What is AVL tree data structure, its operations, and its rotations? What are the applications for AVL trees?

AVL trees are height balancing binary search trees named after their inventors Adelson, Velski, and Landis. The AVL tree compares the heights of the left and right subtrees and ensures that the difference is less than one. This distinction is known as the Balance Factor.

We can perform the following two operations on AVL tree:
Insertion: Insertion in an AVL tree is done in the same way that it is done in a binary search tree. However, it may cause a violation in the AVL tree property, requiring the tree to be balanced. Rotations can be used to balance the tree.
Deletion: Deletion can also be performed in the same manner as in a binary search tree. Because deletion can disrupt the tree’s balance, various types of rotations are used to rebalance it.

An AVL tree can balance itself by performing the four rotations listed below:
Left rotation: When a node is inserted into the right subtree of the right subtree and the tree becomes unbalanced, we perform a single left rotation.
Right rotation: If a node is inserted in the left subtree of the left subtree, the AVL tree may become unbalanced. The tree then requires right rotation.
Left-Right rotation: The RR rotation is performed first on the subtree, followed by the LL rotation on the entire tree.
Right-Left rotation: The LL rotation is performed first on the subtree, followed by the RR rotation on the entire tree.

Following are some real-time applications for AVL tree data structure:
AVL trees are typically used for in-memory sets and dictionaries.
AVL trees are also widely used in database applications where there are fewer insertions and deletions but frequent data lookups are required.
Apart from database applications, it is used in applications that require improved searching.