PPTS FOR CLASS XII -STACK USING LIST

1. Data structures 11-Stacks
using Lists-->BY BABY PATHAK
JNV KHAIRTHAL,ALWAR

2. Data structure
•The term refers to a data collection with
well defined operations and
behaviour or properties.

3. Stack
• It is a linear data structure implemented in LIFO
manner.
• LIFO-->LAST IN,FIRST OUT
• Insertions and deletions are restricted to occur only
at one end-stack's top.
• Stack is a dynamic structure.
• Dynamics means it grows with increase in number of

4. PUSH FUNCTION
• Top = none
40
18
40
top
Push 40 PUSH 18

5. POP OPERATION
18
40
TOP
Fig: Initial Stack
40
TOP
Click to add text
POP 1 ELEMENT

6. SOME TERMS RELATED TO STACK
Peek: refers to inspecting the value at the stack's top without
removing it.Also referred to as inspection.
Overflow:This is an error.It occurs when we try to push on a stack
which is already full.
Underflow: This error occurs when one tries to pop/delete item
from an empty stack.

7. Example of a stack
• Ques: Given a stack of capacity 4 which is initially empty,draw
pictures of the stack after each of the following stacks.Initially the
Stack is empty.
• (I) Stack is empty

8. Push a
a
Top = 0

9. Push b
a b
Top = 1

10. Push c
a b c
Top = 2

11. pop
a b
Top = 1

12. Push d
a b d
Top = 2

13. pop
a b
Top = 1

15. POLISH STRINGS
• Polish strings ,named after a Polish mathematician ,Jan Lukaiewicz,
refers to the notation in which the operator symbol is placed either
before its operands or after its operands.

16. Infix Notation Prefix notation postfix notation
A+B +AB AB+
(A-C)*B *-ACB AC-B*
A+(B*C) +A*BC ABC*+
(A+(B*C))/(C-(D*B) /+A*BC-C*DB ABC*+ CDB*-/

17. HOW TO
CONVERT AN
INFIX
EXPRESSION
TO POST FIX
EXPRESSION
We follow an evaluation order while converting an
infix expression to postfix expression .Evaluation
order is
1 . Brackets or Parenthesis
2. Exponentiation
3. Multiplication or Division
4. Addition or Subtraction

18. What if operators
of the same
priority are in
one expression
The operators with the
same priority are evaluated
from left to right.

19. Ways to
convert an infix
expression to
postfix
expression
1. Converting
Manually
01
2.Converting
using Stack
02

20. Steps for
Manual
Conversion
Determine
Determine the
actual evaluation
order by inserting
braces.
Convert
convert the
expression in the
innermost braces
into postfix
notation by
putting the
operator after the
operands.
Repeat
Repeat
step 2.until entire
expression is
converted
into post fix
notation.

21. Convert (A+B)*C/D into post fix expression
• Step1: Determine the actual evaluation order by inserting braces,
• So.. if we go from left to right ..after (A+B) evaluation(why A+B evaluated
first??.....because they are in parenthesis.
• So .after A+B EVALUATION ,* should be evaluated..
• Therefore expression now is
• ((A+B)*C)/D

22. ((A+B)*C)/D...SO NOW CONVERT IT INTO POST
FIX
• STEP1: evaluate innermost brackets first..
• So now it is: (AB+*C)/D
• NOW evaluate next level parenthesis
• AB+C*/D
• Now evaluate the last operator left
• AB+C*D/

23. Q.2 Convert
((A+B)*C/D+E^F
)/G INTO POST
FIX
INSERT PARENTHESIS
1. (A+B)*C/D+(E^F)/G
2.((A+B)*C)/D+(E^F)/G
3.(((A+B)*C)/D)+(E^F)/G
4.((((A+B)*C)/D)+(E^F))/G

24. ((((A+B)*C)/D)+(E^F))/G...NOW
CONVERT INTO POSTFIX
EVALUATE INNERMOST BRACES FIRST.
(((AB+*C)/D)+(E^F))/G
((AB+C*/D)+(E^F))/G
(AB+C*D/+(E^F))/G
(AB+C*D/EF^+)/G
AB+C*D/EF^+G/

25. Convert to
postfix: A*(B+(C+D)*(E+F)/
G)*H

26. EVALUATE
A+[(B+C)+(D+E)*F]/G

27. EVALUATE NOT A OR NOT B AND NOT C
• In logical expression, preference of NOT is highest ,then comes the
preference of AND....OR has the least precedence
• ((NOT A) OR ((NOT B) AND (NOT C)))
• FIRST NOT'S WILL BE EVALUATED...
• THEN AND WILL BE EVALUATED
• AND THEN OR WILL BE EVALUATED

28. INFIX TO POSTFIX CONVERSION USING STACK

30. Evaluation of Postfix
expression using
Stacks

31. The steps are:
Repeat Repeat it till the end of the expression
Push back Push back the result of the evaluation.
Pop Pop the two operands from the stack,if the element is a
binary operator..In case of Unary operator,pop only one element.
Push Push the element in the stack if it is an operand.
Read Read the expression from left to right;

33. Evaluate: true false true NOT false true OR NOT
AND OR AND
Read from left to right.
I. 'true' is operand; pushed into
stack
TRUE

34. II. 'false' is operand; pushed into stack
FALSE
TRUE

35. III. 'true' is operand;
pushed into stack
true
false
true

36. IV.'NOT' is an Unary
Operator
• Evaluate one operand I.e.
True...NOT(TRUE) = FALSE. Push the result
'FALSE' into the stack
FALSE
FALSE
TRUE

37. V. 'FALSE' is
operand; pushed
FALSE
FALSE
FALSE
TRUE

38. VI. 'TRUE' is
operand,
pushed Stack
• ….
true
false
false
false
true

39. VII. 'OR' is operator.
• Push two operands I.e. true, FALSE.. Evaluate
false OR true = true.
• Push true into the stack
TRUE
FALSE
FALSE
TRUE

40. VIII. 'NOT' is unary
operator
• POP ONE OPERAND...NOT(TRUE) =
FALSE
• PUSH FALSE ,INTO THE STACK
FALSE
FALSE
FALSE
TRUE

41. IX. AND IS OPERATOR
• POP TWO OPERANDS...false AND false =
false
• PUSH result 'FALSE' into the stack
false
false

42. x. 'OR' is
operator. Pop
two operands
• False OR false = False.
• Push the result False onto the
stack
false
true

43. XI.'AND' is operator
• POP two operands I.e.
false,true
• True AND false = false..
• Push result back on STACK
FALSE

44. FINALLY....
NO MORE ELEMENTS POP FROM STACK,THEREFORE ,THE
RESULT IS'FALSE'

45. EVALUATE 562+*12 4/- in tabular form..
showing stack status after every step.
step Input symbol/element Stack Intermediate calculations
1, 5 PUSH 5
2. 6 PUSH 5,6
3. 2 PUSH 5,6,2
4. + POP(2 ELEMENTS) &
evaluate
5. 6+2 = 8
5 Result pushed.. push 8 5,8
6. * Pop(2 elements) &
evaluate
# empty 5*8 = 40
7. Push result(40) 40
8. 12 push 40,12
9. 4 push 40,12,4

46. Convert (TRUE and FALSE) or not(FALSE or
TRUE)
STEP SYMBOL STACK POSTFIX
EXPRESSION
DESCRIPTION
0. [
1. ( [( PUSH (
2. TRUE [( TRUE
3. and [(and TRUE PUSH and
4. FALSE [(and TRUE FALSE
5. ) [ TRUE FALSE and POP and
6. or [or TRUE FALSE and PUSH or
7. not [or not TRUE FALSE and
8. ( [or not( TRUE FALSE and
9. FALSE [or not( TRUE FALSE and
FALSE
10. or [or not(or TRUE FALSE

47. Evaluate 30,5,2^,12,6,/,+,-
step Input symbol/element stack Intemediate calculation
1 (
2. 30..push (,30
3. 5..push (,30,5
4. 2...push (,30,5,2
5. ^ ...pop two operands (30, 5^2=25..push 25
6. (30,25
7. 12..push on stack (30,25,12
8. 6...push (30,25,12,6
9. /..pop two operands (30,25 12/6 = 2..push 2
10. (30,25,2
11. +...pop two operands (30 25+2 = 27 push 27
12 (30,27