Question

I have a piece of code that converts an infix expression to an expression tree in memory. This works just fine. There’s just one small trouble. I just connect work out how to involve the unary operators correctly (the right associative ones).

With the following infix expression :

+1 + +2 - -3 - -4

I would expect an RPN of:

1+2++3-4--

Yet, none of the online infix-post converters I can find handle this example in the way I would expect. Does anyone have a clear explanation of handling right associative operators, specifically the binary ones that can be mistaken for the unary ones?

Edit/Clarification:
I would like to know how to deal with the unary operators during the translation from infix to postfix. Ie: recognizing the same ‘-‘ character for example as being unary instead of binary operator and thus a different precedence. I would think of using a state machine perhaps with two states but …?

Answer 1

Well, you need to determine if a given operator is binary/unary during the parsing stage. Once you do that, when you create the RPN, you can tag the operators as taking 2 or 1 arguments.

You could try using the Shunting Yard algorithm to do the parsing (and creation of RPN at the same time), which was designed to work with unary operators too.

In any case, if all you care about is unary + or -, you could just insert a 0 with brackets when you see a + or – that appears ‘unexpectedly’.

For instance

+1 + +2 - -3 - -4

You should be able to make a pass through it and convert to

(0+1) + (0+2) - (0-3) - (0-4)

Now you don’t need to worry about the unary + or – and can probably forget about tagging the operators with the number of arguments they take.