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What is AVL Tree | AVL Tree meaning

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

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