Q5. Check the following tree is AVL tree or not, if not make it AVL tree and insert the following (10 Marks) after balancing nodes the tree 15, 28, 13, 18 20 10 30 4 3

To check if the given tree is an AVL tree or not, we need to ensure that the heights of the left and right subtrees of every node differ by at most 1, and that both the left and right subtrees are also AVL trees.

Let's analyze the given tree:

   20
  /  \
 10   30
/ \

4 3

To make this tree an AVL tree, we need to perform the following steps:

Step 1: Insert the nodes 15, 28, 13, and 18 into the tree.

After inserting the nodes, the tree will look like this:

     20
    /  \
   10   30
  / \
 4   15
    /  \
   13   28
        /
       18

Step 2: Balance the nodes to ensure that the tree is an AVL tree.

To balance the tree, we need to perform rotations if necessary. In this case, we can see that the subtree rooted at node 10 is unbalanced. To balance it, we perform a right rotation at node 10.

After balancing, the tree will look like this:

     20
    /  \
   15   30
  / \
 10  28
/   /

4 13
18

Now, the tree is balanced and satisfies the AVL tree properties.

Therefore, the given tree is now an AVL tree after inserting the nodes 15, 28, 13, and 18 and balancing the tree.