1. Presented by : Aman Gupta PGT CS KV No.1, Narimedu, Madurai
Stack
Presented by :
Aman Gupta
PGT CS
KV No.1, Narimedu, Madurai
8/27/2019

2. Topics to Cover . . . Introduction to some Data Structures
Stack – An Introduction
Stack – Operations
Implementation of Stack
Stack using Arrays
Applications of Stack
Conversion of Infix to Postfix polish notation
Evaluation of Postfix expression
Questions (Homework Assignment)
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3. Introduction of Some Data Structures
Arrays
Linked List
Queue
Stack
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4. Arrays
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5. LINKED LISTS – Connects Nodes
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6. Queue - FIFO
A queue is like a line of people waiting for a bank teller. The queue has a front and a rear.
$ $
Front
Rear
When you think of a computer science queue, you can imagine a line of people waiting for a teller in a bank. The line has a front (the next person to be served) and a rear (the last person to arrive.
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7. STACKS - LIFO
In this Example, we had entered 1, 3 & 9 in the order but we have to retrieve 9 first .
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8. The Stack Operations
Insertion - New data must enter the Stack at the TOP. It is usually called an Push operation.
Don’t ask me why the C++ STL used the name push. It only confuses matters with a stack. In any case, when a new item enters a queue, it does so at the rear.
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9. The Stack Operations
Deletion - When an item is taken from the Stack, it always comes from the TOP. It is usually called a Pop operation.
When an item is removed from a queue, the removal occurs at the front.
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10. Implementation of Stack
Static Stack – Using Arrays
Dynamic Stack – Using Linked Lists
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11. Implementation using Array
It is also Called as Static Stack
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12. Operations on Stack using Array
PUSH Operation
ALGORITHM :
1. If TOP = N, then : Print OVERFLOW and Return.
2. Set TOP := TOP + 1.
3. Set STACK[TOP] := ITEM.
4. Return.
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13. Operations on Stack using Array
POP Operation
ALGORITHM :
1. If TOP = 0, then : Print UNDERFLOW and Return.
2. Set ITEM:= STACK[TOP].
3. Set TOP := TOP - 1.
4. Return.
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14. Review Questions 1. What do you mean by PUSH in terms of Stack?
2. What do you mean by UNDERFLOW & OVERFLOW.
3. What are the different ways to implement Stack?
4. What do you mean by dynamic Stack?
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15. Applications of Stack Infix to Postfix Conversion
Evaluation of Postfix Expression
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16. Infix to Postfix Conversion
Polish Notation
The order in which any Operation is performed is determined by the position of Operator & Operands in the expression.
Types of Polish notations :
Infix
Prefix
Postfix
A + B
+AB
AB+
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17. Infix to Postfix Conversion
Precedence of Operators
The order in which any Operation is performed in the expression.
Exponentiation (  )
Multiplication ( * ) & Division ( / )
Addition ( + ) & Subtraction( - )
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18. Infix to Postfix Conversion
Need of converting Infix to Postfix
While using INFIX Compiler needs to remember the precedence of operators to solve the equation, which is tedious task but if we convert it into post fix notation then it arranges Operators according to their precedence. So, Compiler doesn’t needs to remember that so it saves time & Complexity.
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19. Infix to Postfix Conversion
ALGORITHM
1. Push “(“ onto Stack and Add “)” to the end of Q.
2. Scan Q from left to right and repeat steps 3 to 6 for each element of Q until Stack is empty:
3. If an operand is encountered, add it to P.
4. If a Left parenthesis is encountered, push it on Stack.
5. If an Operator ¤ encountered, then :
a) Repeatedly pop from Stack and add to P each operator which has the same precedence as or higher precedence than ¤.
b) Add ¤ to the Stack.
[ End of If Structure]
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20. Infix to Postfix Conversion
ALGORITHM
6. If a Right parenthesis is encountered, then :
a) Repeatedly pop from Stack and add to P each operator until a Left parenthesis is encountered.
b) Remove the left Parenthesis.
[ End of If Structure]
[End of step 2 Loop]
7. Exit.
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21. Q : A + ( B * C – ( D / E  F ) * G ) * H
Example :
Q : A + ( B * C – ( D / E  F ) * G ) * H
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22. Q : A + ( B * C – ( D / E  F ) * G ) * H
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23. Q : A + ( B * C – ( D / E  F ) * G ) * H
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24. Evaluation of Postfix Expression
1. Add a right parenthesis “)“ at the end of P.
2. Scan p from left to right and repeat step 3 & 4 for each until the sentinel “)” is encountered.
3. If an operand is encountered, put it on Stack.
4. If an operator ¤ is encountered, then :
a) Pop the two top elements of Stack, Say A(Top most) and B(Second Top).
b) Evaluate A ¤ B.
c) Push the result in Stack.
[End of If structure]
[End of step 2 Loop]
5. Set Value equal to top element of Stack.
6. Exit.
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25. EXAMPLE
P : * / -
As You can see now P is empty i.e. there is no more element in P. So, Value at Stack[TOP] is your answer.
In this case it is 37
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26. Homework Assignment 1. Convert following Infix expression to Postfix :
X – y / (z + u) * V
– 50 / 15 * 4 + (8 + 7)
2. Evaluate Following Postfix Expressions:
T, F, NOT, AND, F, T, OR, AND
* 30 /
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27. THANX A LOT
QUERIES ???
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28. Static vs. Dynamic Structures
Static Data Structures
Fast access to elements
Expensive to insert/remove element
Have fixed maximum size
Memory is reserved at the time of compilation.
e.g. Arrays
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29. Static vs. Dynamic Structures
Dynamic Data Structures
Fast insertion/deletion of element
Slower access to the element
Have flexible size
Memory allocation for the data structure takes place at the run time, only required amount of memory is allocated.
e.g. Linked lists, Stacks, Queues, Trees etc.
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30. Static vs. Dynamic Structures
A static data structure has a fixed size
e.g. Arrays are static; once you define the number of elements it can hold, the number doesn’t change
A dynamic data structure grows and shrinks at execution time as required by its contents
A dynamic data structure is implemented using links
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31. Drawbacks of Static Data Structures
Memory – We had to define memory in advance which will either waste Memory or create the space problem
Time – For Insertion & Deletion
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32. Array Implementation
A Stack can be implemented with an array, as shown here.
Just like our stack implementation in the previous chapter, one way to implement a queue is to store the elements in an array.
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