.getElement() + " ");
if(node.getRight() != null)
inorderTraversal((Position<Integer>)node.getRight());
}
}
}

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Lab110-VenbergGE/src/BinaryTree.java Normal file
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/*
* * 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;
}

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Lab110-VenbergGE/src/Client.java Normal file
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import java.util.Random;
/*
* Copyright (C) 2021 Gabriel Venberg
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
/**
*
* @author Gabriel Venberg
*/
public class Client {
public static void main(String args[]){
//set up stuff needed for test.
final int BSTSize = 10;
long startTime;
long endTime;
String[][] data = new String[7][2];
//acending order test
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");
endTime=System.nanoTime();
data[0][0]=String.format("%,d", endTime-startTime);
testTree.inorderTraversal(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,");
endTime=System.nanoTime();
data[1][0]=String.format("%,d", endTime-startTime);
testTree.inorderTraversal(testTree.root());
System.out.println();
//generate arrray containing numbers 0 through 999,999, for 1 million unique numbers.
int[] uniqueNumbers = new int[BSTSize];
for(int i=0; i<BSTSize; i++){
uniqueNumbers[i]=i;
}
//random tests
for(int i=0; i<5; i++){
testTree = new BinarySearchTree();
shuffleArray(uniqueNumbers);
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);
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"};
System.out.println(ASCIITable.render(data, 2, "Binary search trees", colHeaders));
}
//quick helper function to shuffle an array in place
public static void shuffleArray(int[] array){
Random rgen = new Random();
for(int i=0; i<array.length; i++){
int randomPosition = rgen.nextInt(array.length);
//could do this with a temp array that we later return, but to save a bit of memory, we can do this in place.
int temp = array[i];
array[i]=array[randomPosition];
array[randomPosition]=temp;
}
}
}

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Lab110-VenbergGE/src/LinkedQueue.java Normal file
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/*
* 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();}
}

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Lab110-VenbergGE/src/Position.java Normal file
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/*
* Data Structures & Algorithms 6th Edition
* Goodrich, Tamassia, Goldwasser
* Code Fragment 7.7
*
* An implementation of the position interface
*/
/**
*
* @author Gabriel Venberg
*/
public interface Position<E> {
/**
* Returns the element stored at this position
*
* @return the stored element
* @throws IllegalStateException if position no longer valid.
*/
E getElement() throws IllegalStateException;
}

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Lab110-VenbergGE/src/Queue.java Normal file
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/**
* 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();
}

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Lab110-VenbergGE/src/SinglyLinkedList.java Normal file
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/**
*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;
}
}

29
Lab110-VenbergGE/src/Tree.java Normal file
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@ -0,0 +1,29 @@
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();
}