Question

Describe a binary tree T for which the pre-order and post-order traversals result in precisely the same ordering of T’s nodes. (That is, pre-order-traverse(T) = post-order-traverse(T).)

Answer 1

The only binary tree for which the pre-order and post-order are the same is a binary tree which only contains the root node. Thus, the binary tree looks like this:

There are no children to the root node, it is precisely the only node in the tree.

To see why this is the only tree for which pre-order and post-order is the same, argue as follows. Let there be a child of the root node. When running pre-order traversal, the root node will be visited first and then its children will be traversed. In post-order, the children will be traversed first and then the root node. Therefore, if there is a child of the root, then the pre-order and post-order traversal have to be different.

Comment in case of any doubts.