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An AVL tree is a binary search tree that has the given properties:
Figure illustrated an AVL tree.
Figure: Balance requirement for AVL tree: the left & right sub tree differ by at most one in height
AVL stands for the names of G.M. Adelson - Velskii & E.M. Landis, two Russian mathematicians, who came up along with this method of keeping the tree balanced.
An AVL tree is a binary search tree that has the balance property and additionally to its key, each of the node stores an additional piece of information: the current balance of its subtree. The three possibilities are following:
The left child contain a height which is greater than the right child by 1.
Both of children have the same height
The right child contains a height that is greater by 1.
An AVL tree that remains balanced guarantees O(log n) search time, even into the worst case. Here, n refer to the number of nodes. The AVL data structure gain this property by placing limitation on the difference in heights among the sub- trees of given node and rebalancing the tree even if it violates these limitation.
Assertions and Abstract Data Types Even though we have defined assertions in terms of programs, notion can be extended to abstract data types (which are mathematical entities).
Data array A has data series from 1,000,000 to 1 with step size 1, which is in perfect decreasing order. Data array B has data series from 1 to 1,000,000, which is in random order.
AVL trees are applied into the given situations: There are few insertion & deletion operations Short search time is required Input data is sorted or nearly sorted
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