Splay树最坏案例搜索时间

Question

Since splay tree is a type of unbalanced binary search tree ( brilliant.org/wiki/splay-tree ), it cannot guarantee a height of at most O(log(n)). Thus, I would think it cannot guarantee a worst case search time of O(log(n)).

But according to bigocheatsheet.com :

Splay Tree has worst case search time of O(log(n))???

Answer 1

You're correct; the cost of a lookup in a splay tree can reach Θ(n) for an imbalanced tree.

Many resources like the big-O cheat sheet either make simplifying assumptions or just have factually incorrect data in them. It's unclear whether they were just wrong here, or whether they were talking amortized worst case, etc.

It's always best to know the internals of the data structures you're working with so that you can understand where the runtimes come from.