cs 341 f19 lecture 4 cs 466 fall 2019 lecture 4 - splay trees …cs466/lectures/lecture4.pdf · cs...
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CS 341 F19 Lecture 4
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CS 466 Fall 2019 Lecture 4 - Splay Trees Anna LubiwUniv. Waterloo
CS 341 F19 Lecture 4
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CS 466 Fall 2019 Lecture 4 - Splay Trees Anna LubiwUniv. Waterloo
CS 341 F19 Lecture 4
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CS 466 Fall 2019 Lecture 4 - Splay Trees Anna LubiwUniv. Waterloo
CS 341 F19 Lecture 4
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Algorithms Lecture ��: Scapegoat and Splay Trees [Fa’��]
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Figure 2. A zig-zag at x . The symmetric case is not shown.
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Figure 3. A right roller-coaster at x and a left roller-coaster at z.
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Figure 4. Splaying a node. Irrelevant subtrees are omitted for clarity.
• Search: Find the node containing the key using the usual algorithm, or its predecessor orsuccessor if the key is not present. Splay whichever node was found.
• Insert: Insert a new node using the usual algorithm, then splay that node.
• Delete: Find the node x to be deleted, splay it, and then delete it. This splits the tree intotwo subtrees, one with keys less than x , the other with keys bigger than x . Find the nodew in the left subtree with the largest key (the inorder predecessor of x in the original tree),splay it, and finally join it to the right subtree.
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Figure 5. Deleting a node in a splay tree.
Each search, insertion, or deletion consists of a constant number of operations of the formwalk down to a node, and then splay it up to the root. Since the walk down is clearly cheaper
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CS 466 Fall 2019 Lecture 4 - Splay Trees Anna LubiwUniv. Waterloo
CS 341 F19 Lecture 4
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CS 466 Fall 2019 Lecture 4 - Splay Trees Anna LubiwUniv. Waterloo
CS 341 F19 Lecture 4
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CS 466 Fall 2019 Lecture 4 - Splay Trees Anna LubiwUniv. Waterloo
CS 341 F19 Lecture 4
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CS 466 Fall 2019 Lecture 4 - Splay Trees Anna LubiwUniv. Waterloo
CS 341 F19 Lecture 4
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CS 466 Fall 2019 Lecture 4 - Splay Trees Anna LubiwUniv. Waterloo
CS 341 F19 Lecture 4
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CS 466 Fall 2019 Lecture 4 - Splay Trees Anna LubiwUniv. Waterloo
CS 341 F19 Lecture 4
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CS 466 Fall 2019 Lecture 4 - Splay Trees Anna LubiwUniv. Waterloo