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Unformatted text preview: Bottom-Up Splay Trees–Analysis • Actual and amortized complexity of join is O(1). • Amortized complexity of search, insert, delete, and split is O(log n). • Actual complexity of each splay tree operation is the same as that of the associated splay. • Sufficient to show that the amortized complexity of the splay operation is O(log n). Potential Function • size(x) = #nodes in subtree whose root is x. • rank(x) = floor(log 2 size(x)). • P(i) = Σ x is a tree node rank(x). square4 P(i) is potential after i’th operation. square4 size(x) and rank(x) are computed after i’th operation. square4 P(0) = 0. • When join and split operations are done, number of splay trees > 1 at times. square4 P(i) is obtained by summing over all nodes in all trees. Example • size(x) is in red. 20 10 6 8 40 30 1 • rank(x) is in blue. • Potential = 5. 2 3 1 2 6 1 1 1 2 Example • rank(root) = floor(log 2 n)....
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This note was uploaded on 03/22/2012 for the course CSE 3101 taught by Professor Shani during the Fall '10 term at University of Florida.
- Fall '10
- Data Structures