What is an AVL tree, and how does it maintain its balance during insertion and deletion?

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Aryan Kumar · Answer

An AVL tree is a self-balancing binary search tree. This means that the height of the tree is always logarithmic in the number of nodes, which ensures that operations such as search, insertion, and deletion can be performed in O(log n) time.

The balance factor of a node in an AVL tree is the difference between the heights of the left and right subtrees of that node. The self balancing property of an avl tree is maintained by the balance factor. The value of balance factor should always be -1, 0 or +1.

If the balance factor of a node is greater than 1 or less than -1, then the tree is unbalanced. In this case, the tree is rebalanced by performing one of the following rotations:

LL Rotation: This rotation is performed when the balance factor of a node is 2. The rotation involves swapping the positions of the node and its left child, and then rotating the left subtree of the node to the right.
RR Rotation: This rotation is performed when the balance factor of a node is -2. The rotation involves swapping the positions of the node and its right child, and then rotating the right subtree of the node to the left.
LR Rotation: This rotation is performed when the balance factor of a node is 1 and the balance factor of its left child is -1. The rotation involves swapping the positions of the node and its left child, and then rotating the left subtree of the node to the left.
RL Rotation: This rotation is performed when the balance factor of a node is -1 and the balance factor of its right child is 1. The rotation involves swapping the positions of the node and its right child, and then rotating the right subtree of the node to the right.

The AVL tree insertion and deletion algorithms work by recursively inserting or deleting nodes into the tree. After each insertion or deletion, the balance factors of all the nodes in the affected subtrees are checked. If any of the balance factors are out of bounds, then the tree is rebalanced by performing the appropriate rotations.

The AVL tree rebalancing operations are relatively efficient, and they ensure that the tree remains balanced even after a large number of insertions and deletions. This makes AVL trees a good choice for applications where the data is frequently updated, such as real-time systems and databases.

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What is an AVL tree, and how does it maintain its balance during insertion and deletion?

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