Question

Is there any way to interpret Reverse Polish Notation into ‘normal’ mathematical notation when using either C++ or C#? I work for an engineering firm, so they use RPN occasionally and we need a way to convert it. Any suggestions?

Answer 1

Yes. Think of how a RPN calculator works. Now, instead of calculating the value, instead you add the operation to the tree. So, for example, 2 3 4 + *, when you get to the +, then rather than putting 7 on the stack, you put (+ 3 4) on the stack. And similarly when you get to the * (your stack will look like 2 (+ 3 4) * at that stage), it becomes (* 2 (+ 3 4)).

This is prefix notation, which you then have to convert to infix. Traverse the tree left-to-right, depth first. For each ‘inner level’, if the precedence of the operator is lower, you will have to place the operation in brackets. Here, then, you will say, 2 * (3 + 4), because the + has lower precedence than *.

Hope this helps!

Edit: There’s a subtlety (apart from not considering unary operations in the above): I assumed left-associative operators. For right-associative (e.g., **), then you get different results for 2 3 4 ** ** ⇒ (** 2 (** 3 4)) versus 2 3 ** 4 ** ⇒ (** (** 2 3) 4).

When reconstructing infix from the tree, both cases show that the precedence doesn’t require bracketing, but in reality the latter case needs to be bracketed ((2 ** 3) ** 4). So, for right-associative operators, the left-hand branch needs to be higher-precedence (instead of higher-or-equal) to avoid bracketing.

Also, further thoughts are that you need brackets for the right-hand branch of - and / operators too.