create a AVL tree whose element is 55,25, 65, 9,8,15

Sure, let's create an AVL tree with the elements 55, 25, 65, 9, 8, 15.

Step 1: Start with the first element, 55. This becomes the root of the tree.

Step 2: Insert the second element, 25. Since 25 is less than 55, it becomes the left child of 55.

Step 3: Insert the third element, 65. Since 65 is greater than 55, it becomes the right child of 55.

So far, the tree looks like this:

    55
   /  \
 25   65

Step 4: Insert the fourth element, 9. Since 9 is less than 55 and also less than 25, it becomes the left child of 25.

Step 5: Insert the fifth element, 8. Since 8 is less than all other elements, it becomes the left child of 9.

Step 6: Insert the sixth element, 15. Since 15 is less than 55 but greater than 9, it becomes the right child of 9.

Now, the tree looks like this:

    55
   /  \
 25   65
 /
9
/ \
8  15

Step 7: Now, we need to check if the tree is balanced. The balance factor of a node is the height of its left subtree minus the height of its right subtree. An AVL tree is a binary search tree in which the balance factor of every node is either -1, 0, or 1. If the balance factor of any node is not in this range, we need to balance the tree by performing rotations.

In this case, the node with value 25 has a balance factor of 2 (height of left subtree is 3 and height of right subtree is 0), which means the tree is not balanced. We need to perform a right rotation on the node with value 25.

After the right rotation, the tree becomes:

    55
   /  \
 9    65
/ \  
8  25
   /
  15

Step 8: The tree is still not balanced because the node with value 55 has a balance factor of 2. We need to perform a left rotation on the node with value 55.

After the left rotation, the final AVL tree becomes:

    9
   /  \
  8   55
     /  \
   25   65
   /
  15

This is the final AVL tree for the given elements.