The number of rotations required to insert a sequence of elements 9, 6, 5, 8, 7, and 10 into an empty AVL tree is?

To answer this question, we need to understand what an AVL tree is and how it works. An AVL tree is a self-balancing binary search tree, and the key feature is that the heights of the two child subtrees of any node differ by at most one. If at any time they differ by more than one, rebalancing is done to restore this property.

Let's insert the elements one by one and see how many rotations are required:

1. Insert 9: No rotation required as the tree is empty.
2. Insert 6: No rotation required. The tree remains balanced.
3. Insert 5: A right rotation is required at node 9. So, the count is 1.
4. Insert 8: A left rotation is required at node 6 and then a right rotation at node 5. So, the count is 3.
5. Insert 7: No rotation required. The tree remains balanced.
6. Insert 10: No rotation required. The tree remains balanced.

So, the total number of rotations required to insert the sequence of elements 9, 6, 5, 8, 7, and 10 into an empty AVL tree is 3.