This document provides information about stacks as a data structure. Stacks are linear data structures where items can only be added or removed from one end, called the top. The last item added is the first item removed. Basic stack operations include push to insert an element and pop to remove an element. Stacks can be represented using arrays, with a variable pointing to the top element and another storing the maximum size. Functions like isEmpty() and isFull() check the state of the stack, while push() and pop() insert and remove elements.

1. Data Structure
Stack
C . C++ . Java

2. Stacks
A Stack is a linear data structure in which items may be added or removed only at one
end. This end is called the ‘Top’.
The last item to be added is the first item to be removed.
Basic Stack Operations
PUSH : Insert an element in the stack
POP : Remove an element from the stack 6 10 3

3. Array representation of Stacks
A Linear Array : Stack
6 10 3
A variable pointing to the index of topmost element : Top
A variable to store the maximum size of the stack : MaxStack

4. Showstack( )
Displays the content of the stack
isFull( )
Boolean function for checking if
the stack has reached max array
size.
isEmpty( )
Boolean function for checking if
the stack is empty
Push( )
Insert an element in the
stack
Pop( )
Remove an element from the
stack
01 02 03
04 05

5. Push( ) and Pop( )
6 10 3

6. Polish Notation
Postfix, Infix, Prefix

7. Technopedia.com
Polish notation was invented in 1924 by Jan Lukasiewicz, a Polish
logician and philosopher, in order to simplify sentential logic. The idea
is simply to have a parenthesis-free notation that makes each
equation shorter and easier to parse in terms of defining the evaluation
priority of the operators.
a series or system of written symbols used to represent
numbers, amounts, or elements in something such as
music or mathematics.
Notation

8. Polish Notation
Let Q be an arithmetic expression with the following precedence order for operations:
Highest : Exponentiation (^)
Next Highest : Multiplication (*), Division (/)
Lowest : Addition (+), Subtraction (-)
In a parenthesis free expression, operations on the same level are performed left to
right.
2 ^ 3 + 5 * 2 ^ 2 – 12 / 6 8 + 5 * 4 – 12 / 6
8 + 20 – 2 28 – 2 = 26

9. Infix Notation
It is the notation where operator symbols are placed between operands.
A+B C-D E*F G/H
parenthesis are required to distinguish operations like (A+B)*C and A+(B*C).

10. Prefix/ Polish Notation
It is the notation where operator symbols are placed before operands.
+AB -CD *EF /GH
No parenthesis are required.

11. Postfix/ Reverse Polish Notation
It is the notation where operator symbols are placed after operands.
AB+ CD- EF* GH/
No parenthesis are required.

12. Postfix/ Reverse Polish Notation
It is the notation where operator symbols are placed after operands.
AB+ CD- EF* /GH

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Mercury is the closest planet to the
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Earth is the only known planet to
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Venus has a beautiful name and is
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Job center
Saturn is a gas giant and has
several rings around it

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Hour Mon Tue Wed Thu Fri
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Jupiter is the biggest planet
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Saturn is a gas giant and
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18. Preparing for your degree
Step #01
Jupiter is the biggest
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Step #02
Neptune is the
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Step #03
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Step #04
Pluto is considered a
dwarf planet

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Standard degrees
Jupiter is the biggest planet in the
entire Solar System
Top degrees
Saturn is the ringed planet and also
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Ceres is located in the main asteroid belt
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