1. Linked Lists
Geletaw S.

2. Objective
At the end of the session students should have basic understanding of
Linked lists
Basic operations of linked lists
Insert, find, delete, print, etc.
Variations of linked lists
Simple Linked Lists
Circular Linked Lists
Doubly Linked Lists

3. Array vs Linked List
node
node
Array
node
Linked List

4. What’s wrong with Array ?
Disadvantages of arrays as storage data structures
slow searching in unordered array
slow insertion in ordered array
Fixed size

5. Why lists (Linked lists )?
Solve some of these problems
General purpose storage data structures and are versatile.
More complex to code and manage than arrays, but they have some distinct advantages.
Dynamic: a linked list can easily grow and shrink in size.
We don’t need to know how many nodes will be in the list. They are created in memory as needed.
In contrast, the size of a C++ array is fixed at compilation time.
Easy and fast insertions and deletions
To insert or delete an element in an array, we need to copy to temporary variables to make room for new elements or close the gap caused by deleted elements.
With a linked list, no need to move other nodes. Only need to reset some pointers.

6. Linked Lists Each data item is embedded in a link.
Each Link object contains a reference to the next link in the list of items.
In an array
items have a particular position, identified by its index.
In a list
the only way to access an item is to traverse the list

7. Linked Lists A linked list is a series of connected nodes
Head B C
A linked list is a series of connected nodes
Each node contains at least
A piece of data (any type)
Pointer to the next node in the list
Head: pointer to the first node
The last node points to NULL A
data
pointer
node

8. A Simple Linked List Class
Operations of List
IsEmpty:
determine whether or not the list is empty
InsertNode:
insert a new node at a particular position
FindNode:
find a node with a given value
DeleteNode:
delete a node with a given value
DisplayList:
print all the nodes in the list

9. A Simple Linked List Class
We use two classes: Node and List
Declare Node class for the nodes
data: double-type data in this example
next: a pointer to the next node in the list
class Node {
public:
double data; // data
Node* next; // pointer to next };

10. A Simple Linked List Class
Declare List, which contains
head: a pointer to the first node in the list.
Since the list is empty initially, head is set to NULL
Operations on List
class List {
public:
List(void) { head = NULL; } // constructor
~List(void); // destructor
bool IsEmpty() { return head == NULL; }
Node* InsertNode(int index, double x);
int FindNode(double x);
int DeleteNode(double x);
void DisplayList(void);
private:
Node* head; };

11. Inserting a new node Node* InsertNode(int index, double x) Steps
Insert a node with data equal to x after the index’th elements.
(i.e., when index = 0, insert the node as the first element;
when index = 1, insert the node after the first element, and so on)
If the insertion is successful,
return the inserted node.
Otherwise, return NULL.
(If index is < 0 or > length of the list, the insertion will fail.)
Steps
Locate index’th element
Allocate memory for the new node
Point the new node to its successor
Point the new node’s predecessor to the new node
index’th element
newNode

12. Inserting a new node Possible cases of InsertNode
Insert into an empty list
Insert in front
Insert at back
Insert in middle
But, in fact, only need to handle two cases
Insert as the first node (Case 1 and Case 2)
Insert in the middle or at the end of the list (Case 3 and Case 4)

13. Inserting a new node
Try to locate index’th node. If it doesn’t exist, return NULL.
Node* List::InsertNode(int index, double x) {
if (index < 0) return NULL;
int currIndex = 1;
Node* currNode = head;
while (currNode && index > currIndex) {
currNode = currNode->next;
currIndex++; }
if (index > 0 && currNode == NULL) return NULL;
Node* newNode = new Node;
newNode->data = x;
if (index == 0) {
newNode->next = head;
head = newNode;
else {
newNode->next = currNode->next;
currNode->next = newNode;
return newNode;

14. Inserting a new node Create a new node
Node* List::InsertNode(int index, double x) {
if (index < 0) return NULL;
int currIndex = 1;
Node* currNode = head;
while (currNode && index > currIndex) {
currNode = currNode->next;
currIndex++; }
if (index > 0 && currNode == NULL) return NULL;
Node* newNode = new Node;
newNode->data = x;
if (index == 0) {
newNode->next = head;
head = newNode;
else {
newNode->next = currNode->next;
currNode->next = newNode;
return newNode;
Create a new node

15. Inserting a new node Insert as first element
Node* List::InsertNode(int index, double x) {
if (index < 0) return NULL;
int currIndex = 1;
Node* currNode = head;
while (currNode && index > currIndex) {
currNode = currNode->next;
currIndex++; }
if (index > 0 && currNode == NULL) return NULL;
Node* newNode = new Node;
newNode->data = x;
if (index == 0) {
newNode->next = head;
head = newNode;
else {
newNode->next = currNode->next;
currNode->next = newNode;
return newNode;
Insert as first element
head
newNode

16. Inserting a new node Insert after currNode
Node* List::InsertNode(int index, double x) {
if (index < 0) return NULL;
int currIndex = 1;
Node* currNode = head;
while (currNode && index > currIndex) {
currNode = currNode->next;
currIndex++; }
if (index > 0 && currNode == NULL) return NULL;
Node* newNode = new Node;
newNode->data = x;
if (index == 0) {
newNode->next = head;
head = newNode;
else {
newNode->next = currNode->next;
currNode->next = newNode;
return newNode;
Insert after currNode
currNode
newNode

17. Finding a node int FindNode(double x)
Search for a node with the value equal to x in the list.
If such a node is found, return its position. Otherwise, return 0.
int List::FindNode(double x) {
Node* currNode = head;
int currIndex = 1;
while (currNode && currNode->data != x) {
currNode = currNode->next;
currIndex++; }
if (currNode) return currIndex;
return 0;

18. Deleting a node Steps Like InsertNode, there are two special cases
int DeleteNode(double x)
Delete a node with the value equal to x from the list.
If such a node is found, return its position. Otherwise, return 0.
Steps
Find the desirable node (similar to FindNode)
Release the memory occupied by the found node
Set the pointer of the predecessor of the found node to the successor of the found node
Like InsertNode, there are two special cases
Delete first node
Delete the node in middle or at the end of the list

19. The Scenario Begin with an existing linked list Could be empty or not
head 6 42 4 17
Begin with an existing linked list
Could be empty or not
Could be ordered or not

20. The Scenario Begin with an existing linked list Could be empty or not
head 6 42 4 17
Begin with an existing linked list
Could be empty or not
Could be ordered or not

21. The Scenario Begin with an existing linked list Could be empty or not
head 42 4 17
Begin with an existing linked list
Could be empty or not
Could be ordered or not

22. The Scenario Begin with an existing linked list Could be empty or not
head 42 4 17
Begin with an existing linked list
Could be empty or not
Could be ordered or not

23. Deleting a node Try to find the node with its value equal to x
int List::DeleteNode(double x) {
Node* prevNode = NULL;
Node* currNode = head;
int currIndex = 1;
while (currNode && currNode->data != x) {
prevNode = currNode;
currNode = currNode->next;
currIndex++; }
if (currNode) {
if (prevNode) {
prevNode->next = currNode->next;
delete currNode;
else {
head = currNode->next;
return currIndex;
return 0;
Try to find the node with its value equal to x

24. Deleting a node int List::DeleteNode(double x) {
Node* prevNode = NULL;
Node* currNode = head;
int currIndex = 1;
while (currNode && currNode->data != x) {
prevNode = currNode;
currNode = currNode->next;
currIndex++; }
if (currNode) {
if (prevNode) {
prevNode->next = currNode->next;
delete currNode;
else {
head = currNode->next;
return currIndex;
return 0;
prevNode
currNode

25. Deleting a node int List::DeleteNode(double x) {
Node* prevNode = NULL;
Node* currNode = head;
int currIndex = 1;
while (currNode && currNode->data != x) {
prevNode = currNode;
currNode = currNode->next;
currIndex++; }
if (currNode) {
if (prevNode) {
prevNode->next = currNode->next;
delete currNode;
else {
head = currNode->next;
return currIndex;
return 0;
head
currNode

26. Printing all the elements
void DisplayList(void)
Print the data of all the elements
Print the number of the nodes in the list
void List::DisplayList() {
int num = 0;
Node* currNode = head;
while (currNode != NULL){
cout << currNode->data << endl;
currNode = currNode->next;
num++; }
cout << "Number of nodes in the list: " << num << endl;

27. Destroying the list ~List(void)
Use the destructor to release all the memory used by the list.
Step through the list and delete each node one by one.
List::~List(void) {
Node* currNode = head, *nextNode = NULL;
while (currNode != NULL) {
nextNode = currNode->next;
// destroy the current node
delete currNode;
currNode = nextNode; }

28. Using List result int main(void) { List list;6 7 5
Number of nodes in the list: 3
5.0 found
4.5 not found
Number of nodes in the list: 2
result
int main(void) {
List list;
list.InsertNode(0, 7.0); // successful
list.InsertNode(1, 5.0); // successful
list.InsertNode(-1, 5.0); // unsuccessful
list.InsertNode(0, 6.0); // successful
list.InsertNode(8, 4.0); // unsuccessful
// print all the elements
list.DisplayList();
if(list.FindNode(5.0) > 0) cout << "5.0 found" << endl;
else cout << "5.0 not found" << endl;
if(list.FindNode(4.5) > 0) cout << "4.5 found" << endl;
else cout << "4.5 not found" << endl;
list.DeleteNode(7.0);
return 0; }

29. Linked List Efficiency
Insertion and deletion at the beginning of the list are very fast, O(1).
Finding, deleting or inserting in the list requires searching through half the items in the list on an average, requiring O(n) comparisons.
Although arrays require same number of comparisons, the advantage lies in the fact that no items need to be moved after insertion or deletion.
As opposed to fixed size of arrays, linked lists use exactly as much memory as is needed and can expand.

30. More on Linked Lists

31. Summary list Linked List
is a sequential container optimized for insertion and erasure at arbitrary points in the sequence
Linked List
Each data item is embedded in a link & Each Link object contains a reference to the next link in the list of items.

32. Circular Linked List
In other applications a circular linked list is used;
instead of the last node containing a null pointer, it contains a pointer to the first node in the list.
For such lists,one can use a single pointer to the last node in the list, because then one has direct access to it and "almost-direct" access to the first node.
last 9 17 22 26 34
Each node in a circular linked list has a predecessor (and a successor), provided that the list is nonempty.
insertion and deletion do not require special consideration of the first node.
This is a good implementation for a linked queue or for any problem in which "circular" processing is required

33. Node* prevNode = NULL;
Node* currNode = head;
int currIndex = 1;
while (currNode && currNode->data != x) {
prevNode = currNode;
currNode = currNode->next;
currIndex++; }

34. Inserting a new node
Node* List::InsertNode(int index, double x) {
if (index < 0) return NULL;
int currIndex = 1;
Node* currNode = head;
while (currNode && index > currIndex) {
prevnode=currnode
currNode = currNode->next;
currIndex++; }
if (index > 0 && currNode == NULL) return NULL;
Node* newNode = new Node;
newNode->data = x;
if (index == 0) {
newNode->next = head;
head = newNode;
else {
newNode->next = currNode->next;
currNode->next = newNode;
return newNode;
Try to locate index’th node. If it doesn’t exist, return NULL.

35. Circularly Linked Lists
For example, item can be inserted as follows:
newptr = new Node(item, 0);
if (Index == 0) // list is empty {
newptr->next = newptr;
currentIndex = newptr; }
else // nonempty list
newptr->next = predptr->next;
predptr->next = newptr;
Note that a one-element circularly linked list points to itself.

36. Circularly Linked Lists
Traversal must be modified: avoid an infinite loop by looking for the end of list as signalled by a null pointer.
Like other methods, deletion must also be slightly modified.
Deleting the last node is signalled when the node deleted points to itself.
if (Index == 0) // list is empty
// Signal that the list is empty
else {
ptr = predptr->next; // hold node for deletion
if (ptr == predptr) // one-node list
Index = 0;
else // list with 2 or more nodes
predptr->next = ptr->next;
delete ptr; }

37. Summary In Circular linked lists
The last node points to the first node of the list
How do we know when we have finished traversing the list? (Tip: check if the pointer of the current node is equal to the head.) A B C
Head

38. Double Linked Lists

39. Doubly Linked Lists
All of these lists, however, are uni-directional; we can only move from one node to its successor.
In many applications, bidirectional movement is necessary. In this case, each node has two pointers — one to its successor (null if there is none) and one to its predecessor (null if there is none.) Such a list is commonly called a doubly-linked (or symmetrically-linked) list.
last
prev L
first
mySize 5 9 17 22 26 34
next

40. Con’t….
Similar to an ordinary list with the addition that a link to the last item is maintained along with that to the first.
The reference to the last link permits to insert a new link directly at the end of the list as well as at the beginning.
This could not be done in the ordinary linked list without traversing the whole list.
This technique is useful in implementing the Queue where insertions are made at end and deletions from the front.

41. Insertion
We visualize operation insertAfter(p, X), which returns position q p A B C p q A B C X p q A B X C
Linked Lists

42. Insertion Algorithm Algorithm insertAfter(p,e): Create a new node v
v.setElement(e)
v.setPrev(p) {link v to its predecessor}
v.setNext(p.getNext()) {link v to its successor}
(p.getNext()).setPrev(v) {link p’s old successor to v}
p.setNext(v) {link p to its new successor, v}
return v {the position for the element e}
Linked Lists

43. Deletion We visualize remove(p), where p == last() A B C D p A B C p D
Linked Lists

44. Deletion Algorithm Algorithm remove(p):
t = p.element {a temporary variable to hold the return value}
(p.getPrev()).setNext(p.getNext()) {linking out p}
(p.getNext()).setPrev(p.getPrev())
p.setPrev(null) {invalidating the position p}
p.setNext(null)
return t
Linked Lists

45. Worst-cast running time
In a doubly linked list
+ insertion at head or tail is in O(1)
+ deletion at either end is on O(1)
-- element access is still in O(n)
Linked Lists

46. Summary Each node points to not only successor but the predecessor
There are two NULL: at the first and last nodes in the list
Advantage: given a node, it is easy to visit its predecessor. Convenient to traverse lists backwards

47. Summary A doubly linked list is often more convenient! Nodes store:
element
link to the previous node
link to the next node
Special trailer and header nodes
prev
next
elem
node
trailer
header
nodes/positions
elements
Linked Lists

48. Con’t…. doubly-linked list => bidirectional movement!!
Each node has two pointers — one to its successor (null if there is none) and one to its predecessor (null if there is none.)
Doubly linked lists give one more flexibility (can move in either direction)
BUT at significant cost :
DOUBLE the overhead for links
More complex code

49. The End !!!