On the Dynamic Finger Conjecture for Splay Trees Part I Splay Sorting Log N Bl
On the Dynamic Finger Conjecture for Splay Trees Part I Splay Sorting Log N Bl
Richard Cole
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There are a number of cases. Case 1. Let u be a node, other than the root, in the lazy block tree. Suppose v is not on the left extreme path. Further suppose that v is accessed from its left child, u. Then v is promoted, v's promotion is paid for by gp times the jump in global rank from u', v's left child in the imaginary tree, to v (for, by Lemma 4, v's lazy weight is at lea. St the weight of its left subtree in the actuaJ tree and hence aJso in the imaginary tree; so v's lazy rank is at least... as large as u"s global rank). (Comment. The node u' may be missing; i. E. , v is the bottom node on the right path. ) Let wi be r's right child, if any, in the lazy block tree, and let W2, W3, • ■ ■, Wkhe the maximcd left path descending from wj in the lazy block tree. Wi, W2, ■ • ■, Wk are also promoted. Between them, these promotions require just gp times the jump in global rank from u' to v. For, by Lemma 4, w. 's lazy rank is at least iWi+i's normal rank, for 1
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