Can the pre-order traversal of two different trees be the same even though they are different?
Tree Examples (image):

     A:                 B:
     ‾‾                 ‾‾
     1                  1
    /                  / \
   2                  2   3
  /  
 3   


This is an example that fits your scenario, Tree A root׳s value is 1, having a left child with value 2, and his left child has also a left child with value 3.

Tree B root׳s value is 1, having a left child with value 2 and a right child with value 3.

In both cases the Preorder traversal is 1->2->3.