2-3 Tree help

16. Consider a 2-3 tree. Given a key r, a split is performed by construct two trees Ti and T2, the first with all keys less than r, and the second with all keys more than x. Show how to perform a split efficiently. You may want to augment your tree with height information. (Think about the search path for x. This tells you how to split the original tree into a collection of trees, such that the union of some of them is Ti. This can be done by join operations. To get the optimal algorithm, you will need to carefully consider the running times of the respective joins.)