As a result of a splay, most of the nodes on the access path are moved halfway towards the root, while a couple of nodes on the path move down one level. This suggests using the sum over all nodes of the logarithm of each node's depth as a potential function.
a. What is the maximum value of the potential function?
b. What is the minimum value of the potential function?
c. The difference in the answers to parts (a) and (b) gives some indication that this potential function isn't too good. Show that a splaying operation could increase the potential by Θ(N/ logN).