**Example of Insertion in AVL Tree**

Consider an AVL Tree with following numbers:

50 , 20 , 60 , 10 , 8 , 15 , 32 , 46 , 11 , 48

**Step 1: **Insert 50

**Step 2:** Insert 20

As 20 < 50, so insert 20 in 50’s left sub tree.

**Step 3:** Insert 60

As 60 > 50, so insert 60 in 50’s right sub tree.

**Step 4:** Insert 10

- As 10 < 50, so insert 10 in 50’s left sub tree.
- As 10 < 20, so insert 10 in 20’s left sub tree.

**Step 5:** Insert 8

- As 8 < 50, so insert 8 in 50’s left sub tree.
- As 8 < 20, so insert 8 in 20’s left sub tree.
- As 8 < 10, so insert 8 in 10’s left sub tree.

To balance the tree,

- Find the first imbalanced node on the path from the newly inserted node (node 8) to the root node.
- The first imbalanced node is node 20.
- Now, count three nodes from node 20 in the direction of leaf node.
- Then, use AVL tree rotation to balance the tree.

**Step 6: **Insert 15

- As 15 < 50, so insert 15 in 50’s left sub tree.
- As 15 > 10, so insert 15 in 10’s right sub tree.
- As 15 < 20, so insert 15 in 20’s left sub tree.

To balance the tree,

- Find the first imbalanced node on the path from the newly inserted node (node 15) to the root node.
- The first imbalanced node is node 50.
- Now, count three nodes from node 50 in the direction of leaf node.
- Then, use AVL tree rotation to balance the tree.

**Step 7:** Insert 32

- As 32 > 20, so insert 32 in 20’s right sub tree.
- As 32 < 50, so insert 32 in 50’s left sub tree.

**Step 8:** Insert 46

- As 46 > 20, so insert 46 in 20’s right sub tree.
- As 46 < 50, so insert 46 in 50’s left sub tree.
- As 46 > 32, so insert 46 in 32’s right sub tree.

**Step 9:** Insert 11

- As 11 < 20, so insert 11 in 20’s left sub tree.
- As 11 > 10, so insert 11 in 10’s right sub tree.
- As 11 < 15, so insert 11 in 15’s left sub tree.

**Step 10:** Insert 48

- As 11 < 20, so insert 11 in 20’s left sub tree.
- As 11 > 10, so insert 11 in 10’s right sub tree.
- As 11 < 15, so insert 11 in 15’s left sub tree.

To balance the tree,

- Find the first imbalanced node on the path from the newly inserted node (node 48) to the root node.
- The first imbalanced node is node 32.
- Now, count three nodes from node 32 in the direction of leaf node.
- Then, use AVL tree rotation to balance the tree.

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