AVL or BALANCED BINARY TREES

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AVL or BALANCED BINARY TREES
Definition An AVL Tree is a Binary Tree in which
for every node, the heights of its two subtrees
never differ by more than one
A BALANCE indicator is assigned to each node
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Private members
Public base class members
New public subclass members
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33
43
(0)
53
63
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A Degenerate BST
An AVL Tree
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Non-BST
Non AVL Tree
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Time for Searching a Balanced Tree? In a complete
BST we have Nodes in Tree Height of Tree
2n1 1 n Hence
log(2n1 1) n log(n) Now the left hand
column stands for the size of the data set and
the right hand column for the time required to
search. Thus, n elements in a tree requires O(log
n) search time!
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AVL Trees Insert and Maintain Balance
After an Insertion
Both LEFT HEAVY
(-2) Critical
subtree
Length of longest path to parent
K
Note INORDER on Both Before-After T1DT2KT3
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Perform right rotation pivot is
K
Symmetric Case Both Trees RIGHT HEAVY
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After Insertion
Left rotate with C as pivot
Right rotate with M as pivot
Another E.G. of Insert