1. Ordered Containers CMPUT 115 - Lecture 19 Department of Computing Science University of Alberta ©Duane Szafron 2003 Some code in this lecture is based on code from the book: Java Structures by Duane A. Bailey or the companion structure package

2. ©Duane Szafron 2003 2 About This Lecture In this lecture we will learn about Ordered containers. An ordered container is a container where the order of the elements depends not on the order they are added, but rather on comparisons of the elements that are added.

3. ©Duane Szafron 2003 3 Outline Ordered Containers OrderedStructure Interface OrderedStructure Example OrderedVector class OrderedList class

4. ©Duane Szafron 2003 4 Ordered Containers An ordered container is a container whose elements are ordered by comparing them with each other. This requires a binary operation to be defined that applies to any pair of elements that can be added to the container. In Java, we use the compareTo(Object) method from the Comparable Interface. As each element is added to the container it immediately goes to the proper location in the container based on comparing it with all other elements that are in the container.

5. ©Duane Szafron 2003 5 OrderedStructure Hierarchy The structure package adds the OrderedStructure interface below the Collection interface. Store Collection ListOrderedStructure

6. ©Duane Szafron 2003 6 Structure Interface - Store public interface Store { public int size(); //post: returns the number of elements contained in // the store. public boolean isEmpty(); // post: returns the true iff store is empty. public void clear(); // post: clears the store so that it contains no // elements. } code based on Bailey pg. 18

7. ©Duane Szafron 2003 7 Structure Interface - Collection public interface Collection extends Store { public boolean contains(Object anObject); // pre: anObject is non-null // post: returns true iff the collection contains the object public void add(Object anObject); // pre: anObject is non-null // post: the object is added to the collection. The // replacement policy is not specified public Object remove(Object anObject); // pre: anObject is non-null // post: removes object “equal” to anObject and returns it, // otherwise returns null public Iterator elements(); // post: return an iterator for traversing the collection } code based on Bailey pg. 19

8. ©Duane Szafron 2003 8 Structure Interface - OrderedStructure public interface OrderedStructure extends Collection {} code based on Bailey pg. 173 The unusual thing about the OrderedStructure interface is that it does not add any new methods to those provided by Collection. However, any class that implements this interface must ensure that when elements are added, they go to the correct location. In essence, it changes the postcondition of the add method in Collection: // post: the object is added to the collection. The // replacement policy is not specified

9. ©Duane Szafron 2003 9 OrderedStructure Example public static void main(String[] args) { OrderedStructure container; RandomInt generator; int index; Iterator iterator; container = new OrderedVector(); generator = new RandomInt(1); for (index = 0; index < 100; index++) { container.add(new Integer(generator.next(100))); iterator = container.elements(); while(iterator.hasMoreElements()) System.out.print(iterator.nextElement() + ' '); } code based on Bailey pg. 158 1 1 1 2 2 3 3 3 4 4 5 7 7 7 8 9 9 10 13 13 14 14 15 17...

10. ©Duane Szafron 2003 10 OrderedVector One implementation of OrderedStructure uses a Vector. As each element is added, a binary search is used to put the element in the appropriate location in the Vector. The following method will be used in the implementation of the add method and in many other methods as well. protected int indexOf(Comparable anObject) { // pre: anObject is non-null // post: returns index of object in the collection or where // it should be placed if it is not in the collection

11. ©Duane Szafron 2003 11 OrderedVector - State and Constructor class OrderedVector implements OrderedStructure { protected Vector data; public OrderedVector(){ // post: initializes the OrderedVector to have 0 elements this.data = new Vector(); } code based on Bailey pg. 173

12. ©Duane Szafron 2003 12 OrderedVector - Store Interface /* Interface Store Methods */ public int size() { //post: returns the number of elements contained in // the store. return this.data.size(); } public boolean isEmpty() { // post: returns the true iff store is empty. return this.size() == 0; } public void clear(){ // post: clears the store so that it contains no // elements. this.data.clear(); } code based on Bailey pg. 178

13. ©Duane Szafron 2003 13 OrderedVector - contains(Object) /* Interface Collection Methods */ public boolean contains(Object anObject) { // pre: anObject is non-null // post: returns true iff the collection contains the object int index; index = this.indexOf((Comparable) anObject); return (index < this.size()) && (this.data.elementAt(index).equals(anObject)); } code based on Bailey pg. 176

14. ©Duane Szafron 2003 14 OrderedVector - add(Object) public void add(Object anObject){ // pre: anObject is non-null // post: the object is added to the collection at the // appropriate position based on comparing it to the other // elements. int index; index = this.indexOf((Comparable) anObject); this.data.insertElementAt(anObject, index); } code based on Bailey pg. 176

15. ©Duane Szafron 2003 15 OrderedVector - remove(Object) public Object remove(Object anObject){ // pre: anObject is non-null // post: removes object “equal” to anObject and returns it, // otherwise returns nil int index; Object result; index = this.indexOf((Comparable) anObject)); if (index < this.size()) && (this.data.elementAt(index).equals(anObject)) { result = this.data.elementAt(index); this.data.removeElementAt(index); return result; } return null; } code based on Bailey pg. 177

16. ©Duane Szafron 2003 16 OrderedVector - elements() public Iterator elements(){ // post: return an iterator for traversing the collection return this.data.elements(); } code based on Bailey pg. 177

17. ©Duane Szafron 2003 17 The Search Problem To complete this class, we need to solve the search problem for a sorted container. Given a container, find the index of a particular element, called the key. If it is not there, find the index where it should be. We use a modified version of a Binary search: –start with one extra space since the index we are looking for may be one past the end. –stop when there is only one element left - it is either the element we are looking for or the element should be inserted before it. 30 102530505560707580 0123456789

18. ©Duane Szafron 2003 18 Modified Binary Search - found 30 middle = (low + high) / 2 high = middle - 1 HML 102530505560707580 0123456789 low = middle + 1 LHM 102530505560707580 0123456789 HHHHHLHM 102530505560707580 0123456789

19. ©Duane Szafron 2003 19 Element not found - 1 35 middle = (low + high) / 2 high = middle - 1 HML LHM low = middle + 1 LHM middle = (low + high) / 2 102530505560707580 0123456789 102530505560707580 0123456789 102530505560707580 0123456789

20. ©Duane Szafron 2003 20 Element not found - 2 35 H low = middle + 1 LHM low < high middle = (low + high) / 2 LM 102530505560707580 0123456789 102530505560707580 0123456789 Notice that if we were looking for 50, the same steps would be taken so when (low < high) becomes false, it is either because we found the key or because the key should be inserted before the stopping index.

21. ©Duane Szafron 2003 21 Element past end -1 90 middle = (low + high) / 2 HML LHM low = middle + 1 LHM middle = (low + high) / 2 102530505560707580 0123456789 102530505560707580 0123456789 102530505560707580 0123456789 low = middle + 1

22. ©Duane Szafron 2003 22 Element past end - 2 90 H low = middle + 1 LHM low < high middle = (low + high) / 2 LM 102530505560707580 0123456789 102530505560707580 0123456789

23. ©Duane Szafron 2003 23 OrderedVector - indexOf(Object) 1 /* Protected Methods */ protected int indexOf(Comparable anObject) { // pre: anObject is non-null // post: returns index of object in the collection or where // it should be placed if it is not in the collection Comparable midObject; int low; int high; int middle; int comparison; low = 0; high = this.data.size(); middle = (low + high) / 2; code based on Bailey pg. 174

24. ©Duane Szafron 2003 24 OrderedVector - indexOf(Object) 2 while (low < high) { midObject = (Comparable) this.data.elementAt(middle); comparison = midObject.compareTo(anObject); if (comparison) < 0) low = middle + 1; else if (comparison > 0) high = middle - 1; else return middle; middle = (low + high) / 2; } return low; //low is either the index of the key or } // the key should be inserted at this index. code based on Bailey pg. 174

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27. ©Duane Szafron 2003 27 Time Complexity of OrderedVector The indexOf(Object) method does O(log(n)) comparisons to find the index. Since the contains(Object) method makes a single call to indexOf(Object), the contains(Object) method is O(log(n). The add(Object) and remove(Object) methods also call indexOf(Object). However, they also requires O(n) assignments to move elements in methods add(Object) and remove(Object). Therefore, add(Object) and remove(Object) are O(n) in OrderedVector.

28. ©Duane Szafron 2003 28 OrderedList We can also implement the OrderedStructure Interface using a linked list in a class called OrderedList. However, we do not simply bind an instance variable to a linked list object like a SinglyLinkedList since we require access to the middle of the list to put added elements in the correct location. Therefore we use SinglyLinkedListElements and link them together manually.

29. ©Duane Szafron 2003 29 OrderedList - difference from OrderedVector The important difference between OrderedList and OrderedVector is that the internal implementation of OrderedVector has access to the indexes of the underlying Vector elements. –This allows us to find the index of a particular element so that it can be found, added, or removed. –It also allows us to do a binary search since we can divide the search list in half using the indexes.

30. ©Duane Szafron 2003 30 OrderedList - Sequential Search In OrderedList, we create an analog of the indexOf(Object) method called previousOf(Object) which returns the node before the node containing the object, or the node before the node where the object should be inserted. Unfortunately, we must do a sequential search instead of a binary search. However, we can stop early if we encounter an element that is larger than the one we are looking for.

31. ©Duane Szafron 2003 31 OrderedList - State and Constructor public class OrderedList implements OrderedStructure { protected SinglyLinkedListElement head; protected int count; public OrderedList(){ // post: initializes the OrderedList to have 0 elements this.clear(); } code based on Bailey pg. 180

32. ©Duane Szafron 2003 32 OrderedList - Store Interface /* Interface Store Methods */ public int size() { //post: returns the number of elements in the store. return this.count; } public boolean isEmpty() { // post: returns the true iff store is empty. return this.size() == 0; } public void clear(){ // post: clears the store so that it contains no // elements. this.head = null; this.count = 0; } code based on Bailey pg. 180

33. ©Duane Szafron 2003 33 OrderedList - elements() public Iterator elements(){ // post: return an iterator for traversing the collection return new SinglyLinkedListIterator(this.head); } code based on Bailey pg. 182

34. ©Duane Szafron 2003 34 OrderedList - previousOf(Object) 1 /* Protected Methods */ protected SinglyLinkedListElement previousOf(Object anObject) { // pre: anObject is non-null // post: returns the node before the node that contains the // given object, if the object is in the collection or the // node before where it should be placed if it is not in the // collection SinglyLinkedListElement cursor; SinglyLinkedListElement previous; Comparable key; cursor = this.head; previous = null; key = (Comparable) anObject; code based on Bailey pg. 181

35. ©Duane Szafron 2003 35 OrderedList - previousOf(Object) 2 while ((cursor != null) && (((Comparable) cursor.value()).compareTo(key) < 0)) { previous = cursor; cursor = cursor.next(); } return previous; } code based on Bailey pg. 181

36. ©Duane Szafron 2003 36 OrderedList - contains(Object) /* Interface Collection Methods */ public boolean contains(Object anObject) { // pre: anObject is non-null // post: returns true iff the collection contains the object SinglyLinkedListElement previous; SinglyLinkedListElement current; previous = this.previousOf((Comparable) anObject); if (previous == null) // no previous element, first node current = this.head; else current = previous.next(); if (current == null) return false; else return current.value().equals(anObject); } code based on Bailey pg. 180