1. Department of Technical Education Andhra Pradesh
Name : B Vijaya Kumari
Designation : Lecturer
Branch : Computer Engineering
Institute : Smt.B.Seetha Polytechinic, Bhimavaram
Year/Semester : III SEM
Subject : DATA STRUCTURES THROUGTH C
Sub.Code : 9CM305
Topic : STACK
Duration : 50 Minutes
Subtopic : Conversion of Infix to Postfix
Teaching Aids : ppt, Animations, Photographs
Revised by : Bapuji naik
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2. Recap
In the last class we have discussed about Stack operations and applications of Stack
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3. Objective After the end of this class you would be able to know
Expression Notations
Infix, prefix, postfix expressions
Convert infix to postfix expression
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4. Expression Notations Expression can be represented in three ways
Infix Notation
Prefix Notation
Postfix Notation
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5. Expression Notations Contin…..
Infix Expression: The Operators are placed between the Operands
Example: A + B
A,B are Operands and + is Operator
+ is placed between A and B
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6. Expression Notations Infix Expression Uses Contin…..
These expressions are used in mathematical calculations.
Most commonly used notation
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7. Expression Notations Contin…..
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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8. Conversion of Infix to Postfix
Contin…..
Conversion of Infix to Postfix
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 Operands
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9. Conversion of Infix to Postfix
Contin…..
Conversion of Infix to Postfix
Examples of Infix to Prefix and corresponding expressions
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10. Convert Infix Expression to Postfix notation
Contin…..
Convert Infix Expression to Postfix notation
Conversion of Infix to Postfix
To convert Infix notation to Postfix the scan will be done character wise. From left to right
A character is read each and every time.
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11. Conversion of Infix to Postfix
Contin…..
Conversion of Infix to Postfix
Operator Precedence table
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12. Conversion of Infix to Postfix
Contin…..
Conversion of Infix to Postfix
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13. Conversion of Infix to Postfix
Contin…..
Conversion of Infix to Postfix
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14. Rules to convert Infix to Postfix Expression
Contin…..
Conversion of Infix to Postfix
Rules to convert Infix to Postfix Expression
The read character is an operand then put the operand into Postfix String.
The read character is left parentheses then push that on to the Stack.
The read character is an Operator then check the priorities of the operator.
(a) If the top of the stack is left parenthesis or the stack is empty, then push the operator on to the stack
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15. Conversion of Infix to Postfix
Contin…..
Conversion of Infix to Postfix
(b) If the top of the stack is an operator then check for priorities
If the priorities of the operator on the top of stack
is greater than the priority operator read OR
if the priority are same
Pop the top stack operator and put it in to postfix string and push the operator read on to the stack.
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16. Conversion of Infix to Postfix
Contin…..
Conversion of Infix to Postfix
If the priority of the read Operator is greater than the priority of the operator on top of the stack Push read operator on to the stack
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17. Conversion of Infix to Postfix
Contin…..
Conversion of Infix to Postfix
(c) If the read character is a right parenthesis pop the
operators from stack and put them into output till a left
parentheses is encountered
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18. Conversion of Infix to Postfix
Contin…..
Conversion of Infix to Postfix
If the character read is an end expression, then pop all the
elements from the stack and put them on to output string
Example:
Infix notation:
a (b c).
Postfix notation:
a b c + * + *
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19. Conversion of Infix to Postfix
Contin…..
Conversion of Infix to Postfix
Example to Convert Infix to Postfix using stack
a + (b*c)
Read character
Stack
Output a
Empty + ( +( b ab *
+(* c
abc )
abc*
abc*+
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20. Example how to Convert Infix to Postfix
Contin…..
Conversion of Infix to Postfix
Example how to Convert Infix to Postfix
Infix expression: a + ( b c ) *
empty stack
Push + * ( ( + + +
Postfix expression:
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21. Example how to Convert Infix to Postfix
Contin…..
Conversion of Infix to Postfix
Example how to Convert Infix to Postfix
Infix expression: a + ( b c ) *
Push ) * ( ( + +
Postfix expression: a b c
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22. Conversion of Infix to Postfix
Contin…..
Conversion of Infix to Postfix
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23. Conversion of Infix to Postfix
Contin…..
Conversion of Infix to Postfix
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24. Conversion of Infix to Postfix
Contin…..
Conversion of Infix to Postfix
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25. Examples to convert Infix to Postfix expression
Contin…..
Conversion of Infix to Postfix
Examples to convert Infix to Postfix expression
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26. Summary We have discussed about Infix,Postfix,Prefix Expressions
Algorithm for converting an Infix expression to Postfix notation
Examples for conversion of Infix to Postfix Expression
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27. Quiz (a) a + b 1.Infix expression is Cont..... (b) + ab (c) ab +
(d) both a & b
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28. 2.Which of the following has highest precedence?
Cont.....
Quiz
2.Which of the following has highest precedence?
(a) + , -
(b) * . /
(c) both a & b
(d) none
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29. Quiz 3. Postfix expression is Cont..... (a) a + b (b) + ab (c) ab +
(d) both a & b
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30. 4. Reverse polish notation is also called as
Cont.....
Quiz
4. Reverse polish notation is also called as
(a) Infix
(b) prefix
(c) postfix
(d) none
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31. Quiz 5. Prefix expression is Cont..... (a) a + b (b) + ab (c) ab +
(d) both a & b
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32. Polish notation is also called as
Cont.....
Quiz
Polish notation is also called as
(a) Infix
(b) prefix
(c) postfix
(d) none
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33. Frequently Asked Questions
Explain how to convert an infix expression to postfix expression?
Convert the following infix expression to postfix expression?
(a) (a + b*c) / (c - d)
(b) a/ (b + c)+ d * (e - f)
Explain an algorithm for converting to infix postfix?
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