Algebraic Expressions

An algebraic expression $X \ast Y$ is represented as a binary tree with:

• Root: operator $\ast$
• Left child: $X$
• Right child: $Y$

Unambiguous (unlike infix form without parentheses).

Forms

There are 3 common forms of algebraic expressions.

Infix form

The symbol is written in-between the operands. The form we usually use.

Example: $x*y$

Prefix form

Aka. Polish form. The symbol is written before the operands.

$x*y$’s prefix form is: $* x y$

Parentheses are not required. Start solving from right end.

Postfix form

Aka. reverse Polish form. The symbol is written after the operands. Used commonly when parsing algebraic expressions in calculators.

$x*y$’s prefix form is: $x y *$

Start solving from left end.