End of Term Review 1.7

End of Term Review 1.7 - Splay Trees Self-balancing BST...

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Unformatted text preview: Splay Trees Self-balancing BST Invented by Daniel Sleator and Bob Tarjan Allows quick access to recently accessed elements D. Sleator Bad: worst-case O(n) Good: average (amortized) case O(log n) Often perform better than other BSTs in practice R. Tarjan CSE 2011 Prof. J. Elder - 31 - Last Updated: 4/1/10 2:37 PM Splaying Splaying is an operation performed on a node that iteratively moves the node to the root of the tree. In splay trees, each BST operation (find, insert, remove) is augmented with a splay operation. In this way, recently searched and inserted elements are near the top of the tree, for quick access. CSE 2011 Prof. J. Elder - 32 - Last Updated: 4/1/10 2:37 PM 3 Types of Splay Steps Each splay operation on a node consists of a sequence of splay steps. Each splay step moves the node up toward the root by 1 or 2 levels. There are 2 types of step: Zig-Zig Zig-Zag Zig CSE 2011 Prof. J. Elder - 33 - Last Updated: 4/1/10 2:37 PM Zig-Zig Performed when the node x forms a linear chain with its parent and grandparent. i.e., right-right or left-left x z y y T4 x T3 T1 T1 T2 T2 CSE 2011 Prof. J. Elder z zig-zig T3 - 34 - T4 Last Updated: 4/1/10 2:37 PM Zig-Zag Performed when the node x forms a non-linear chain with its parent and grandparent i.e., right-left or left-right z x y z zig-zag y x T1 T4 T2 T1 T2 T3 T4 T3 CSE 2011 Prof. J. Elder - 35 - Last Updated: 4/1/10 2:37 PM ...
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This note was uploaded on 02/14/2012 for the course CSE 2011Z taught by Professor Elder during the Fall '11 term at York University.

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End of Term Review 1.7 - Splay Trees Self-balancing BST...

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