Work Note 4, DM803, fall 2016

Exercises September 26

1. Use illustrations to go through the recursive method for the restructuring of a subtree of a Scapegoat tree which is used in Section 6.1, and make it clear which references must be maintained during the process. You should basically make a correctness proof drawings.
2. In Scapegoat trees we often need to know the sizes of subtrees. Instead of computing these, we could consider storing these values in the nodes. Consider the pros & cons of this.
3. One could also register the potential of a node with that node. What could that be used for?
4. Make an algorithmic sketch of how the insertion procedure should be coded. Note that there are no parents pointers. Assume that you have the following procedures available: restructure(T) restructures the subtree T and count(T) counts the nodes in the subtree T.
5. You can ask questions regarding skip lists and scapegoat trees implementations in the light of the first obligatory assignment.

Lecture September 29

• Disjoint Sets [K90].