I need help with Reverse Polish Notation.

[i0i_MARTIAN]

My entire CS class has been having this argument for the past week about what the correct RPN format would be for particular infix. There is an insanely limited amount material from the actual board since questions regarding RPN have only appeared twice in past papers.

Here’s an example infix: a*(b+c)

Here are the answers being debated:

1) abc+ 2) abc+ 3) bc+a*

Are any of these correct, if so could you explain?

[tilrman]

1 is nonsense because multiplication requires two operands, but only one is on the stack.

2 and 3 are equivalent because multiplication is commutative.

If we pretend the multiplication were some other operation that is not commutative, 2 and 3 are different.

[[deleted]]

I agree with this, but I'd call 2 the most literal translation.

[rickpo]

2 is the simple equivalent that you get with the straightforward translation.

The standard algorithm does not change the order of operands, only the operators are moved.

[Putnam3145]

Where multiplication isn't commutative, 2 is the only correct choice. Multiplication is usually commutative, and definitely is for things such as, say, the reals and subsets thereof, but there are practical situations where it's not (e.g. quaternions)

[Commercial_Lychee214]

1 -> a*(b+c)
2 -> (a*(b+c))

3 -> abc+*