Table of Contents

- 1 How do you find the time complexity of an AVL tree?
- 2 What is the time complexity of AVL tree for addition and deletion operation?
- 3 What is the maximum height of any AVL tree with 7 nodes?
- 4 What is the purpose of AVL tree?
- 5 What is the space complexity of an AVL tree insert?
- 6 How to check the height of an AVL tree?

## How do you find the time complexity of an AVL tree?

The time required is O(log n) for lookup, plus a maximum of O(log n) retracing levels (O(1) on average) on the way back to the root, so the operation can be completed in O(log n) time.

## What is the time complexity of AVL tree for addition and deletion operation?

Time Complexity Due to the balancing property, the insertion, deletion and search operations take O ( l o g n ) O(log n) O(logn) in both the average and the worst cases. Therefore, AVL trees give us an edge over Binary Search Trees which have an O ( n ) O(n) O(n) time complexity in the worst case scenario.

**What is size in AVL tree?**

Size of a tree is the number of elements present in the tree. Size of a tree = Size of left subtree + 1 + Size of right subtree.

**How much time does AVL tree take to perform search insert and delete operation in the average as well as worst case?**

In an AVL tree, the heights of the two child subtrees of any node differ by at most one; therefore, it is also said to be height-balanced. Lookup, insertion, and deletion all take O(log n) time in both the average and worst cases, where n is the number of nodes in the tree.

### What is the maximum height of any AVL tree with 7 nodes?

3

It means, height 3 is achieved using minimum 7 nodes. Therefore, using 7 nodes, we can achieve maximum height as 3.

### What is the purpose of AVL tree?

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.

**What is the maximum height of any AVL tree with 7 nodes assume that the height of a tree with a single node?**

So, the max height with 7 nodes is 3.

**What is the maximum height of any AVL tree?**

If there are n nodes in AVL tree, minimum height of AVL tree is floor(log2n). If there are n nodes in AVL tree, maximum height can’t exceed 1.44*log2n.

## What is the space complexity of an AVL tree insert?

Due to the balancing property, the insertion, deletion and search operations take O (logn) in both the average and the worst cases. Therefore, AVL trees give us an edge over Binary Search Trees which have an O (n) time complexity in the worst case scenario. The space complexity of an AVL tree is O (n) in both the average and the worst case.

## How to check the height of an AVL tree?

The height of an AVL tree is always O (Logn) where n is the number of nodes in the tree. In AVL tree, after performing every operation like insertion and deletion we need to check the balance factor of every node in the tree.

**How to insert and delete an AVL tree?**

AVL trees have a worst case lookup, insert and delete time of O (log n). You will do an insertion similar to a normal Binary Search Tree insertion. After inserting, you fix the AVL property using left or right rotations. If there is an imbalance in left child of right subtree, then you perform a left-right rotation.

**When to do a left or right rotation in AVL tree?**

If there is an imbalance in right child of right subtree, then you perform a left rotation. If there is an imbalance in right child of left subtree, then you perform a right-left rotation. AVL Tree 7 complete example of adding data to an AVL tree.