1. Stacks

2. Overview of Stacks Stack of books Stack of plates Stack of CD’s
A stack is restricted list in which items are inserted or deleted only at the top of the list. .
Example
Stack of books
Stack of plates
Stack of CD’s

4. Overview of Stacks
Operations are allowed only at one point of the structure, normally termed the “top” of the stack.
The stack’s storage policy is Last-In, First-Out (LIFO). This means that the last element inserted will be the first to be removed.
pop
pop
top
push 85
top 85
230
-20
100
230
push
-20
100

5. Stacks – As a conceptual aids
Stack is created to carry out particular task during the operation of a program rather than data storage.
Lifetime short – discarded when operation completed
Stack interface – to enforce restricted access to other items. Only one item either to be read or remove at a given time.
More abstract than arrays – defined with certain permissible operations and not visible to user.
Only the top element of a stack is visible, therefore the number of operations performed by a stack are few…
Inspect the top element
Retrieve the top element
Push a new element on the stack
Test for an empty stack

6. Application of Stacks
Stacks are used in many areas, which include the following:
Page-Visited history in a web browser.
Undo sequence in a text editor.
Evaluation of Expression.
Matching of Parentheses.
Chain of method calls in JAVA virtual machine.

7. Stack Operations Stack operations are:
Push -> inserts an element on to top of stack
Pop -> deletes an element from the top of the stack

8. Stack Operations Stack operations are:
Name: Mohammed Rafi
Couse Code: MIS201
Title: Data and Information Structures
Stack operations are:
Push -> inserts an element on to top of stack
Pop -> deletes an element from the top of the stack
isFull() is False for this Stack.
isEmpty() is False for this Stack and Size() is 2.

9. Implementation of Stacks
Stacks can be implemented in two ways:
Using arrays
Using Linked Lists

10. Using Arrays First the size has to be defined.
For example: take size of stack is 6.
Size of the stack is 6
push(10)
push(-5) 10 -5 10
top
top

11. Using Arrays size() = 3 Elements push(100) push(55) push(-20) push(25)
isfull() = False
isempty() = False
top() = 100
push(100)
100 -5 10
push(55)
top
push(-20) 55
-20
100 -5 10
-20
100 -5 10
push(25)
top
size() = 6 Elements
isfull() = True
isempty() = False
top() = 25 25 55
-20
100 -5 10
top
top

12. Using Arrays push(75) pop() pop() pop() size() = 6 Elements
isfull() = True
isempty() = False
top() = 25
No space is available, this state is called overflow.
push(75) 25 55
-20
100 -5 10
top
pop()
pop()
pop() 55
-20
100 -5 10
-20
100 -5 10
100 -5 10
top
top
top
size() = 3 Elements
isfull() = Fasle
isempty() = False
top() = 100

13. Using Arrays pop() push(75) pop() pop() pop() size() = No Elements
100 -5 10 75
100 -5 10
top
top
pop()
pop()
pop() -5 10 10
top
top
size() = No Elements
isfull() = Fasle
isempty() = True
top() = Error
This state is called underflow.

14. Stacks - Exceptions
Attempting the execution of an operation of ADT may sometimes cause an error condition, called an exception
Exceptions are said to be “thrown” by an operation that cannot be executed
In the Stack ADT, operations pop and top cannot be performed if the stack is empty
Attempting the execution of pop or top on an empty stack throws an EmptyStackException.

15. Stacks - Exceptions Stack overflow Stack underflow
The condition resulting from trying to push an element onto a full stack
if(!stack.IsFull())
stack.Push(item);
The condition resulting from trying to pop an empty stack.
if(!stack.IsEmpty())
stack.Pop(item);

16. The Algorithm Using Array
Inserting Algorithm:
Deleting Algorithm:
push(stack, top, item){
if(top == max – 1)
Display “Stack Overflow”
else
top = top + 1
stack[top] = item }
pop(stack, top){
if(top < 0)
Display “Stack Uderflow”
else
item = stack[top]
top = top – 1
return(item) }

17. Stacks – Evaluation Performance Each operation runs in time O(1)
The time is not dependent on how many items are in the stack and is therefore very quick retrieval, no comparisons and moves necessary.
Limitations
The maximum size of the stack must be defined a priori and cannot be changed
Trying to push a new element into a full stack causes an implementation-specific exception

18. Stacks – Evaluation Efficiency
Push -> O(1) (Insertion is fast, but only at the top)
Pop -> O(1) (Deletion is fast, but only at the top)
Peek -> O(1) (Access is fast, but only at the top)

19. Stack LinkedList Implementation
public class Node<T> extends Object {
public T data;
public Node<T> next;
public Node () {
data = null; next = null; }//constructor }

20. Stack LinkedList Implementation
public class LinkListStack<T> extends Object { private Node<T> top; public LinkListStack () { top = null; } //constructor //operation public boolean isEmpty () { return top == null; } public boolean isFull () { return false; }

21. Stack LinkedList Implementation
public T topE () {
if(top.data==null)
throw EmptyStackException
return top.data; }
public void push (T val) {
Node n = new Node(val);
n.next = top;
top = n;

22. Stack LinkedList Implementation
public T pop (){
if(top.data==null)
throw EmptyStackException
Node temp = top;
top = top.next;
return temp.data; }

23. Homewrk
Implement stack (the array based stack ) given the following specification:
The array based stack class should contain only the following ( max – top – the array itself)
The classes should contain the following methods :
-push(int e): inserts an element.
-int pop(): removes and returns the last inserted element.
-int topE(): returns the last inserted element without removing it (data).
-boolean isEmpty(): indicates whether no elements are stored.
-boolean isFull(): indicates whether the stack full or not.