AVL Data Structure
Binary Trees with Height of O (log2n) AVL representation of BST.
oThe difference in height of the two AVL trees of any node in an AVL is at most equal to 1.
oHeight-balanced 1-tree
+ BST.
oElements/Nodes:
Structure BST + Height-balanced-10Ture:
Operations: Insert and Delete operations are different when compared with BST
equivalents.
(if 0, then same balance)
(if +. Then right sub-tree taller than 1. ) If (-), then left sub-tree is smaller.
Insert
o1.) performs the BST insert operation as if the tree was an ordinary BST.
o2.) Reorganize the tree to get an AVL Tree.
Three Cases:
Case 1.) Find the node on the search path whose balance field is either
(-)or (+) & is closest of the new node. This node is called the pivot node.
B-Tree
Each node, excluding the root node in a b-tree contains between d and 2d elements, where d is
the order of the tree.
The root node contains between 1 & 2d elements. Elements are in sorted order in each node.
Each node, except the root node has a unique parent. Each note except the leaf nodes has one
more child than the number of elements it contains.
Designed with hard-drive efficient in mind.
B-tree are empty initially.
oIf we were to create a B-tree of order 2.