An AVL is a self-balancing Binary Search Tree (BST) where the difference between the heights of left and right subtrees of any node cannot be more than one.
KEY POINTS
- It is height balanced tree
- It is a binary search tree
- It is a binary tree in which the height difference between the left subtree and right subtree is almost one
- Height is the maximum depth from root to leaf
Characteristics of AVL Tree:
- It follows the general properties of a Binary Search Tree.
- Each subtree of the tree is balanced, i.e., the difference between the height of the left and right subtrees is at most 1.
- The tree balances itself when a new node is inserted. Therefore, the insertion operation is time-consuming
Application of AVL Tree:
- Most in-memory sets and dictionaries are stored using AVL trees.
- Database applications, where insertions and deletions are less common but frequent data lookups are necessary, also frequently employ AVL trees.
- In addition to database applications, it is employed in other applications that call for better searching.
- Most STL implementations of the ordered associative containers (sets, multisets, maps and multimaps) use red-black trees instead of AVL trees.
Advantages of AVL Tree:
- AVL trees can self-balance.
- It also provides faster search operations.
- AVL trees also have balancing capabilities with a different type of rotation
- Better searching time complexity than other trees, such as the binary Tree.
- Height must not be greater than log(N), where N is the total number of nodes in the Tree.
Disadvantages of AVL Tree:
- AVL trees are difficult to implement
- AVL trees have high constant factors for some operations.
Maximum & Minimum number of Nodes
Maximum number of nodes = 2H+1 – 1
Minimum number of nodes of height H = min no of nodes of height (H-1) + min no of nodes of height(H-2) + 1
where H(0)=1
H(1)=2