STACK, STACK OPERATIONS, IMPLEMENTING OF STACK, POLISH NOTATION, APPLICATIONS

1. INTRODUCTION
 What is Stack?
 Stack Representation
 ADT specification of Stack
 Operations on Stack
 Stack Overflow and Stack Underflow
 Implementing of Stack
 Prefix, Postfix, Infix Notation
 Polish Notation
 Precedence and Priority
 Applications

2. WHAT IS STACK??
 Stores a set of elements in a particular order.
 Stack is like a container of memory.
 Stack principle- LAST IN FIRST OUT(LIFO)
Examples:-

3. LAST IN FIRST OUT

4. STACK REPRESENTATION

5. ADT SPCIFICATIONS OF STACK
Operations:
 Make Empty
 Boolean Is Empty
 Boolean Is Full
 Push (Item Type new Item)
 Pop (Item Type& item) (or pop and top)

6. TOP
 A list with the restriction that insertion and deletion
can be performed only from one end is called top.
 If stack is empty, then top is at -1 position.
 If stack is not empty, then top is at last position(n-1).

7. PUSH OPERATION
 Stack is empty, top is at -1 position.
 Function: Adds new Item to the top of the stack.
 Preconditions: Stack has been initialized and is not full.
 Post conditions: new Item is at the top of the stack.

8. PSEUDO CODE IN C
Void push() {
int item;
printf(“Enter item to push”);
scanf(“%d”.&item);
if(top == max – 1) { // overflow condition
printf(“Stack overflow”);
}
else {
top = top + 1;
stack[top] = item;
}
}

9. PUSH OPERATION

10. POP OPERATION
 Stack is not empty, then top is at last position (n-1).
 Removes top Item from stack and returns it in item.
 Always done on the top of stack
 The top most element is deleted first
 Preconditions: Stack has been initialized and is not
empty.
 Post conditions: Top element has been removed from
stack and item is a copy of the removed element.

11. PSEUDO CODE IN C
Void pop () {
if(top == -1)
printf(“Stack underflow”);
else {
printf(“The deleted item is %d”,stack[top]);
top--;
}
}

12. POP OPERATION

13. STACK OVERFLOW
 The condition resulting from trying to push an element
onto a full stack.
 Top is at last position(n-1).

14. STACK UNDERFLOW
 The condition resulting from trying to pop an
empty stack.
 Top is at -1 position.

15. IMPLEMENTING OF STACK
Basics two choices:-
 Array
 Linked list
1) Array:-
Array is quick, but limited in size.

16. IMPLEMENTING OF STACK
2) Linked list:-
Linked List requires overhead to allocate, link,
unlink, and deallocate, but is not limited in size

17. INFIX EXPRESSION
 Operator is used in between operands.
 Example:-

18. POSTFIX EXPRESSION
 Operator is used after operands.
 Example:-

19. PREFIX EXPRESSION
 Operator is used before operands.
 Example:-

20. POLISH NOTATION
 Prefix notation requires that all operators precede the two
operands that they work on.
 Postfix notation requires that its operators come after the
corresponding operands.

21. PRECEDENCE AND PRIORITY

22. INFIX TO POSTFIX
 The infix string from left to right.
 Initialize an empty stack.
 Character is an operand, add it to the Postfix
string.
 If the stack is empty, push the character is an
operator to stack
 stack is not empty, compare the precedence of
the character with the element on top of the
stack.

23. EXAMPLE OF INFIX TO
POSTFIX

24. INFIX TO PREFIX
 Reverse given prefix expression.
 Conversion same as infix to postfix expression.
 Reverse the expression.

25. EXAMPLE OF INFIX TO
PREFIX

26. EVALUATION OF POSTFIX
 Create a stack to store operands (or values).
 If the element is a number, push it into the stack.
 If the element is a operator, pop operands for the operator
from stack.
 Evaluate the operator and push the result back to the stack
when the expression is ended, the number in the stack is
the final answer.

27. EXAMPLE OF EVALUATION
OF POSTFIX

28. EVALUATION OF PREFIX
 Accept a prefix string from the user.
 The string from the right one character at a time.
 If it is an operand, push it in stack.
 If it is an operator, pop and perform the operation,
specified by the operator.
 Push the result in the stack.
 The number in stack is final answer.

29. EXAMPLE OF
EVALUATION OF PREFIX

30. APPLICATIONS
 Parsing
 Recursive Function
 Calling Function
 Expression Evaluation
 Expression Conversion
 Infix to Postfix
 Infix to Prefix
 Postfix to Infix
 Prefix to Infix