# Strict-Binary Tree - Same Post-order & Pre-order sequences?

I'm going through some past exam papers for my course and I'm having trouble completing this one question.

It is as follows: "Draw a strict binary tree with seven nodes that has the same pre-order and post-order traversal sequence".

Is this actually possible? Wouldn't I need to visit the root node before anything else for both sequences, that isn't possible with post-order traversal in a strict binary tree right? Unless the tree consisted of a single node?

I assume I'm missing something obvious. Post-order = LRN, Pre-order = NLR.

• Are you allowed to duplicate node labels? – Raphael Apr 1 '17 at 7:37

• @YuvalFilmus The claim here is that $\operatorname{pre}(T) = \operatorname{post}(T)$ if and only if all labels of $T$ are the same. That is a valid statement -- the question is if it is true. If it is, it does answer the question: take any tree (structure) and label every node $1$. (In fact, that construction answers the question even if the reverse direction of the claim is false.) – Raphael Apr 1 '17 at 7:37