INFIX EXPRESSION TO POSTFIX EXPRESSION

CONVERSION OF INFIX EXPRESSION TO POSTFIX EXPRESSION

The conventional method of representing an arithmetic expression is known as infix because the operand is placed in between the operands. If the operator is placed before the operands then this notation is called prefix or Polish notation. If the operator is placed after the operand then this notation is called postfix or reverse polish notation. So now we have three ways to represent an arithmetic expression.
Infix:   A+B

Prefix:   +AB

Postfix:   AB+


Now, let us see how to convert an infix expression to postfix expression. The rules of parenthesis and precedence would be followed in the following way. If there are parenthesis in the expression, then the portion inside the parenthesis will be converted first. After this the operations are converted according to their precedence. (* and / first, followed by + and -). If there are operators of equal precedence then the operator which is on the left is converted first. In order to understand this with an example, let us solve an example from June 2014, Paper III, Question No. 41.
JUNE 2014 - PAPER III - Q.No 41
41. The reverse polish notation equivalent to the infix expression

((A + B) * C + D) / (E + F + G)

(A) A B + C * D + E F + G + /

(B) A B + C D * + E F + G + /

(C) A B + C * D + E F G + +/

(D) A B + C * D + E + F G + /


Ans:-A
Explanation:-

First, always the expression given within parenthesis is converted first. Since there are 2 expressions with the parenthesis, I am going with the expression (E + F + G) first, although the order does not matter.

In the expression (E + F + G), there are 3 operands E,F and G and two operators, both being +. Since both the operators are the same, the expression is going to be evaluated from left to right. So E + F is considered first and converted into postfix form which is EF+. So, the expression becomes,

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

Any expression converted into postfix form is going to be written in square brackets.

( ( A + B ) * C + D) / [ E F + G + ]
. Here EF+ is one operand, G is another operand and + is the operator.

The next expression to be converted into postfix is ( A + B).

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

Now, the expression which is enclosed in parenthesis is evaluated and so, we get

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

[ A B + C * D + ] / [ E F + G + ]

[ A B + C * D + ] [ E F + G + ] /

So, the final postfix expression is A B + C * D + E F + G + /. This answer is available in option A. So option A is the correct answer.