Problem Solving: Reverse Polish Notation

Reverse Polish notation (otherwise known as post-fix, RPN for short) is a way of representing mathematical equations. The notation is used because the format that the equation is in is easier for machines to interpret rather than the notation we are used to, infix notation, where the operator is in between the numbers. The equation can be complex or simple. RPN doesnt require brackets as the equations are layed out in such a format that it isn't required for machines to understand.

The name RPN is named after Jan Łukasiewicz, a Polish logician who invented Polish notation (prefix notation) some time in the 1920s.

Reverse Polish Notation

Reverse polish notation should be ordered like this:

<FirstNumber> <SecondNumber> <Operation>

Rather than the normal convention(infix) of:

<FirstNumber> <Operation> <SecondNumber>

Examples

Examples of equivalent equations

PostFix	Infix	Answer
3 4 +	3 + 4	7
3 5 6 + *	(5 + 6) * 3	33
2 4 / 5 6 - *	(2/4)*(5-6)	-0.5
2 3 ↑	2³	8

Implementation as a Stack

An example of how a stack can be used to compute reverse polish notation.

YouTube Video Example

A video example can be seen here from Computerphile on Youtube: https://www.youtube.com/watch?v=7ha78yWRDlE

Practice Questions

Exercise: Infix to RPN Conversion. Convert x + y into RPN. Answer: x y + Convert (x + y)*z into RPN. Answer: x y + z * Convert 3 / (5 + y * x) into RPN. Answer: 3 5 y x * + /

Exercise: RPN to Infix Conversion Convert x y * into infix. Answer: x * y Convert 5 y + z x 3 - * / into infix. Answer: (5 + y) / (z * (x - 3))