1. DATA STRUCTURES
STACK APPLICATIONS
By
Shanthi.S
Saradhaswathi.G
Thangapriyaa.V.B
Sriram.N
Ramesh.R
Poornachandran.R

2. Conversion And Evaluation
of Expressions
Group - 4

3. Conversion And Evaluation of Expressions
• Stack
A Stack is an ordered list in which all
insertions and deletions are made at one end
called Top.

4. Expressions
Expression is a string of operands and operators.
Operands are some numeric values and operators
are of two types :
 Unary operators such as ‘+’ and ‘-’.
Binary operators such as ‘+’, ‘-’, ‘*’, ‘/’ and
exponential.

5. Types of Expressions
• Infix Expressions
• Postfix Expressions
• Prefix Expressions

6. Infix Expressions
• Parenthesis can be used in these expressions.
• Infix expressions are the most natural way of
representing expressions.
Infix expression = Operand1 operator Operand2
Examples: 1) (a+b)
2) (a+b)*(c-d)
3) a+b/c)*(d+f)

7. Postfix Expression
In postfix expression, there are no
parenthesis used. All the corresponding operands
come first and then operator can be placed.
Postfix Expression = Operand1 operand2 operator
Examples:
1) ab+
2) ab+cd-
3) ab+c/df+*

8. Prefix Expression
In prefix expression, there are no
parentheses used. All the corresponding operators
come first and then the operands are arranged.
Prefix Expression = Operator Operand1 Operand2
Examples:
1) +ab
2) *+ab-cd
3) */+abc+df

9. Conversion of Infix to Postfix Expressions:
Eg.: ((a-b)*(a+b))
S.No Input
Character
Stack Postfix Expressions
1. ( (
2. ( ((
3. a (( a
4. - ((- a
5. b ((- ab
6. ) ( ab-
7. * (* ab-
8. ( (*( ab-
9. a (*( ab-a
10. + (*(+ ab-a
11. b (*(+ ab-ab
12. ) (* ab-ab+
13. ) Empty ab-ab+*
The postfix expression is ab-ab+*

10. Conversion of Postfix to Prefix:
Eg.:ABCDE/*-F/G++
Prefix = Operator Operand1 Operand2
Step1: ABCDE/*-F/G++
Step2: ABC(/DE)*-F/G++
Step3: AB(*C/DE)-F/G++
Step4: A(-B*C/DE)F/G++
Step5: A(/-B*C/DEF)G++
Step6: A(+/-B*C/DEFG)+
Step7: +A+/-B*C/DEFG
+A+/-B*C/DEFG is the prefix expression.

11. Conversion of Postfix to Infix form:
Eg.:ABC(DE/*-F/G++
Infix = Operand1 Operator Operand2
Step1: ABCDE/*-F/G++
Step2: ABC/DE*-F/G++
Step3: AB(C*(D/E)-F/G++
Step4: A(-B(C*D/E)))F/G++
Step5: A(((B-(C(D/E)))/F)G++
Step6: A(((B-(C(D/E))/F+G)+
Step7: (A+(B-(C*(D/E)))/F)+G))
(A+(B-(C*(D/E)))/F)+G)) is the infix expression.

12. Evaluation of Expressions
Algorithm:
Add the right paranthesis.
Scan the expressions from left to right of each
element until the closed parenthesis is
encountered.
If operand is encountered, then Push to Stack.
If operator is encountered, then next two
elements from Stack is Poped.
Evaluate the expression with the operator .
E.g.(b*c).
Set the result to the Top of the Stack.
Exit.

13. Evaluation of Postfix expression
p=abc*/d+
Assume a=50, b=10, c=7, d=0
Steps Symbols Scanned Stack
1. (
2. 50{a} (,50
3. 10{b} (,50,10
4. 7{c} (,50,10,7
5. * (,50,70
6. / (,1.4
7. 2{d} (,1.4,2
8. + (,3.4
9. ) 3.4