Preorder and postorder do not uniquely define a tree.
In general, a single tree traversal does not uniquely define the
structure of the tree. For example, as we have seen, for both
the following trees, an inorder traversal yields [1,2,3,4,5,6].
4 3
/ \ / \
2 5 2 5
/ \ \ / / \
1 3 6 1 4 6
The same ambiguity is present for preorder and postorder
traversals. The preorder traversal for the first tree above is
[4,2,1,3,5,6]. Here is a different tree with the same preorder
traversal.
4
/ \
2 1
/ \
3 6
\
5
Similarly, we can easily construct another tree whose postorder
traversal [1,3,2,6,5,4] matches that of the first tree above.