AVL trees are a type of self-balancing binary search tree crucial for fast data operations in computer science. Invented by Adelson-Velsky and Landis in 1962, they maintain balance through specific rotations—LL, RR, LR, and RL—ensuring optimal performance. Understanding AVL trees, including their balance factors and algorithmic operations, is vital for database and file system applications.
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AVL trees are self-balancing binary search trees named after their inventors Georgy Adelson-Velsky and Evgenii Landis
AVL trees play a critical role in computer science and are widely used in applications that require fast data retrieval
AVL trees maintain their self-balancing property by adhering to a set of rules and using the balance factor of each node to determine balance
There are four types of tree rotations used to correct imbalances in AVL trees: Left-Left (LL), Right-Right (RR), Left-Right (LR), and Right-Left (RL)
Visual representations of AVL trees can aid in understanding their structure, including key-value pairs, balance factors, and hierarchical order
The balance factor is crucial in assessing and maintaining the balance of an AVL tree, as it indicates when rotations are necessary
The AVL tree algorithm includes key operations such as insertion, deletion, and search, all optimized by the tree's balanced structure
After each insertion or deletion, the balance factor is recalculated to determine if rotations are needed to restore balance
AVL trees offer high efficiency with search, insert, and delete operations performed in O(log n) time, thanks to their self-balancing and rotation techniques
The AVL tree's historical significance as the first self-balancing binary search tree highlights its impact and relevance in contemporary computing
A thorough understanding of the balance factor is vital for effectively implementing AVL trees in various computer science applications
Students and professionals must have proficiency in AVL tree concepts, including visualization and algorithmic operations, to fully utilize this data structure in computational tasks
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An AVL tree is a self-balancing binary search tree created by ______ and ______ that maintains balance by ensuring the height difference between left and right subtrees of any node does not exceed ______.
Georgy Adelson-Velsky
Evgenii Landis
one
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AVL Tree Balance Factor Definition
Balance factor of a node is height difference between its left and right subtrees.
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AVL Tree Height Definition
Height of a node is the longest path's edge count from that node to a leaf.
