Binary Search Tree Deletion

Deleting a Node in a BST

• When node A in a Binary Search Tree (BST) is deleted, the two candidates to take its place are H and E.

Rebalancing a Node

• The node that requires rebalancing is referred to as "a".

Insertion Cases

• In case 1, an insertion occurs into the left subtree of the left child of "a".
• In case 2, an insertion occurs into the right subtree of the right child of "a".
• In both cases, a single rotation can fix the balance if the insertion occurs outside (i.e., left-left or right-right).

Accessing Elements in AVL Tree

• Elements in an AVL Tree can be accessed in both linear and non-linear ways.

AVL Tree Data Structure

• An AVL Tree is a non-linear data structure.

Binary Trees

• The number of nodes in an AVL tree can be calculated using the formula Log2(n+1) - 1, which is approximately equal to 1.44 Log2n or 1.66 Log2n.
• An AVL tree may have cases of rotation, specifically, there is 1 case of rotation.

Binary Search Trees

• A binary tree can contain at least 2L Nodes at level L.
• A complete binary tree of depth d is a binary tree that contains 2L Nodes at each level L between 0 and d, both inclusive.
• The total number of nodes (Tn) in a complete binary tree of depth d is 2^d+1 - 1.
• The height of the complete binary tree can be written as h = log2 (Tn+1)-1 where Tn is the Total number of Nodes.

Postfix Notation

• The infix expression 5 + 6/2 can be converted into postfix notation as 56/ + 2 or 562/+.
• The postfix notation of A+B*C-D is ABC+D- or ABC+D-.

Data Structures

• A tree is a nonlinear data structure.
• A stack is a LIFO (Last-In-First-Out) data structure, whereas a queue is a FIFO (First-In-First-Out) data structure.
• A binary search tree (BST) is a nonlinear data structure.

Operators and Arrays

• The multiplication operator has a higher priority than other operators.
• Arrays have a fixed size that cannot be changed after creation.

Linked Lists

• Each item in a linked list is known as a node.
• The next item in a linked list is known as a node.

Binary Search Trees

• Each node in a binary search tree has 2 pointers.
• Searching an element in an AVL tree takes maximum Log2(n+1) time.

AVL Trees

• Deleting a parent with two childs in a straight line in an AVL tree requires single or double rotations.
• The time taken to check the depth of an AVL tree is 1.66 Log2n or 1.44 Log2n.