Conversion of Infix to Postfix
Infix to Postfix
expression
Dr B R Ambedkar National Institute of Technology, Jalandhar
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INFIX TO POSTFIX CONVERSION IN C++, Study notes of Data Structures and Algorithms
sHSqhsjKdawjidada5wihow to convert from Infix expression to postfix expression (with c++ code).
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2018/2019
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Conversion of
Infix to Postfix
Infix to Postfix
expression
Dr B R Ambedkar National Institute of Technology, Jalandhar
Infix Notation
Postfix Notation
Operator Precedence
Infix to Postfix Conversion Algorithm
Example
C++ Code for Infix to Postfix Conversion
Conclusion
Contents
Used to represent algebraic expressions
This notation is easier to parse for a machine
Characterized by placement of operators after the operand
Example :
ABC*+
ABC+*D/E-
Postfix Notation
Operator Precedence
Token Operator Precedence Associativity
()
[]
.
Function call
Array element
Structure element
17 Left to Right
++
--
Increment
decrement
16 Left to Right
++
--
!
-+
Sizeof
Increment
Decrement
Logical not
Unary minus,plus
Size(in bytes)
15 Right to left
type Type cast 14 Right to Left
- / % Multiplicative 13 Left to Right
- Binary sum and
diff
12 Left to Right
<< >> shift 11 Left to Right
Infix to Postfix Conversion Algorithm
Step 1: Scan the infix expression from left to right for
tokens(operators, operands and parenthesis).
Step 2: If the token is operand append it in postfix expression
Step 3: If the token is a left parenthesis โ(โ, push it in the stack
Infix to Postfix Conversion
Algorithm(continued)
Step 4: If token is an operator,
Pop all operators which are of higher or equal
precedence then the incoming token(in same order)
and append them to output expression
After popping out all such operators, push new token
on the stack.
Infix to Postfix Conversion
Algorithm(continued)
Step 6: After all tokens of infix expression have been scanned.
Pop all elements from stack and append them to
output expression
Step 7: Output expression obtained is the required Postfix
expression
Example
Let Infix expression be : A*(B+C)/D โ E
Stage 1: Initially stack is empty
Scan the infix expression from left to right
Infix Notation :
A*(B+C)/D โ E
Postfix Notation :
STACK
top NULL
Example (continued)
Stage 3 : Next token is operator * , Push it into the stack
Infix Notation :
(B+C)/D โ E
Postfix Notation :
A
STACK
top
Example (continued)
Stage 4: Next token is left parenthesis (, Push it into the stack
Infix Notation :
B+C)/D โ E
Postfix Notation :
A
STACK
top
Example (continued)
Stage 6: Next token is operator +,
We consider the outgoing precedence of top element of
stack,(
Outgoing precedence of ( is least, so + is pushed into the
stack
Infix Notation :
C)/D โ E
Postfix Notation :
AB
STACK
top
Example (continued)
Stage 7: Next token is operand C, operands are appended to output
expression as it is
Infix Notation :
)/D โ E
Postfix Notation :
ABC
STACK
top
Example (continued)
Stage 9: Next token is operator /,
We consider the outgoing precedence of top element of
stack,*
Outgoing precedence of * is same as /,
So, pop * and push / into the stack
Infix Notation :
D โ E
Postfix Notation :
ABC+*
STACK
top
Example (continued)
Stage 10: Next token is operand D, operands are appended to
output expression as it is
Infix Notation :
โ E
Postfix Notation :
ABC+*D
STACK
top