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CSE 3358 Note Set 13

CSE 3358 Note Set 13. Data Structures and Algorithms. Tree Balancing. Binary Search Based Method Needed all data a priori Needed a separate array to store data DSW Algorithm In-place balance Still need to have data first Or perform periodically on the tree to re-balance. DSW.

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CSE 3358 Note Set 13

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  1. CSE 3358 Note Set 13 Data Structures and Algorithms

  2. Tree Balancing • Binary Search Based Method • Needed all data a priori • Needed a separate array to store data • DSW Algorithm • In-place balance • Still need to have data first • Or perform periodically on the tree to re-balance

  3. DSW • Based on two symmetrical rotation operations, right and left. rotateRight(Gr, Par, Ch) If Par is not the root Gr of Ch becomes Ch’s parent Right subtree of Ch becomes left subtree of Ch’s parent Par Ch acquires Par as its right child Gr Gr Par Ch Ch R Par P P Q Q R

  4. DSW Algorithm • Idea • Convert any binary tree into a backbone (sometimes called vine) • In a series of passes, backbone is transformed into a perfectly balanced tree • Repeatedly rotating every second node of the backbone about its parent CreateBackbone(root, n) tmp = root while (tmp != 0) if tmphas left child rotate this child about tmp set tmp to the child that just became parent else tmp = tmp->right

  5. Example – Convert to Backbone 5 5 10 5 tmp 10 15 10 15 20 20 20 15 tmp 25 tmp 30 30 30 25 40 25 40 23 28 40 23 28 23 28

  6. Example 5 5 10 10 15 15 20 20 23 23 25 25 28 tmp 30 30 40 28 tmp 40

  7. DSW Algorithm CreatePerfectTree(n) m = 2floor(lg(n+1))-1 make n – m rotations starting from the top of the backbone while(m > 1) m = m/2 make m rotations starting from the top of the backbone

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