Programming Languages Lab $2$

Infix, Postfix and Prefix

While we use infix expressions in our day to day lives. Computers have

trouble understanding this format because they need to keep in mind rules

of operator precedence and also brackets. Prefix and Postfix expressions

are easier for a computer to understand and evaluate.

Infix Postfix and Prefix notations are three different but equivalent ways of

writing expressions. It is easiest to demonstrate the differences by looking

at examples of operators that take two operands.

Given two operands a and b and an operator $,$ the infix notation implies

that $$ will be placed in between a and b i$.$e a $$ b $.$ When the operator is

placed after both operands i$.$e ab $,$ it is called postfix notation. And when

the operator is placed before the operands i$.$e $$ a b$,$ the expression in

prefix notation.

Infix notation: X $+$ Y

Operators are written in$-$between their operands. This is the usual way we

write expressions. An expression such as A $*($ B $+$ C $)/$ D is usually taken to

mean something like: "First add B and C together, then multiply the result

by A$,$ then divide by D to give the final answer."

Postfix notation $($also known as "Reverse Polish notation"$)$: X Y $+$

Operators are written after their operands. The infix expression given

above is equivalent to A B C $+*$ D $/$

Prefix notation $($also known as "Polish notation"$)$: $+$ X Y

Operators are written before their operands. The expressions given above

are equivalent to $/*$ A $+$ B C D