This document discusses stacks and their applications. It defines a stack as a linear list where additions and deletions are restricted to one end, called the top, resulting in Last-In First-Out (LIFO) behavior. The key applications of stacks discussed are: reversing data order, parsing data, postponing operations, and backtracking. Specific examples covered include infix to postfix notation conversion, expression evaluation, parentheses matching, goal seeking problems, and the eight queens problem.

1. STACK
Seminar By Naresh
SKU_CST_M.Sc.
DATA STRUCTURES
A Pseudo code Approach with C++

2. Stack
 A stack is linear list in which all additions and deletions are restricted to one end,
called top. If you inserted a data series into stack and then removed it, the order
of the data would be reversed, it also called as Last- in- First out (LIFO) data
structure.
SKU_CST_M.Sc.

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Example

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Stack Applications can be classified into four categories
They are:
Reversing Data
Parsing Data
Postponing data
backtracking

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 Reversing data requires that a given set of data be reordered so that
first and last elements are exchanged. For example {1 ,2,3,4}
becomes {4,3,2,1}
 We examine two different reversing applications:
 Reverse a list
 Convert decimal to binary

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Postponement: Evaluating arithmetic expressions.
Expression: expression is a legal combination of operands and the operators.
 Operand: is the quantity (unit of data) on which a mathematical operation is performed.
 Operand may be a variable like x, y, z or a constant like 5, 4,0,9,1 etc.
 The difference between variables and constants is that variables can change their value at any time
but constants can never change their value. (The constants value is locked for the duration of the
program)
 Operator: is a symbol which is a mathematical or logical operation between the operands.
Example of familiar operators include +,-,*, /, ^
 Considering these definitions of operands and operators now we can write an example of
expression as x+y*z.

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We develop two stack postponement applications in this section:
Infix to Postfix transformation and postfix expression evaluation.
An arithmetic expression can be represented in three different formats they are
Infix, Prefix, Postfix
Which we write an operator in between two operands is called Infix Notation
<Operands><Operator><Operands>
2 + 3
Example
2+3=5
4+6*2=?

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Order of the Operations
Parentheses { }, ( ), [ ]
Exponents ^, 2^3^2 = 512(right to left)
Multiplication and Division (left to right)
Addition and Subtraction (left to right)
Example:
2 * 6 / 2 – 3 + 7 = ?
12 / 2 – 3 + 7
6-3+7= 3+7=10

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{(2 * 6 ) / 2 } – (3 + 7) = ?
{12 / 2} – ( 3+7)= 6-10= -4
Prefix notation was proposed earlier in 1924 by polish legition. In Prefix Notation the operator is placed
before two operands
<Operator><Operands> <Operand>
+ 2 3
a + (b * c)=
a + ( * bc)
+a * bc

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 Postfix notation is another way of writing arithmetic expressions.
 In postfix notation, the operator is written after the two operands.
 infix: 2+5 postfix: 2 5 +
 Expressions are evaluated from left to right.
Postfix notation are also Known as Reverse Polish Notation.
They are different from the infix and prefix notations in the sense that in the postfix notation,
operator comes after the operands, e.g. xy+, xyz+* etc.
<Operands> <Operand> <Operator>
2 3 +

11. Examples of infix to prefix and post fix
Infix PostFix Prefix
A+B AB+ +AB
(A+B) * (C + D) AB+CD+* *+AB+CD
A-B/(C*D^E) ABCDE^*/- -A/B*C^DE

12. Postfix Examples
Infix Postfix Evaluation
2 - 3 * 4 + 5 2 3 4 * - 5 + -5
(2 - 3) * (4 + 5) 2 3 - 4 5 + * -9
2- (3 * 4 +5) 2 3 4 * 5 + - -15

13. Algorithm for Infix to Postfix
1) Examine the next element in the input.
2) If it is operand, output it.
3) If it is opening parenthesis, push it on stack.
4) If it is an operator, then
i) If stack is empty, push operator on stack.
ii) If the top of stack is opening parenthesis, push operator on stack
iii) If it has higher priority than the top of stack, push operator on stack.
iv) Else pop the operator from the stack and output it, repeat step 4
5) If it is a closing parenthesis, pop operators from stack and output them
until an opening parenthesis is encountered. pop and discard the
opening parenthesis.
6) If there is more input go to step 1
7) If there is no more input, pop the remaining operators to output.

14. Suppose we want to convert 2*3/(2-1)+5*3 into Postfix form,
So, the Postfix Expression is 23*21-/53*+
2 Empty 2
* * 2
3 * 23
/ / 23*
( /( 23*
2 /( 23*2
- /(- 23*2
1 /(- 23*21
) / 23*21-
+ + 23*21-/
5 + 23*21-/5
3 +* 23*21-/53
Expression Stack Output
* +* 23*21-/53
Empty 23*21-/53*+

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Example: postfix expressions

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Another application of stack is Parsing. Parsing is any logic that breaks data into independent
pieces for further processing.
For example
To translate a source program to machine language, a compiler must parse the program into
individual parts such as key words, names and tokens.
One common programming problem is unmatched parentheses in an algebraic
expression. When parentheses are unmatched, two types of errors can occur: The
opening parentheses can be missing or the closing parentheses can be messing.
( (A + B) / C (A + B) / C )
(a) Operating Parentheses not matched (b) Operating Parentheses not matched

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Backtracking is another stack use found in applications such as computer gaming, decision
analysis, and expert system.
We examine backtracking applications in this section: Goal Seeking and Eight Queens
Problem
Backtracking is a methodical way of trying out various sequences of decisions, until you
find one that “works”

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