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:


I get these post-fix expressions:




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


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


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  • $\begingroup$ Are you aware of operator precedence and operator associativity? $\endgroup$ – Yuval Filmus Mar 26 at 15:35
  • $\begingroup$ Yes, I'm aware of these stuff:-) $\endgroup$ – user8718165 Mar 26 at 18:13
  • $\begingroup$ Every expression, whether infix or postfix, has a unique parse tree. The two parse trees should match for the two expressions to be considered the same. $\endgroup$ – Yuval Filmus Mar 26 at 18:48
  • $\begingroup$ Also known as syntax trees. See for example Wikipedia. This is a basic concept in context-free languages, which you might want to brush up on. $\endgroup$ – Yuval Filmus Mar 26 at 19:04

(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.

  • $\begingroup$ Thanks a lot but I don't get why should (a+b)-c be different from a+(b-c). I'm sure I'll get it if you could include an example of each case(int and float). $\endgroup$ – user8718165 Mar 26 at 18:31
  • $\begingroup$ Also could you please tell me why does that online conversion site not give an error on inputting ABDX/-+? Both the postfix expressions return the same infix. $\endgroup$ – user8718165 Mar 26 at 18:40

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