Is it possible to construct a tree of postfix or prefix form?

Question

Let I have some expression as 2*3/(2-1) +5*(4-1) . It is infix notation. Of course I can construct for this expression a tree that you can see on image. enter image description here

Then, let's write this expression in postfix and prefix forms. Postfix: 2 3 * 2 1 - / 5 4 1 - * + Prefix : + / * 2 3 - 2 1 * 5 - 4 1

And the question is: a tree for above expressions will be the same? If not,how to construct it?

Answer 1

And the question is: a tree for above expressions will be the same?

Yes, it's the same tree -- the different notations represent the same calculation.

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The different ways to write the expression correspond just to different traversals of the same tree:

• pre-order for prefix notation

(pre-order: F, B, A, D, C, E, G, I, H)

• in-order for infix notation

(in-order: A, B, C, D, E, F, G, H, I)

• post-order for postfix notation

(post-order: A, C, E, D, B, H, I, G, F)