Linked Lists PDF

Linked Lists 1 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  What is a Linked List? Linked list is a data structure that is free from the restrictions of array. A linked list does not store its elements in consecutive memory locations and the user can...

Linked Lists 1 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  What is a Linked List? Linked list is a data structure that is free from the restrictions of array. A linked list does not store its elements in consecutive memory locations and the user can add any number of elements to it. Unlike an array, a linked list does not allow random access of data. Elements in a linked list can be accessed only in a sequential manner. Like an array, insertions and deletions can be done at any point in the list in a constant time. 2 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Basic terminologies A linked list is a linear collection of data elements, called nodes. Each node is divided into two parts: ✓ The left part of the node contains data ✓ The right part of the node contains a pointer to the next node Linked list is a data structure which in turn can be used to implement other data structures. 3 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Basic terminologies (Cont’d) Figure: Simple linked list In figure, every node contains two parts, an integer and a pointer to the next node. The last node will have no next node connected to it, so it will store a special value called NULL. ✓ In figure, the NULL pointer is represented by X. ✓ In programming, we usually define NULL as –1. ✓ A NULL pointer denotes the end of the list. Since in a linked list, every node contains a pointer to another node which is of the same type, it is also called a self-referential data type. 4 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Basic terminologies (Cont’d) Linked lists contain a pointer variable START that stores the address of the first node in the list. We can traverse the entire list using START which contains the address of the first node; the next part of the first node in turn stores the address of its succeeding node. If START = NULL, then the linked list is empty and contains no nodes. Let’s see how a linked list is maintained in the memory. Figure: START pointing to the first element of the linked list in the memory 5 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Basic terminologies (Cont’d) Let’s see how two linked lists are maintained together in the computer’s memory. For example, the students of Class XI of Science group are asked to choose between Biology and Computer Science. Now, we will maintain two linked lists, one for each subject. That is, the first linked list will contain the roll numbers of all the students who have opted for Biology and the second list will contain the roll numbers of students who have chosen Computer Science. Note Linked lists provide an efficient way of storing related data and perform basic operations such as insertion, deletion, and updation of information Figure: Two linked lists which at the cost of extra space required for storing address of the next node. are simultaneously maintained in the memory 6 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Basic terminologies (Cont’d) Example Roll No Name Marks Grade Next Consider a scenario of figure in which 1 S01 Ram 78 Distinction 6? 2 S02 Shyam 64 First division 14? the roll number, name, marks, and 3 grade of students are stored using 4 S03 Mohit 89 Outstanding 17 ? 5 linked lists. NEXT pointer is used to 6 S04 Rohit 77 Distinction 2? 7 S05 Varun 86 Outstanding 10? store the data alphabetically. Please 8 S06 Karan 65 First division 12? 9 fill the value of Next. 10 S07 Veena 54 Second division -1? 11 S08 Meera 67 First division 4? 12 S09 Krish 45 Third division 13? 13 S10 Kusum 91 Outstanding 11? 14 S11 Silky 72 First division 7? START 18 15 16 17 S12 Monica 75 Distinction 1? 18 S13 Ashish 63 First division 19? 19 S14 Gaurav 61 First division 8? 7 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Memory allocation and de-allocation for a Linked List If we want to add a node to an already existing linked list in the memory, we first find free space in the memory and then use it to store the information. When we delete a node from a linked list, then who changes the status of the memory occupied by it from occupied to available? The answer is the operating system. The computer maintains a list of all free memory cells. This list of available space is called the free pool. We have seen that every linked list has a pointer variable START which stores the address of the first node of the list. Likewise, for the free pool (which is a linked list of all free memory cells), we have a pointer variable AVAIL which stores the address of the first free space. 8 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Memory allocation and de-allocation for a Linked List (Cont’d) For example, consider the linked list shown in Figure. START 11 Roll No Marks Next (Biology) (Biology) 11 S01 S01 78 78 22 The linked list contains the roll number of students, 22 S02 S02 84 84 33 marks obtained by them in Biology, and finally a NEXT 33 S03 S03 45 45 55 AVAIL 64 4 S12 75 6 -1 field which stores the address of the next node in 5 S04 98 7 sequence. 6 9 Now, when a new student’s record has to be added, the 7 S05 55 8 8 S06 34 10 memory address pointed by AVAIL will be taken and 9 14 used to store the desired information. 10 S07 90 11 11 S08 87 12 When the first free memory space is utilized for inserting 12 S09 86 13 13 S10 67 15 the new node, AVAIL will be set to contain address 6. 14 -1 15 S11 56 -1 4 Figure: Linked list after the insertion of new student’s record 9 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Types of Linked List There are different types of Linked Lists and shown in figures. 1) Singly Linked List Figure: Singly Linked List 2) Doubly Linked List Figure: Doubly Linked List 3) Circular Linked List Figure: Circular Linked List 4) Circular Doubly Linked List Figure: Circular Doubly Linked List 10 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Singly Linked List A singly linked list is the simplest type of linked list in which every node contains some data and a pointer to the next node of the same data type. A singly linked list allows traversal of data only in one way. Figure shows a singly linked list. Figure: Single Linked List 11 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Traversing a Linked List Traversing a linked list means accessing the nodes of the list in order to perform some processing on them. Remember a linked list always contains a pointer variable START which stores the address of the first node of the list. End of the list is marked by storing NULL or –1 in the NEXT field of the last node. For traversing the linked list, we also make use of another pointer variable PTR which points to the node that is currently being accessed. 12 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Traversing a Linked List (Cont’d) Example Algorithm CountNodes (START) Algorithm TraverseList (START) count ← 0 PTR ← START PTR ← START while PTR ≠ NULL do while PTR ≠ NULL do print PTR.DATA count ← count + 1 PTR ← PTR.NEXT PTR ← PTR.NEXT return count Algorithm to traverse a linked list Algorithm to count the number of nodes in a linked list 13 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Searching for a Value in a Linked List Searching a linked list means to find a particular element in the linked list. If it is present, the algorithm returns the address of the node that contains the value. If we have value = 4, then the flow of the algorithm can be Algorithm SearchList (START, value) explained as follows: PTR ← START while PTR ≠ NULL do Here PTR.DATA = 1. Since PTR.DATA ≠ 4, we move to the next node. if value = PTR.DATA pos ← PTR Here PTR.DATA = 7. Since PTR.DATA ≠ 4, we move to the next node. return pos else Here PTR.DATA = 3. Since PTR.DATA ≠ 4, we move to the next node. PTR ← PTR.NEXT pos ← NULL return pos Here PTR.DATA = 4. Since PTR.DATA = 4, pos ← PTR. pos now stores the address of the node that contains value 14 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Inserting a New Node in a Linked List Case 1: The new node is inserted at the beginning. Case 2: The new node is inserted at the end. Case 3: The new node is inserted after a given node. Case 4: The new node is inserted before a given node. When inserting a new node in a linked list, overflow can occur. Overflow is a condition that occurs when AVAIL = NULL or no free memory cell is present in the system. When this condition occurs, the program must give an appropriate message. 15 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Inserting a Node at the Beginning of a Linked List Suppose we want to add a new node with data 9 and add it Algorithm InsertBegin (START, AVAIL, value) as the first node of the list. if AVAIL = NULL print “Overflow” Allocate memory for the new node and initialize its DATA part to 9. else newNode ← AVAIL Add the new node as the first node of the list by making the NEXT part of the AVAIL ← AVAIL.NEXT new node contain the address of START. newNode.DATA ← value newNode.NEXT ← START Now make START to point to the first node of the list. START ← newNode Algorithm to insert a new node at the beginning 16 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Inserting a Node at the End of a Linked List Suppose we want to add a new node with data 9 as the Algorithm InsertEnd (START, AVAIL, value) last node of the list. if AVAIL = NULL print “Overflow” Allocate memory for the new node and initialize its DATA part to 9 and else NEXT part to NULL. newNode ← AVAIL AVAIL ← AVAIL.NEXT Take a pointer variable PTR which points to START. newNode.DATA ← value newNode.NEXT ← NULL Move PTR so that it points to the last node of the list. PTR ← START while PTR.NEXT ≠ NULL do Add the new node after the node pointed by PTR. This is done by PTR ← PTR.NEXT storing the address of the new node in the NEXT part of PTR. PTR.NEXT ← newNode Algorithm to insert a new node at the end 17 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Inserting a Node After a Given Node in a Linked List //Assuming the given number is on the list. //Assuming the given number is on the list. Algorithm InsertAfter (START, AVAIL, value, num) Algorithm InsertAfter (START, AVAIL, value, num) if AVAIL = NULL if AVAIL = NULL print “Overflow” print “Overflow” else else newNode ← AVAIL newNode ← AVAIL AVAIL ← AVAIL.NEXT AVAIL ← AVAIL.NEXT OR newNode.DATA ← value newNode.DATA ← value PREPTR ← START PTR ← START PTR ← START.NEXT while PTR.DATA ≠ num do while PREPTR.DATA ≠ num do PTR ← PTR.NEXT PREPTR ← PTR newNode.NEXT ← PTR.NEXT PTR ← PTR.NEXT PTR.NEXT ← newNode PREPTR.NEXT ← newNode newNode.NEXT ← PTR Algorithm to insert a new node after a node that has value num 18 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Inserting a Node Before a Given Node in a Linked List Algorithm InsertBefore (START, AVAIL, value, num) if AVAIL = NULL print “Overflow” else newNode ← AVAIL AVAIL ← AVAIL.NEXT newNode.DATA ← value PTR ← START while PTR.DATA ≠ num do PREPTR ← PTR PTR ← PTR.NEXT if PTR = START newNode.NEXT ← START START ← newNode else PREPTR.NEXT ← newNode newNode.NEXT ← PTR Algorithm to insert a new node before a node that has value num 19 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Deleting a Node from a Linked List Case 1: The first node is deleted. Case 2: The last node is deleted. Case 3: The node after a given node is deleted. When deleting a new node in a linked list, underflow can occur. Underflow is a condition that occurs when we try to delete a node from a linked list that is empty. This happens when START = NULL or when there are no more nodes to delete. Note that when we delete a node from a linked list, we actually have to free the memory occupied by that node. 20 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Deleting the First Node from a Linked List Algorithm DeleteFirst (START, AVAIL) if START = NULL print “Underflow” else PTR ← START START ← START.NEXT temp ← AVAIL AVAIL ← PTR AVAIL.NEXT ← temp Algorithm to delete the first node 21 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Deleting the Last Node from a Linked List Algorithm DeleteLast (START, AVAIL) if START = NULL print “Underflow” else PTR ← START while PTR.NEXT ≠ NULL do PREPTR ← PTR PTR ← PTR.NEXT PREPTR.NEXT ← NULL temp ← AVAIL AVAIL ← PTR AVAIL.NEXT ← temp Algorithm to delete the last node 22 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Deleting the Node After a Given Node in a Linked List Algorithm DeleteAfter (START, AVAIL, num) if START = NULL print “Underflow” else PREPTR ← START PTR ← START.NEXT while PREPTR.DATA ≠ num do PREPTR ← PTR PTR ← PTR.NEXT PREPTR.NEXT ← PTR.NEXT temp ← AVAIL AVAIL ← PTR AVAIL.NEXT ← temp Algorithm to delete the node after a given node 23 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Doing Exercises 1. Character string is stored in the linked list of the following figure. i. Find the string result. ii. Suppose P is deleted from the list and then X is inserted at the beginning of the list. Find the final structure. DATA NEXT 1 S 4 2 I 6 START 3 3 F 2 4 T 5 AVAIL 7 5 E 11 6 R 8 7 9 8 S 10 9 -1 10 T 1 11 P -1 24 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Doing Exercises (Cont’d) 2. The following list of names is assigned (in order) to a linear array INFO: Mary, June, Barbara, Paula, Diana, Audrey, Karen, Nancy, Ruth, Eileen, Sandra, Helen Fill values to a NEXT and a variable START to form an alphabetical listing of the names. START INFO NEXT 1 8 2 Mary AVAIL 3 June 15 4 Barbara 5 Paula 6 Diana 7 Audrey 8 -1 9 Karen 10 Nancy 11 Ruth 12 Eileen 13 Sandra 14 Helen 15 1 25 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Doing Exercises (Cont’d) 3. The following figure is a list of five hospital patients and their room numbers. (a) Fill in values for NSTART and N_NEXT so that they form an alphabetical listing of the names. (b) Fill in values for RSTART and R_NEXT so that they form an ordering of the room numbers. NAME ROOM N_NEXT R_NEXT NSTART 1 Brown 650 2 Smith 422 RSTART 3 Adams 704 4 Jones 462 5 Burns 632 26 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Doubly Linked Lists A doubly linked list or a two-way linked list is a more complex type of linked list which contains a pointer to the next as well as the previous node in the sequence. Therefore, it consists of three parts—data, a pointer to the next node, and a pointer to the previous node as shown in Figure. The PREV field of the first node and the NEXT field of the last node will contain NULL. The PREV field is used to store the address of the preceding node, which enables us to traverse the list in the backward direction. Figure: Doubly Linked List 27 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Doubly Linked Lists (Cont’d) A doubly linked list calls for more space per node and more expensive basic operations. However, a doubly linked list provides the ease to manipulate the elements of the list as it maintains pointers to nodes in both the directions (forward and backward). Figure: Memory representation of a doubly linked list 28 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Inserting a New Node in a Doubly Linked List Case 1: The new node is inserted at the beginning. Case 2: The new node is inserted at the end. Case 3: The new node is inserted after a given node. Case 4: The new node is inserted before a given node. 29 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Inserting a Node at the Beginning of a Doubly Linked List Algorithm InsertBegin (START, AVAIL, value) if AVAIL = NULL print “Overflow” else newNode ← AVAIL AVAIL ← AVAIL.NEXT newNode.DATA ← value newNode.PREV ← NULL newNode.NEXT ← START START.PREV ← newNode START ← newNode Algorithm to insert a new node at the beginning 30 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Inserting a Node at the End of a Doubly Linked List Algorithm InsertEnd (START, AVAIL, value) if AVAIL = NULL print “Overflow” else newNode ← AVAIL AVAIL ← AVAIL.NEXT newNode.DATA ← value newNode.NEXT ← NULL PTR ← START while PTR.NEXT ≠ NULL do PTR← PTR.NEXT PTR.NEXT ← newNode newNode.PREV ← PTR Algorithm to insert a new node at the beginning 31 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Inserting a Node After a Given Node in a Doubly Linked List Algorithm InsertAfter (START, AVAIL, value, num) if AVAIL = NULL print “Overflow” else newNode ← AVAIL AVAIL ← AVAIL.NEXT newNode.DATA ← value PTR ← START while PTR.DATA ≠ num do PTR← PTR.NEXT newNode.NEXT ← PTR.NEXT newNode.PREV ← PTR PTR.NEXT.PREV ← newNode PTR.NEXT ← newNode Algorithm to insert a new node after a given node 32 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Inserting a Node Before a Given Node in a Doubly Linked List Algorithm InsertBefore (START, AVAIL, value, num) if AVAIL = NULL print “Overflow” else newNode ← AVAIL AVAIL ← AVAIL.NEXT newNode.DATA ← value PTR ← START while PTR.DATA ≠ num do PTR← PTR.NEXT if PTR = START newNode.NEXT ← START newNode.PREV ← NULL START.PREV ← newNode START ← newNode else newNode.NEXT ← PTR newNode.PREV ← PTR.PREV PTR.PREV.NEXT ← newNode PTR.PREV ← newNode Algorithm to insert a new node after a given node 33 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Deleting a Node from a Doubly Linked List Case 1: The first node is deleted. Case 2: The last node is deleted. Case 3: The node after a given node is deleted. Case 4: The node before a given node is deleted. 34 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Deleting the First Node from a Doubly Linked List Algorithm DeleteFirst (START, AVAIL) if START = NULL print “Underflow” else PTR ← START START ← START.NEXT START.PREV ← NULL temp ← AVAIL temp.PREV ← PTR AVAIL ← PTR AVAIL.PREV ← NULL AVAIL.NEXT ← temp Algorithm to delete the first node 35 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Deleting the Last Node from a Doubly Linked List Algorithm DeleteLast (START, AVAIL) if START = NULL print “Underflow” else PTR ← START while PTR.NEXT ≠ NULL do PTR ← PTR.NEXT PTR.PREV.NEXT ← NULL temp ← AVAIL temp.PREV ← PTR AVAIL ← PTR AVAIL.PREV ← NULL AVAIL.NEXT ← temp Algorithm to delete the last node 36 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Deleting the Node After a Given Node in a Doubly Linked List Algorithm DeleteAfter (START, AVAIL, num) if START = NULL print “Underflow” else PTR ← START while PTR.DATA ≠ num do PTR ← PTR.NEXT tempPTR← PTR.NEXT PTR.NEXT ← PTR.NEXT.NEXT PTR.NEXT.PREV ← PTR temp ← AVAIL temp.PREV ← tempPTR AVAIL ← tempPTR AVAIL.PREV ← NULL AVAIL.NEXT ← temp Algorithm to delete a node after a given node 37 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Deleting the Node Before a Given Node in a Doubly Linked List Algorithm DeleteBefore(START, AVAIL, num) if START = NULL print “Underflow” else PTR ← START while PTR.DATA ≠ num do PTR ← PTR.NEXT if PTR = START print “Underflow” else tempPTR← PTR.PREV PTR.PREV ← PTR.PREV.PREV PTR.PREV.NEXT ← PTR temp ← AVAIL temp.PREV ← tempPTR AVAIL ← tempPTR AVAIL.PREV ← NULL AVAIL.NEXT ← temp Algorithm to delete a node before a given node 38 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Doing Exercises DATA PREV NEXT 1. Character string is stored in the doubly linked list of 1 D 10 4 the following figure. 2 E 3 6 START 3 i. Find the string result. 3 S -1 2 4 S 1 5 ii. Suppose E is deleted from the list and then O is AVAIL 7 5 T 4 11 inserted before P value of the list. Find the final 6 C 2 8 structure. 7 -1 9 8 O 6 10 9 7 -1 10 N 8 1 11 E 5 12 12 P 11 -1 39 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Circular Linked Lists In a circular linked list, the last node contains a pointer to the first node of the list. We can have a circular singly linked list as well as a circular doubly linked list. While traversing a circular linked list, ✓ Traversal begins from any node in the list ✓ Traverse the list in: 1. Forward direction: Moving to the next node. 2. Backward direction (if it's a doubly circular linked list): Moving to the previous node. ✓ Traversal stops when the starting node reaches again. Figure: Circular Linked List 40 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Circular Linked Lists (Cont’d) Note that there are no NULL values in the NEXT part of any of the nodes of list. Circular linked lists are widely used in operating systems for task maintenance. The list can traverse until the NEXT entry finds that it contains the address of the first node of the list. Figure: Memory representation of circular linked list 41 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Inserting a new node in a circular Linked List Case 1: The new node is inserted at the beginning of the circular linked list. Case 2: The new node is inserted at the end of the circular linked list. 42 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Inserting a Node at the Beginning of a Circular Linked List Algorithm InsertBegin (START, AVAIL, value) if AVAIL = NULL print “Overflow” else newNode ← AVAIL AVAIL ← AVAIL.NEXT newNode.DATA ← value newNode.NEXT ← START PTR ← START while PTR.NEXT ≠ START do PTR← PTR.NEXT PTR.NEXT← newNode START ← newNode Algorithm to insert a new node at the beginning 43 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Inserting a Node at the End of a Circular Linked List Algorithm InsertEnd (START, AVAIL, value) if AVAIL = NULL print “Overflow” else newNode ← AVAIL AVAIL ← AVAIL.NEXT newNode.DATA ← value newNode.NEXT ← START PTR ← START while PTR.NEXT ≠ START do PTR← PTR.NEXT PTR.NEXT← newNode Algorithm to insert a new node at the end 44 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Deleting a Node from a Circular Linked List Case 1: The first node is deleted. Case 2: The last node is deleted. 45 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Deleting the First Node from a Circular Linked List Algorithm DeleteFirst (START, AVAIL) if START = NULL print “Underflow” else PTR ← START while PTR.NEXT ≠ START do PTR← PTR.NEXT tempSTART ← START PTR.NEXT ← START.NEXT START ← START.NEXT temp ← AVAIL AVAIL ← tempSTART AVAIL.NEXT ← temp Algorithm to delete the first node 46 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Deleting the Last Node from a Circular Linked List Algorithm DeleteLast (START, AVAIL) if START = NULL print “Underflow” else PTR ← START while PTR.NEXT ≠ START do PREPTR ← PTR PTR← PTR.NEXT PREPTR.NEXT ← START temp ← AVAIL AVAIL ← PTR AVAIL.NEXT ← temp Algorithm to delete the last node 47 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Doing Exercises START DATA NEXT 1 7 1 I 4 1. Write an algorithm to delete a node after a given node from 2 5 2 I 14 3 10 3 A 6 a circular linked list. 4 O -1 5 M 12 6 S -1 2. Character strings are stored in the three linked lists in figure. 7 O 9 8 E 13 9 H 1 (a) Find the three strings. (b) Form circular list. AVAIL 10 T 8 20 11 E -1 12 A 2 13 X 3 14 N 11 15 -1 16 15 17 16 18 17 19 18 20 19 48 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Circular Doubly Linked Lists A circular doubly linked list or a circular two-way linked list is a more complex type of linked list which contains a pointer to the next as well as the previous node in the sequence. The circular doubly linked list does not contain NULL in the previous field of the first node and the next field of the last node. The next field of the last node stores the address of the first node of the list, i.e., START. Similarly, the previous field of the first node stores the address of the last node. Figure: Memory representation of a Figure: Circular doubly linked list circular doubly linked list 49 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Inserting a New Node in a Circular Doubly Linked List Case 1: The new node is inserted at the beginning. Case 2: The new node is inserted at the end. 50 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Inserting a Node at the Beginning of a Circular Doubly Linked List Algorithm InsertBegin (START, AVAIL, value) if AVAIL = NULL print “Overflow” else newNode ← AVAIL AVAIL ← AVAIL.NEXT newNode.DATA ← value PTR ← START while PTR.NEXT ≠ START do PTR← PTR.NEXT PTR.NEXT← newNode newNode.PREV ← PTR newNode.NEXT ← START START.PREV← newNode START ← newNode Algorithm to insert a new node at the beginning 51 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Inserting a Node at the End of a Circular Doubly Linked List Algorithm InsertEnd (START, AVAIL, value) if AVAIL = NULL print “Overflow” else newNode ← AVAIL AVAIL ← AVAIL.NEXT newNode.DATA ← value newNode.NEXT ← START PTR ← START while PTR.NEXT ≠ START do PTR← PTR.NEXT PTR.NEXT← newNode newNode.PREV ← PTR START.PREV← newNode Algorithm to insert a new node at the end 52 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Deleting a Node from a Circular Doubly Linked List Case 1: The first node is deleted. Case 2: The last node is deleted. 53 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Deleting the First Node from a Circular Doubly Linked List Algorithm DeleteFirst (START, AVAIL) if START = NULL print “Underflow” else PTR ← START while PTR.NEXT ≠ START do PTR← PTR.NEXT PTR.NEXT ← START.NEXT START.NEXT.PREV ← PTR temp ← AVAIL temp.PREV ← START AVAIL ← START AVAIL.PREV ← NULL AVAIL.NEXT ← temp START ← PTR.NEXT Algorithm to delete the first node 54 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Deleting the Last Node from a Circular Doubly Linked List Algorithm DeleteLast (START, AVAIL) if START = NULL print “Underflow” else PTR ← START while PTR.NEXT ≠ START do PTR← PTR.NEXT PTR.PREV.NEXT ← START START.PREV ← PTR.PREV temp ← AVAIL temp.PREV ← PTR AVAIL ← PTR AVAIL.PREV ← NULL AVAIL.NEXT ← temp Algorithm to delete the last node 55 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Applications of Linked Lists Linked lists can be used to represent polynomials and the different operations that can be performed on them. Let’s see how a polynomial is represented in the memory using Figure : Linked representation of a polynomial a linked list. COEF EXP NEXT 1 Consider a polynomial 6x3 + 9x2 + 7x + 1. Every individual term START 2 6 3 4 2 3 in a polynomial consists of two parts, a coefficient and a power. 4 9 2 6 5 Here, 6, 9, 7, and 1 are the coefficients of the terms that have 3, 6 7 1 8 2, 1, and 0 as their powers respectively. 7 8 1 0 -1 Every term of a polynomial can be represented as a node of the 9 10 linked list Figure : Memory representation of a polynomial 56 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57  Doing Exercises START COEF EXP NEXT 1. Write an algorithm to delete a given node from a 1 1 1 2 1 9 2 2 2 1 5 -1 circular doubly linked list. 3 3 3 5 2 6 4 -5 3 7 2. Find the polynomials stored in the three linked lists in 5 -9 2 8 figure. 6 6 3 5 AVAIL 7 1 1 10 11 8 4 0 -1 9 3 4 4 10 -8 0 -1 11 12... 49 50 50 -1 57 ㅡ Faculty of Computer Science © Daw Laet Laet Lin 57