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1. Arithmetic Expression –
INFIX TO POSTFIX
SARASWATHI RAMALINGAM
SRI AKILANDESWARI WOMENS
COLLEGE – WANDIWASH.

2. Arithmetic Expression
• Arithmetic Expression contains
– Operators (+,-,*,/,%,() )
– Operands (a..z)
– Ex:- (a*b),(a+b)-c

3. Classification of Expression
– Depending upon the position of the
operators with respect to the position of
the operands.
– Infix
– Prefix
– Postfix

4. Classification of Expression
INFIX PREFIX POSTFIX
Operator In between the
operands
Operator before the
operands
Operator after the
operands
Infix notation Prefix notation(Polish
notation)
Postfix notation(Reverse
Polish notation)
A+B +AB AB+
A+B*C +A*BC ABC*+
(A+B)*(C-D) *+AB-CD AB+CD-*

5. INFIX TO POSTFIX
• Conversion of Expression
• Evaluation of Postfix Expression

6. Conversion of Expression
• Steps
– Initialize an empty stack.
– Read the token from Infix string one at a
time from left to right.

7. Conversion of Expression
– If the scanned character is an operand
add it to the Postfix string.
– If the scanned character is an operator
• if the stack is empty push the character to
stack.
• If the stack is not empty, compare the
precedence of the character with element on
top of the stack.

8. Conversion of Expression
– If the character is a left parentheses,
push it on to the stack.
– If the character is a right parentheses,
• Repeatedly pop the stack and add popped out
element in to the string until a left
parentheses is encountered.
• Remove the left parentheses from the stack
and ignore it.

9. Conversion of Expression
• When top Stack has higher precedence over
the scanned character pop the stack else
push the scanned character to stack.
– (Repeat the step until the operator in the stack
has higher precedence than the scanned
character)
• After all the characters are read and the
stack is not empty then pop the stack and
add the string.

10. Example
A+B
1.
SYMBOL SCANNED STACK POSTFIX EXPRESSION
A A

11. 2
SYMBOL SCANNED STACK POSTFIX EXPRESSION
A A
+ + A

12. 3
SYMBOL SCANNED STACK POSTFIX EXPRESSION
A A
+ + A
B + AB
AB+

13. Example
A+B*C
1.
SYMBOL SCANNED STACK POSTFIX EXPRESSION
A A

14. 2
SYMBOL SCANNED STACK POSTFIX EXPRESSION
A A
+ + A

15. 3
SYMBOL SCANNED STACK POSTFIX EXPRESSION
A A
+ + A
B + AB

16. 4
SYMBOL SCANNED STACK POSTFIX EXPRESSION
A A
+ + A
B + AB
* +* AB

17. 5
SYMBOL SCANNED STACK POSTFIX EXPRESSION
A A
+ + A
B + AB
* +* AB
C +* ABC
ABC*+