Removing duplicate subtrees from binary tree

Question

I have to design an algorithm under the additional homework. This algorithm have to compress binary tree by transforming it into DAG by removing repetitive subtrees and redirect

Answer 1

This is a problem commonly solved to do common sub-expression elimination in programming languages.

The approach is as follows (and is easily generalized to more than 2 children in a node):

Algorithm (Assumes mutable tree structure; You can easily build a new tree along the way):

MakeDAG(tree):

    HASH = a new hash-table-based dictionary

    foreach subtree NODE in the tree // traverse this however you like

        if NODE is in HASH
            replace NODE with HASH[NODE]
        else
            HASH[NODE] = N // insert the current node, N, in the dictionary

To compute the hash code for a node, you need to recursively compute the hash nodes until you reach the leaves of the tree.

Simply calculating these hash codes naively will bump up your runtime to O(n^2).

It is crucial that you store the results on your way down the tree to avoid repeated recursive calls and to improve the runtime to O(n).