What Is the Difference Between Bottom-up and Top Down Methods in Splay Tree?

The methods define how you use splaying when searching:

Bottom-up: you search the tree and rotate at the same iteration

Top-down: you first search and at another iteration you rotate

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This ideas hold to the creation also, when using the top down you insert the key as if it was a binary serach tree and than move it to the head in another iteration.

A top-down splay tree: performs rotations on the initial access path. Thus a top-down splay tree node does not need a parent link. The splay operation finishes as soon as the search does. That means the overhead for operations of a top-down splay tree is of a relatively small amount.

Bottom-up splay tree: requires a traversal from the root down the tree and then a bottom-up traversal to implement the splaying step, so a bottom-up splay tree implementation looks similar to that of an AVL tree. Besides, it needs a parent link or a stack to store the search path.

An implementation of a top-down splay tree can be found in the data structure book (Chapter 12) written by Weiss.