Array linked list.ppt

Linked Lists / Slide 2
Outline
 Abstract Data Type (ADT)
 List ADT
 List ADT with Array Implementation
 Linked lists
 Basic operations of linked lists
 Insert, find, delete, print, etc.
 Variations of linked lists
 Circular linked lists
 Doubly linked lists

Abstract Data Type (ADT)
 Data type
 a set of objects + a set of operations
 Example: integer
set of whole numbers
operations: +, -, x, /
 Can this be generalized?
 (e.g. procedures generalize the notion of an
operator)
 Yes!
 Abstract data type
 high-level abstractions (managing complexity
through abstraction)
 Encapsulation

Encapsulation
 Operation on the ADT can only be done by calling the
appropriate function
 no mention of how the set of operations is
implemented
 The definition of the type and all operations on that
type can be localized to one section of the program
 If we wish to change the implementation of an ADT
 we know where to look
 by revising one small section we can be sure that
there is no subtlety elsewhere that will cause errors
 We can treat the ADT as a primitive type: we have no
concern with the underlying implementation
 ADT  C++: class
 method  C++: member function

ADT…
 Examples
 the set ADT
A set of elements
Operations: union, intersection, size and complement
 the queue ADT
A set of sequences of elements
Operations: create empty queue, insert, examine, delete,
and destroy queue
 Two ADT’s are different if they have the same
underlying model but different operations
 E.g. a different set ADT with only the union and find
operations
 The appropriateness of an implementation
depends very much on the operations to be
performed

Pros and Cons
 Implementation of the ADT is separate from its use
 Modular: one module for one ADT
 Easier to debug
 Easier for several people to work simultaneously
 Code for the ADT can be reused in different
applications
 Information hiding
 A logical unit to do a specific job
 implementation details can be changed without affecting user
programs
 Allow rapid prototying
 Prototype with simple ADT implementations, then tune them
later when necessary
 Loss of efficiency

The List ADT
 A sequence of zero or more elements
A1, A2, A3, … AN
 N: length of the list
 A1: first element
 AN: last element
 Ai: position i
 If N=0, then empty list
 Linearly ordered
 Ai precedes Ai+1
 Ai follows Ai-1

Operations
 printList: print the list
 makeEmpty: create an empty list
 find: locate the position of an object in a list
 list: 34,12, 52, 16, 12
 find(52)  3
 insert: insert an object to a list
 insert(x,3)  34, 12, 52, x, 16, 12
 remove: delete an element from the list
 remove(52)  34, 12, x, 16, 12
 findKth: retrieve the element at a certain
position

Implementation of an ADT
 Choose a data structure to represent the
ADT
 E.g. arrays, records, etc.
 Each operation associated with the ADT is
implemented by one or more subroutines
 Two standard implementations for the list ADT
 Array-based
 Linked list

Array Implementation
 Elements are stored in contiguous array
positions

Array Implementation...
 Requires an estimate of the maximum size of
the list
 waste space
 printList and find: linear
 findKth: constant
 insert and delete: slow
 e.g. insert at position 0 (making a new element)
requires first pushing the entire array down one spot to
make room
 e.g. delete at position 0
requires shifting all the elements in the list up one
 On average, half of the lists needs to be moved for
either operation

Pointer Implementation (Linked List)
 Ensure that the list is not stored contiguously
 use a linked list
 a series of structures that are not necessarily adjacent
in memory
 Each node contains the element and a pointer to a
structure containing its successor
the last cell’s next link points to NULL
 Compared to the array implementation,
the pointer implementation uses only as much space as is needed
for the elements currently on the list
but requires space for the pointers in each cell

Linked Lists
 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 
Head
B C
A
data pointer
node

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
};

 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;
};

 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

Inserting a new node
 Node* InsertNode(int index, double x)
 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
1. Locate index’th element
2. Allocate memory for the new node
3. Point the new node to its successor
4. Point the new node’s predecessor to the new node
newNode
index’th
element

 Possible cases of InsertNode
1. Insert into an empty list
2. Insert in front
3. Insert at back
4. 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)

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;
}
Try to locate
index’th node. If it
doesn’t exist,
return NULL.

int currIndex = 1;
currIndex++;
}
newNode->data = x;
if (index == 0) {
head = newNode;
}
else {
}
return newNode;
}
Create a new node

int currIndex = 1;
currIndex++;
}
newNode->data = x;
if (index == 0) {
head = newNode;
}
else {
}
return newNode;
}
Insert as first element
head
newNode

int currIndex = 1;
currIndex++;
}
newNode->data = x;
if (index == 0) {
head = newNode;
}
else {
}
return newNode;
}
Insert after currNode
newNode
currNode

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) {
int currIndex = 1;
while (currNode && currNode->data != x) {
currIndex++;
}
if (currNode) return currIndex;
return 0;
}

Deleting a node
 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

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

Deleting a node
int currIndex = 1;
currIndex++;
}
if (currNode) {
if (prevNode) {
delete currNode;
}
else {
delete currNode;
}
return currIndex;
}
return 0;
}
currNode
prevNode

Deleting a node
int currIndex = 1;
currIndex++;
}
if (currNode) {
if (prevNode) {
delete currNode;
}
else {
delete currNode;
}
return currIndex;
}
return 0;
}
currNode
head

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;
while (currNode != NULL){
cout << currNode->data << endl;
num++;
}
cout << "Number of nodes in the list: " << num << endl;
}

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;
}
}

Using List
int main(void)
{
List list;
list.InsertNode(0, 7.0); // successful
list.InsertNode(-1, 5.0); // unsuccessful
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);
list.DisplayList();
return 0;
}
6
7
5
Number of nodes in the list: 3
5.0 found
4.5 not found
6
5
Number of nodes in the list: 2
result

Variations of Linked Lists
 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
Head
B C

Variations of Linked Lists
 Doubly linked lists
 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
A
Head
B
 C 

Array versus Linked Lists
 Linked lists are 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.

Example: The Polynomial ADT
 An ADT for single-variable polynomials
 Array implementation



N
i
i
i x
a
x
f
0
)
(

The Polynomial ADT…
 Acceptable if most of the coefficients Aj are
nonzero, undesirable if this is not the case
 E.g. multiply
most of the time is spent multiplying zeros and stepping
through nonexistent parts of the input polynomials
 Implementation using a singly linked list
 Each term is contained in one cell, and the cells
are sorted in decreasing order of exponents
5
11
2
3
)
(
1
5
10
)
(
1492
1990
2
14
1000
1







x
x
x
x
P
x
x
x
P

Array linked list.ppt

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