Prepare an implementation of splay trees that uses top-down splaying as described in Exercise C-11.52. Perform extensive experimental studies to compare its performance to the standard bottom-up splaying implemented in this chapter.

Exercise C-11.52

The standard splaying step requires two passes, one downward pass to find the node x to splay, followed by an upward pass to splay the node x. Describe a method for splaying and searching for x in one downward pass. Each substep now requires that you consider the next two nodes in the path down to x, with a possible zig substep performed at the end. Describe how to perform the zig-zig, zig-zag, and zig steps.