正则表达式验证前缀，中缀和后缀表达式

Question

I need to create a program in C# that converts an Infix expression into Prefix and Postfix, Prefix expression into Postfix and Infix, Postfix expression into Infix and Prefix. This is not the problem though, the "processing part" of the program is already done.

What I need now is a regular expression to verify if the user input is an Infix, Prefix or Postfix expression, so depending on the input I call a different function to perform the conversions.

The input will always be:
For operands: capital single letters from A to Z
For operators: +, -, * and /

For the Infix expression I made this regular expression (which seems to be working fine):
"^(([AZ])(([+]|[-]|[*]|[/])([AZ]))*)$"

But I extinguished my ideas trying to make a regular expression for Prefix and Postfix expressions. I also found nothing on internet.

Could someone give me a light?

Answer 1

Unfortunately this isn't possible without recursive regex (which C# doesn't support). While (well-formed) infix notation can be matched with the simple regex [AZ](?:[*/+-][AZ])* , pre- and postfix notation don't follow such a simple pattern that they could be matched by non-recursive regex.

That said, a very simple way to determine if an expression uses pre-/postfix notation (without verifying its correctness) is to check whether the first/last character is an operator: ^[*/+-] would match a well-formed prefix expression and .*[*/+-]$ a well-formed postfix expression.