A-level Computing 2009/AQA/Problem Solving, Programming, Operating Systems, Databases and Networking/Problem Solving/Reverse Polish Notation

Backus-Naur Form (BNF) 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 thumb|600px|centre|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 Video link to Computerphile a Youtube channel: https://www.youtube.com/channel/UC9-y-6csu5WGm29I7JiwpnA Practice Questions Exercise: Infix to RPN Conversion. Convert x + y into RPN. x y + Convert (x + y)*z into RPN. x y + z * Convert 3 / (5 + y * x) into RPN. 3 5 y x * + / Exercise: RPN to Infix Conversion Convert x y * into infix. x * y Convert 5 y + z x 3 - * / into infix. (5 + y) / (z * (x - 3)) References