Table of Contents
- 1 How does an AVL tree maintain balance?
- 2 Why balancing is required AVL tree?
- 3 What is an unbalanced node?
- 4 What is the balance factor of an AVL tree node?
- 5 What is an AVL tree explain the procedure to delete a node in an AVL tree?
- 6 What is the AVL condition?
- 7 Why is the above tree not AVL?
- 8 What happens when a node is added to an unbalanced tree?
- 9 How many bits do I need to balance an AVL tree?
How does an AVL tree maintain balance?
In AVL trees, after each operation like insertion and deletion, the balance factor of every node needs to be checked. If every node satisfies the balance factor condition, then the operation can be concluded. Otherwise, the tree needs to be rebalanced using rotation operations.
Why balancing is required AVL tree?
So, a need arises to balance out the existing BST. Named after their inventor Adelson, Velski & Landis, AVL trees are height balancing binary search tree. AVL tree checks the height of the left and the right sub-trees and assures that the difference is not more than 1. This difference is called the Balance Factor.
How do you find the unbalanced node in AVL tree?
To check whether it is left left case or not, compare the newly inserted key with the key in left subtree root. If balance factor is less than -1, then the current node is unbalanced and we are either in Right Right case or Right Left case.
What is an unbalanced node?
Here’s a quote from the article: The balance factor of a node is the height of its right subtree minus the height of its left subtree and a node with balance factor 1, 0, or -1 is considered balanced. A node with any other balance factor is considered unbalanced and requires rebalancing the tree.
What is the balance factor of an AVL tree node?
Properties of an AVL tree: The balance factor of a node is the height of its right subtree minus the height of its left subtree and a node with a balance factor 1, 0, or -1 is considered balanced.
What is an AVL tree explain the balancing methods of an AVL tree with an example?
AVL Tree can be defined as height balanced binary search tree in which each node is associated with a balance factor which is calculated by subtracting the height of its right sub-tree from that of its left sub-tree….Complexity.
| Algorithm | Average case | Worst case |
|---|---|---|
| Insert | o(log n) | o(log n) |
| Delete | o(log n) | o(log n) |
What is an AVL tree explain the procedure to delete a node in an AVL tree?
Deleting a node from an AVL tree is similar to that in a binary search tree. Deletion may disturb the balance factor of an AVL tree and therefore the tree needs to be rebalanced in order to maintain the AVLness. For this purpose, we need to perform rotations. The two types of rotations are L rotation and R rotation.
What is the AVL condition?
AVL Trees: AVL tree’s are height balanced trees. These trees maintain the following invariant: AVL balance condition: For every node in the tree, the heights of its left subtree and right subtree differ by at most 1. (The height of a null subtree is defined to be -1 by convention.)
Which rotations are performed to balanced AVL tree?
A double right rotation, or right-left rotation, or simply RL, is a rotation that must be performed when attempting to balance a tree which has a left subtree, that is right heavy. This is a mirror operation of what was illustrated in the section on Left-Right Rotations, or double left rotations.
Why is the above tree not AVL?
The above tree is not AVL because differences between heights of left and right subtrees for 8 and 12 is greater than 1. Why AVL Trees? Most of the BST operations (e.g., search, max, min, insert, delete.. etc) take O (h) time where h is the height of the BST.
What happens when a node is added to an unbalanced tree?
In this case, the node always replaces a NULL reference (left or right) of an external node in the tree i.e., the node is either made a left-child or a right-child of the external node. After this insertion if a tree becomes unbalanced, only ancestors of the newly inserted node are unbalanced.
What is the temporary balance factor of an AVL subtree?
Since with a single deletion the height of an AVL subtree cannot decrease by more than one, the temporary balance factor of a node will be in the range from −2 to +2. If the balance factor remains in the range from −1 to +1 it can be adjusted in accord with the AVL rules.
How many bits do I need to balance an AVL tree?
For holding the AVL balance information in the traditional way, two bits per node are sufficient. However, later research showed if the AVL tree is implemented as a rank balanced tree with delta ranks allowed of 1 or 2—with meaning “when going upward there is an additional increment in height of one or two”, this can be done with one bit.