# How to insert Strings into an AVL Tree

AVL Tree is a self-balancing Binary Search Tree (BST) where the difference between heights of left and right subtrees cannot be more than one for all nodes.

**Examples:**

The above tree is AVL because the **differences between the heights of the left and right subtrees for every node** are less than or equal to **1**. Below is the example that is not an AVL Tree:

The above tree is not AVL because the differences between the heights of the left and right subtrees for 8 and 12 are greater than 1. It can be defined as a type of binary search tree that has all its nodes with a balance factor of -1, 0, or 1.

**What is the balance factor:** It is the difference in height between the two subtrees. (Balance Factor: Height of Left subtree – Height of right subtree)

__Insertion of Strings in AVL Tree__:

__Insertion of Strings in AVL Tree__:

Below example demonstration of inserting the days of the week in the order: **{Tuesday, Monday, Thursday, Saturday, Sunday, Friday, Wednesday}**

**Approach:**

- If the
**node**is empty(**NULL**), create the node with the first value given. - If the
**new node**is less than the**previous node**then insert the new node at the left - If the
**new node**is greater than the**previous node**then insert the new node at the right

**Check if the tree is balanced:**

- If the
**balance factor**is greater than**1**then it can be either:- Left-Left Case (then a single rotation is required to make it balanced).
- Or Left-Right Case(Double rotation required).

- If the balance factor is lesser than -1 then it can be either:
- Right-Right Case (Single rotation required).
- Or Right-Left Case (Double rotation required)

This process should be repeated for the insertion of all of the remaining nodes.

__Points to Remember__:

**Insert nodes accordingly:**To make sure that the given tree remains AVL after every insertion, augment the standard BST insert operation to perform some re-balancing. Following are two basic operations that can be performed to re-balance a BST without violating the BST property**(keys(left) < key(root) < keys(right))**.**Check the Balance Factor:**The balance factor should always be -1, 0, 1 if not then there is a need to rotate the tree accordingly.

__Steps To Create AVL Tree__:

- So according to the given order, let’s insert
**Tuesday**, as it has no node so it has a**balance factor**of**0**.

- The next step is to insert
**Monday**to the left of Tuesday as it is**alphabetically smaller(M < T)**. There is a need to check the balance factor of each node before inserting a new node. The tree is balanced as Tuesday is balanced because it has one subtree towards the left:

Balance Factor = height of the left subtree – the height of right subtree = 1 – 0 = 1

Therefore, the tree is balanced. Monday is also balanced because of balance factor 0.

- Next, insert
**Thursday**. It is inserted to the left of Tuesday**(as Th < Tu)**and it is inserted to the right of Monday**(as T>M)**. Now if the balance factor, is checked it can be seen that the balance factor of Tuesday is 2 so it is unbalanced, so there is a need to rotate the tree to make it balanced.

Note:In case if we don’t remember the rules of rotation of AVL tree, still it can be balanced we just need to remember that:Left node < Root < Right node.

Example:5 4

/ / \

3 —–> 3 5

\

4

- After that, insert
**Saturday,**to the left of Thursday**(S < T)**and to the right of Monday**(M < S)**. **Sunday**is inserted to the right of Saturday**(Sa < Su)**. Now the tree is unbalanced, so it is rotated to make it again balanced.

**Friday**is inserted following the same rules and the balance factor of Thursday becomes 2, so rotation is again done.

- After rotation, now the last node
**Wednesday**is inserted to the right of Tuesday (as T<W).

If the AVL tree is checked, now the entire AVL tree is height-balanced as all the nodes have balance factors **-1**, **0**, **1**.

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