Singly Linked Lists

1. Singly Linked Lists • Representation • Space Analysis • Creation and Insertion • Traversal • Search • Deletion

2. list head tail Representation • We are using a representation in which a linked list has both head and tail references. public class MyLinkedList{ protected Element head; protected Element tail; public final class Element{ Object data; Element next; Element(Object obj, Element element){ data = obj; next = element; } public Object getData(){return data;} public Element getNext(){return next;} } }

3. Representation: Space Analysis • Now, we can take a look at the space requirements: S(n) = sizeof(MyLinkedList) + n sizeof(MyLinkedList.Element) = 2 sizeof(MyLinkedList.Element ref) + n [sizeof(Object ref) + sizeof(MyLinkedList.Element ref)] = (n + 2) sizeof(MyLinkedList.Element ref) + n sizeof(Object ref)

4. List Creation and Insertion head • An empty list is created as follows: • Once created, elements can be inserted into the list using either the append or prepend methods • Also if we have reference to a node (an element), we can use insertAfter or InsertBefore of the Element class. MyLinkedList list = new MyLinkedList(); tail • for (int k = 0; k < 10; k++) • list.append(new Integer(k));

5. Insertion at the end (Append) public void append(Object obj){ Element element = new Element(obj, null); if(head == null) head = element; else tail.next = element; tail = element; } Complexity is O(1)

6. Insertion at the beginning (Prepend) public void prepend(Object obj) { Element element = new Element(obj, head); if(head == null) tail = element; head = element; } Complexity is O(1)

7. Insertion before and after an element public void insertBefore(Object obj) { Element element = new Element(obj, this); if(this == head) { head = element; return; } Element previous = head; while (previous.next != this) { previous= previous.next; } previous.next = element; } Complexity is O(n) • public void insertAfter(Object obj) { • next = new Element(obj, next); • if(this == tail) • tail = next; • } Complexity is O(1)

8. Traversal To move a reference e from one node to the next: Example: Count the number of nodes in a linked list. e = e.next; • public int countNodes(){ • int count = 0; • Element e = head; • while(e != null){ • count++; • e = e.next; • } • return count; • } Complexity is O(n)

9. Searching • To search for an element, we traverse from head until we locate the object. Example: Count the number of nodes with data field equal to a given object. public int countNodes(Object obj){ int count = 0; Element e = head; while(e != null){ if(e.data.equals(obj)) count++; e = e.next; } return count; } Complexity is ….

10. Deletion • To delete an element, we use either the extract method of MyLinkedList or that of the Element inner class. public void extract(Object obj) { Element element = head; Element previous = null; while(element != null && ! element.data.equals(obj)) { previous = element; element = element.next; } if(element == null) throw new IllegalArgumentException("item not found"); if(element == head) head = element.next; else previous.next = element.next; if(element == tail) tail = previous; } Complexity is …

11. Deletion - Difference between the MyLinkedList and the Element extracts • To delete an element, we use either the extract method of MyLinkedList or that of the Element inner class. • try{ • list.extract(obj1); • } catch(IllegalArgumentException e){ • System.out.println("Element not found"); • } • MyLinkedList.Element e = list.find(obj1); • if(e != null) • e.extract(); • else • System.out.println("Element not found");

12. Deletion – Deleting First and Last Element public void extractFirst() { if(head == null) throw new IllegalArgumentException("item not found"); head = head.next; if(head == null) tail = null; } Complexity is … public void extractLast() { if(tail == null) throw new IllegalArgumentException("item not found"); if (head == tail) head = tail = null; else { Element previous = head; while (previous.next != tail) previous = previous.next; previous.next = null; tail = previous; } } Complexity is …

13. Exercises • For the MyLinkedList class, Implement each of the following methods: • String toString() • Element find(Object obj) • void insertAt(int n) //counting the nodes from 1. State the complexity of each method. • Which methods are affected if we do not use the tail reference in MyLinkedList class.

14. Doubly Linked Lists • Representation • Space Analysis • Creation and Insertion • Traversal • Deletion

15. head list tail Representation public class DoublyLinkedList{ protected Element head, tail; //. . . public class Element { Object data; Element next, previous; Element(Object obj, Element next, Element previous){ data = obj; this.next = next; this.previous = previous; } public Object getData(){return data;} public Element getNext(){return next;} public Element getPrevious(){return previous;} // . . . } }

16. Doubly Linked Lists : Space Analysis • The space requirements of our representation of the doubly linked lists is as follows: S(n) = sizeof(DoublyLinkedList) + n sizeof(DoublyLinkedList.Element) = 2 sizeof(DoublyLinkedList.Element ref) + n [sizeof(Object ref) + 2 sizeof(DoublyLinkedList.Element ref)] = (2n + 2) sizeof(DoublyLinkedList.Element ref) + n sizeof(Object ref)

17. head b) tail List Creation and Insertion • An empty doubly linked list is created as follows: DoublyLinkedList list = new DoublyLinkedList(); • Like singly link list, once created, elements can be inserted into the list using either the append or prepend methods for (int k = 0; k < 10; k++) list.append(new Int(k)); • Also if we have reference to a node (an element), we can use insertAfter or InsertBefore of the Element class..

18. Insertion at the end (append) public void append(Object obj){ Element element = new Element(obj, null, tail); if(head == null) head = tail = element; else { tail.next = element; tail = element; } } Complexity is …

19. Insertion at the beginning (prepend) public void prepend(Object obj){ Element element = new Element(obj, head, null); if(head == null) head = tail = element; else { head.previous = element; head = element; } } Complexity is …

20. Insertion before an element • Inserting before the current node (this) that is neither the first nor the last node: Element element = new Element(obj, this, this.previous); this.previous.next = element; this.previous = element; Complexity is …

21. Traversal For DoublyLinked list, traversal can be done in either direction. Forward, starting from head, or backward starting from tail. Example: Count the number of nodes in a linked list. Element e = head; while (e != null) { //do something e = e.next; } Element e = tail; while (e != null) { //do something e = e.previous; } • public int countNodes(){ • int count = 0; • Element e = head; • while(e != null){ • count++; • e = e.next; • } • return count; • } Complexity is …

22. Traversal Example: The following computes the sum of the last n nodes: • public int sumLastNnodes(int n){ • if(n <= 0) • throw new IllegalArgumentException("Wrong: " + n); • if(head == null) • throw new ListEmptyException(); • int count = 0, sum = 0; • Element e = tail; • while(e != null && count < n){ • sum += ((Integer)e.data).intValue(); • count++; • e = e.previous; • } • if(count < n) • throw new IllegalArgumentException(“No. of nodes < "+n); • return sum; • } Complexity is …

23. Deletion • To delete an element, we use either the extract method of DoublyLinkedList or that of the Element inner class. • public void extract(Object obj){ • Element element = head; • while((element != null) && (!element.data.equals(obj))) • element = element.next; • if(element == null) • throw new IllegalArgumentException("item not found"); • if(element == head) { • head = element.next; • if(element.next != null) • element.next.previous = null; • }else{ • element.previous.next = element.next; • if(element.next != null) • element.next.previous = element.previous; • } • if(element == tail) • tail = element.previous; • } Complexity is …

24. Exercises • For the DoublyLinkedList class, Implement each of the following methods and state its complexity. • String toString() • Element find(Object obj) • void ExtractLast() • void ExtractFirst() • void ExtractLastN(int n) • For the DoublyLinkedList.Element inner class, implement each of the following methods and state its complexity. • void insertBefore() • void insertAfter() • void extract() • What are the methods of DoublyLinkedList and its Element inner class are more efficient than those of MyLinkedList class?