DATA STRUCTURE
MSc.IT Ali Abdul Karem Habib
STACK APPLICATIONS


Web browser: stores the addresses of recently
visited sites on a stack. Each time a user visits a new
site, the address of the site is pushed into the stack of
addresses. Use the back button the user can pop pack
to previously visited sites! .
Text editors: powerful text editors keep text changes
in a stack. The user can use the undo mechanism to
cancel recent editing operations .
ARITHMETIC EXPRESSION

An arithmetic expression is one which is
evaluated by performing a sequence of arithmetic
operations to obtain a numeric value.

Levels of Precedence for the usual five binary
operations on arithmetic operation Q .

Highest: Exponentiation (^)

Next Highest: Multiplication (*)and division (/)

Lowest: Addition (+) and subtraction (-)
PREFIX, POSTFIX & INFIX NOTATION

Infix : the operator is placed between operands.
Example: (A+B)*C

parentheses necessary
Prefix: the operator is placed before the operands
Example: *+ABC

Postfix ( Reveres polish notation): the operator is
placed after the operands .
Example: AB+C*
TRANSFORMING INFIX EXPRESSION INTO PREFIX
EXPRESSION
(A+B) – (C*D)
 Step 1 : +AB
 Step2 : *CD



+AB-*CB
Prefix :- -+AB*CB
TRANSFORMING INFIX EXPRESSION INTO POSTFIX
EXPRESSION
(A+B) – (C*D)
 Step 1 : AB+
Step 2 : CD*

AB+-CD*
Postfix : AB+CD*-
TRANSFORM PREFIX TO INFIX :
+/*A B C D
 Note : We will Start the tack operator from the
right and the operands from the left .
 Step 1 : First 2 Operands from the left and first
operator from the right .
 +/(A*B)CD

o Step2 : +((A*B)/C)D
o Step3 :
((A*B)/C)+D
Infix Expression
TRANSFORM POSTFIX TO INFIX

ABC+–

Note :- We will tack the operator from the left and 2
operands from the left also .

Step 1 : (A+B)C-

Step2 : (A+B)- C
EXAMPLE :- INFIX : (7+8)-((6*3)/2)) TRANSFORMED
(78+63*2/-)
Steps
Input
Stack
1
7
7
2
8
7
3
+ Pop ( 8 and 7 ) push 15
result
4
6
15
6
5
3
15
6
6
* Pop ( 6 and 3 ) push 15
result
18
7
2
15
18
15
9
/ pop ( 18
result
8
2 ) push
- Pop ( 15 and 9 )
push result
6
TO
POSTFIX
8
3
2
Final Result in Stack
ASSIGNMENT -41)Convert these INFIX to PREFIX and POSTFIX :
A/B–C/D
 (A + B) ^ 3 – C * D
 A ^ (B + C)
 2)Convert these PREFIX to INFIX and POSTFIX :
+–/ABC^DE
–+DE/XY
^+23–CD
 3)Convert these POSTFIX to INFIX and PREFIX :
ABC+–
GH+IJ/*
AB^CD+ –
