Why is inorder and preorder traversal useful for creating an algorithm to decide if T2 is a subtree of T1

Question

I\'m looking at an interview book and the question is:

You have two very large binary trees: T1, with millions of nodes, and T2

Answer 1

Here is a counter-example to the method.

Consider the tree T1:

  B
 / \
A   D
   / \
  C   E
       \
        F

And the sub-tree T2:

  D
 / \
C   E

The relevant traversals are:

• T1 pre-order: BADCEF
• T2 pre-order: DCE
• T1 in-order: ABCDEF
• T2 in-order: CDE

While DCE is in BADCEF and CDE is in ABCDEF, T2 is not actually a sub-tree of T1. The author's definition of sub-tree must have been different or it was just a mistake.

Related question: Determine if a binary tree is subtree of another binary tree using pre-order and in-order strings