1) AVL trees are self-balancing binary search trees where the heights of the left and right subtrees of every node differ by at most one. This keeps the tree balanced during insertions and deletions and maintains O(log n) time for search, insert, and delete operations. 2) Rotations are used to rebalance the tree when insertions or deletions cause height differences greater than one between subtrees. There are four types of rotations: single left, single right, double left-right, and double right-left. 3) The advantages of AVL trees are that they are always balanced, guaranteeing fast O(log n) performance for search, insert, and delete operations

1. AVL Trees
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2. Presentation
Data Structure & Algorithms
Presented By: Group 11
By
Komal 6622
Tayyaba 6648
Maryam 6626
Kanwal 6619
Mahnoor 6623
AVL Trees
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3. AVL Trees
6
v
8
3
z
4
AVL Trees
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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
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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
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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
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8. Why we need AVL Tree?
o To keep binary search tree perfectly
balanced we need AVL Tree with
O(log N) complexity…
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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
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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
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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)
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17. Thank You

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