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
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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

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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

AVL Trees
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