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 T2 has hundreds of nodes.

Answer 1

Traverse T1. If the current node is equal to the root node of T2, traverse both of the trees (T2 and the current subtree of T1) at the same time. Compare the current node. If they are always equal, T2 is a subtree of T1.

Answer 2

I suggest an algorithm, that uses preprocessing:

1) Pre-process the T1 tree, keeping the list of all possible subtree roots (the cache list will have a millions of entries);

2) Sort the cached list of roots by the descending order of data, kept in root. You may choose more elegant sorting function, for example, parse a character tree into string.

3) Use binary search to locate the necessary sub-tree. You may quickly reject subtrees, with the number of nodes, not equal to the T2 number of nodes (or with the different depth).

Note that steps 1) and 2) must be done only once, then you can test many sub-tree candidates, using the same preprocessed result.