Multiple post-fix expressions for an in-fix expression Today I was learning to convert post-fix expressions to in-fix expressions and vice versa. What I want to know is whether a post-fix expression can have more than one infix representations.

For example, if I consider the following in-fix expression:

A+B-D/X


I get these post-fix expressions:

ABDX/-+


and

AB+DX/-


I didn't use the stack table method for solving these. I did these conceptually and both these expressions evaluate to 

A+B-D/X


post-fix expression. I even verified my result with this site and both the post-fix expressions evaluate to:

A+B-D/X
(A+b)-c and a+(b-c) are not the same. Not with integers (one expression might overflow while the other one doesn’t), not with floating-point numbers ( different rounding errors). 

Only the second postfix expression is correct.