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- 1. AVL Trees 1
- 2. Presentation Data Structure & Algorithms Presented By: Group 11 By Komal 6622 Tayyaba 6648 Maryam 6626 Kanwal 6619 Mahnoor 6623 AVL Trees 2
- 3. AVL Trees 6 v 8 3 z 4 AVL Trees 3
- 4. Contents 1) Defination 2) Why we need? 3) Difference beteen AVL and Non AVL by example 4) Techniques with examples 5) Advantage and Disadvantage 6) Time complexity AVL Trees 4
- 5. AVL Trees: AVL trees were invented in 1962 by two Russian scientist G.M Adelson Velsky & E.M Landis. Definition: An AVL tree is a binary search tree in which the balance factor of every node is either 0 or +1 or -1 .
- 6. Height Of A Tree: The height of a binary tree is the maximum path length from root to the leaf Level 0 Level 1 Level 2 Level 3 The height of this tree is= 3 AVL Trees 6
- 7. Balance Factor: It is defined as the difference b/w the heights of the node’s left & right sub trees Balance factor=ht of left sub tree – ht of right sub tree. ht=height AVL Trees 7
- 8. Why we need AVL Tree? o To keep binary search tree perfectly balanced we need AVL Tree with O(log N) complexity… AVL Trees 8
- 9. Example : AVL tree BST ( not AVL tree ) 1 2 0 0 0 -1 0 0 0 0 0 0 -1 0 0
- 10. Techniques to make AVL Tree: If an insertion of a new node makes an AVL tree unbalanced , we transform the tree by a rotation there are four types of rotation we have: 1. 2. 3. 4. Single right rotation or R-rotation Single left rotation or L-rotation Double right-left rotation or RL-rotation Double left-right rotation or LR-rotation AVL Trees 10
- 11. 1.Straight line with positive unbalanced. apply Right rotation for unbalanced node. +2 +1 0 2 4 5 0 4 0 2 0 5
- 12. 2.Straight line with negative unbalanced. apply left rotation for unbalanced node. 5 -2 0 6 -1 7 0 5 0 6 0 7
- 13. 3.Curved line with positive unbalanced. apply left-right rotation. Right rotation for unbalanced node and left rotation for the nearest node. For example: C,A,B +2 C C 0 B B A -1 B 0 A 0 A C 0
- 14. 4.Curved line with negative unbalanced. apply right-left rotation. Left rotation for unbalanced node and right rotation for the nearest node. For example: A,C,B A -2 C B 0 A 0 B B +1 C 0 A C 0
- 15. Advantages &Disadvantages The advantage of an AVL tree is that it is always balanced, guaranteeing the O(logn) speed of the Binary Search algorithm. The disadvantages the complex rotations used by the insertion and removal AVL Trees 15
- 16. Running Times for AVL Trees find is O(log n) height of tree is O(log n) insert is O(log n) initial find is O(log n) remove is O(log n) initial remove is O(log n) AVL Trees 16
- 17. Thank You AVL Trees 17

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