Find whether a tree is a subtree of other

Question

There are two binary trees T1 and T2 which store character data, duplicates allowed.
How can I find whether T2 is a subtree of T1 ? .
T1 has millions of nodes and

Answer 1

I am not sure, whether my idea is correct. Nevertheless, for your persual.

1. Conduct a postorder walk in Tree 1 & Tree 2, call it P1 and P2.
2. Compare P1 & P2. If they are different. The tree is not subtree. Exit.
3. If they are same, or P1 contained in P2. You can decide which one is sub tree.