Department of Technical Education
Andhra Pradesh
Name
Designation
Branch
Institute
Year/Semester
Subject
Sub.Code
Topic
Duration
Subtopic
Teaching aids
Revised by
: B.Vijaya Kumari
: Lecturer
: Computer Engineering
: Smt.B.Seetha Polytechinic,
Bhimavaram
: III SEM
: Data Structures THROUGTH C
: 9CM305
: Stacks & Queues
: 50 Mins
: Evaluation of Postfix Expression.
: ppt, Animations, Photographs
: Bapuji naik
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Recap
• Last class we have discussed about and Infix, Prefix, Postfix
expressions and conversion of Infix to Postfix notation
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Objective
On completion of this class, you would be able to learn
• Evaluation of Postfix expression
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Recap
• Infix Expression: The Operators are placed between
the Operands
• Example: A + B
• A,B are Operands and + is Operator
• + is placed between A&B
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Contd..
Recap
Postfix Expression: The Operator s are placed after the Operands.
also known as reverse Polish notation
• Example: AB+
• Here A&B are Operands and + is an Operator
• + is placed after the Operands
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Contd..
Recap
• Prefix Expression: The Operators are placed before the
Operands is known as Prefix Expression. And also known as
Polish notation
• Example: + AB
Here A&B are Operands and + is an Operator
+ is placed before the Operand
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Contd..
Recap
Evaluation of postfix expression
• Postfix form can be evaluated by reading the expression from
left to right.
• The operands are stored in a Stack.
• The arithmetic expressions to evaluate the Postfix expression
using Stack.
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Algorithm to Evaluate Postfix Expression
• Step 1: Start
• Step 2: Scanning the Postfix expression from left to right
when an operand is encountered then push the value
of operand into Stack.
• Step 3: The Scanned character is an operator then pop the
two operands from top of the Stack.
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Algorithm to Evaluate Postfix Expression
• Step 4: Perform the operation on the operands
• Step 5: The result is pushed into the Stack.
• Step 6: This process is continued until the Postfix expression is
completed.
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Example for Evaluation of Postfix Expression
Example :
AB+C*. where A=7,B=4,C=2.
• Step 1:
• Step 2:
Start
Scanning the Postfix expression AB+C* from left to
right first an operand “A” is encountered then push
the value of “A” i.e. 7 onto the Stack.
Empty
Push A=7
7
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Example for Evaluation of Postfix Expression
Contd.,
• Step 3: The scanned character is an operand then push “B”
value into the Stack.
• Step 4: The scanned character is an arithmetic operator i.e “+”.
pop A,B values into the Stack and perform an operation
using that operator. i.e. 7+4=11.
Push B=4
4
7
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Example for Evaluation of Postfix Expression
Contd.,
• Step 5: The result will be pushed into the Stack.
• Step 6: Next the scanned character is an operand i.e., C then
push C value into the Stack.
• Step7: Next the scanned character is an operator i.e “+”
then pop the values into the stack and perform
the operation.
Push result=11
Push c=2
2
11
11
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Example for Evaluation of Postfix Expression
Contd.,
• Step 8: The operation “*” is performed on the two operands.
i.e. 11*2=22.
• Step 9: The result will be pushed into the Stack.
• Step 10: Pop the result from the stack
The process is completed.
• Step 11: Stop.
Push c=22
Result :11*2=22
22
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Example for Evaluation of Postfix Expression
Items
Stack
7
7
4
7 4
+
11
2
11 2
*
Contd.,
22
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Contd.,
Examples on Evaluation of Postfix Expression.
1
The stack during the evaluation of the postfix expression
a b / when a is 2 and b is 4
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2
The stack during the evaluation of the postfix expression a b +
c / when a is 2, b is 4 and c is 3
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3
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Contd.,
Quiz
1.A+B+C is an
a) Infix Expression
b) Prefix Expression
c) Postfix Expression
d) None
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Contd.,
Quiz
2. When an operator enconntered while evaluating a
postfix expression
(a) Push the operands into the stack
(b) Pop the operands from the stack
(c) Both a&b
(d) None
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Contd.,
Quiz
3. Postfix expression means
a) The operators are placed between operands
b) The operators are placed after the operands
c) The operators are placed before the operands
d) Both b&c
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Contd.,
Quiz
4.Prefix expression means
a) The operators are placed between operands
b) The operators are placed after the operands
c) The operators are placed before the operands
d) Both b&c
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Contd.,
Quiz
5.+AB is a
a) Infix Expression
b) Prefix Expression
c) Postfix Expression
d) None
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Contd.,
Quiz
6.AB+C* is a
a) Infix Expression
b) Prefix Expression
c) Postfix Expression
d) None
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Contd.,
Quiz
7.Infix expression means
a) The operators are placed between operands
b) The operators are placed after the operands
c) The operators are placed before the operands
d) Both b&c
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Frequently Asked Questions
• Explain how to evaluate a postfix expression
• For the values of a=5, b=3, c=4 &d=2;
Evaluate the following postfix expression
ab-cd*/
• Write an algorithm to evaluate a postfix expression
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