Concatenating red-black trees

Question

The OCaml standard library has a wonderful Set implementation that uses a very efficient divide-and-conquer algorithm to compute the union of two sets.

Answer 1

Can do better than O(log^2(n)) when concatenating and not augmenting the tree with height information in each node. You can concatenate in 2* [log(n1) + log(n2)] where n1 and n2 represent the number of nodes in the trees you are concatenating. After you compute the height in O(log(n)), use the Balance information in each node when going down the tree to find the right concatenation point!