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Amortization for Splay Trees
Definition
- Let n(v) be the size of the subtree rooted at v
- For the root t of the tree Di, we have n(t) = 2 ni + 1
- Let the rank of node v be defined as r(v) = log n(v)
- For the root t of the tree Di, we have r(t) = log (2 ni + 1)
- Let the savings function be defined as
- Clearly, we have