Binary Tree Traversal Questions

I was given the preorder sequence --> * + / a b c - d e

I was told to draw a binary expression tree which I completed and received the following tree

Code:

---

                                              *
                                          /      \
                                        +          -
                                    /    \      /  \
                                  -      c    d    e
                                /  \
                              a      b

---

I was then asked two questions about the tree. Is this tree unique?

unique defined as --> A tree for a sequence is not unique if given that (here, preorder) sequence it is possible to generate a different tree

Do preorder traversal's generate unique trees? why or why not.


The same thing was asked about inorder traversals , but given the following sequence.

a - b * e + c + b
Pay attention to operator precedence, if applicable.

The expression tree I got was as follows

Code:

---

                                              +
                                          /      \
                                        +          b
                                    /    \   
                                  -      c 
                                /  \
                              a      *
                                    /    \
                                  b      e

---

Is this tree unique?

Do inorder sequences produce unique trees? why or why not.

I have no clue whether the trees are really unique, because I can find another tree that will generate the same value, but will not have the same preorder sequence.


Any input is well appreciated, THANK YOU.