So the question is to convert the following expression to postfix:


The answer I get when I calculate is: ab+pq+^rs*t*^

But the answer is given to be ab+pq+rs*t*^^

I assume that the step when you need to push second '^' into stack when there is already a '^' in the stack is where I went wrong (I pop out the '^' before pushing). Shouldn't we pop out the first '^' as they are of equal precedence ? Or is it an exception to '^' operator ?

  • $\begingroup$ Welcome to Computer Science! The critical information is what is your "^" operator. Does it mean bit-xor or raising to a power? It would be nice to provide a url or reference to tell us the context. $\endgroup$ – John L. Nov 3 '18 at 17:52
  • $\begingroup$ Thanks! It is an exponent operator. And regarding the reference, it was a question in a small online quiz related to stacks. $\endgroup$ – Debasish Das Nov 3 '18 at 19:02

There is a sort of an exception to '^', the exponentiation operator since it is right associative. That is, $a^{b^c}$ means $a^{\left({b^c}\right)}$ instead of $\left(a^b\right)^c$. That is, (a+b)^(p+q)^(r*s*t) means (a+b)^((p+q)^(r*s*t)) instead of ((a+b)^(p+q))^(r*s*t).

When you reach the first ^ while evaluating postfix expression ab+pq+rs*t*^^, you will pop out the result of rs*t* and the result of pq+. You get the expected exponentiation as expected.

  • $\begingroup$ The use of extra brackets made it all clear. Thanks a lot ! $\endgroup$ – Debasish Das Nov 6 '18 at 10:22
  • $\begingroup$ You are welcome! Please consider accepting my answer. (Thanks in word without upvote or acceptance is more like the antithesis of thanks on StackExchange.) $\endgroup$ – John L. Nov 10 '18 at 16:49
  • $\begingroup$ I actually upvoted (since I have less than 15 reputation, it doesn't show up) $\endgroup$ – Debasish Das Nov 11 '18 at 17:03
  • $\begingroup$ I see. I just upvoted this nice question of yours so that you are nearer to the privilege of upvoting. $\endgroup$ – John L. Nov 11 '18 at 18:33

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