Singly Linked Lists

• Representation

• Space Analysis

• Creation and Insertion

• Traversal

• Search

• Deletion

Representation

• We are using a representation in which a linked list has both head and tail references .

list headtail

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;}

}}

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)

Space RequireExplanation

sizeof(MyLinkedList)

The list reference has two fields: head (type: Element) and tail (type: Element) = 2 sizeof(MyLinkedList.Element ref)

nsizeof(MyLinkedList.Element)

The list has n elements of type Element. Each element has two fields-- data (type Object) and next (type Element).

List Creation and Insertion

• 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.

head

tail

MyLinkedList list = new MyLinkedList;()

for (int k = 0; k < 10; k++) list.append(new Integer(k));

public void append(Object obj){ Element element = new Element(obj, null); if(head == null) head = element; else tail.next = element; tail = element;}

Insertion at the end (Append)

Complexity is O(1)

public void prepend(Object obj) { Element element = new Element(obj, head); if(head == null) tail = element; head = element;}

Insertion at the beginning (Prepend)

Complexity is O(1)

Insertion before and after an elementpublic 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

public void insertAfter(Object obj) { next = new Element(obj, next); if(this == tail) tail = next;}

Complexity is O(1)

O(n)

TraversalTo move a reference e from one node to the next:

Example: Count the number of nodes in a linked list.

public int countNodes(){ int count = 0; Element e = head; while(e != null){ count++;

e = e.next; } return count;}

e = e.next;

Complexity is O(n)

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.…

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;}

Deletion• To delete an element, we use either the extract method of

MyLinkedList or that of the Element inner class.

Complexity is…

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");

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;}

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…

Complexity is…

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.

Doubly Linked Lists

• Representation

• Space Analysis

• Creation and Insertion

• Traversal

• Deletion

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;} // . . . }}

list head

tail

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)

Required spaceExplanationsizeof(DoublyLinkedList)The list reference has two fields:

head (type: Element) and tail (type: Element) = 2 sizeof(DoublyLinkedList.Element ref)

n sizeof(DoublyLinkedList.Element)

The list has n elements of type Element. Each element has three fields-- previous (type Element), data (type Object), and next (type Element)

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..

b(

head

tail

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…

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…

Insertion before an element• Inserting before the current node (this) that is neither the first

nor the last node:

Complexity is…

Element element = new Element(obj, this, this.previous);this.previous.next = element;this.previous = element;

TraversalFor 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…

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; }

TraversalExample: The following computes the sum of the last n nodes:

Complexity is…

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…

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?