https://file.aiquickdraw.com/mathbot/file/1726736917396hs0u42gc.jpg

It looks like you have confirmed that the correct insertion order to produce the given AVL tree is option \(a\) (86, 25, 98, 83, 27, 90, 71, 94). Let's verify that this sequence indeed produces the AVL tree shown in the image:

1. **86** is inserted as the root.
2. **25** goes to the left of 86.
3. **98** goes to the right of 86.
4. **83** goes to the left of 98.
5. **27** goes to the right of 25.
6. **90** goes to the left of 98, under 83.
7. **71** goes between 25 and 83, under 27.
8. **94** is added under 98, completing the tree structure as shown.

This sequence of insertions must have been handled by appropriate AVL tree rotations to maintain the balance factors as needed for an AVL tree, which prioritizes the tree remaining balanced after each insertion. The tree structure in the image indicates that such rotations were successfully executed.

Do you need more details on how AVL tree rotations work or have any other questions? Here are some follow-up topics you might find interesting:

1. What is an AVL tree and why is it important?
2. How does inserting a value affect the balance of an AVL tree?
3. What are the different types of rotations used in maintaining an AVL tree?
4. How do you remove a node from an AVL tree while maintaining balance?
5. How can AVL trees be used in real-world applications?

**Tip:** When working with AVL trees, always consider the balance factor after each insertion or deletion to decide whether a rotation is necessary to maintain the tree's balance.

Which of the following order of elements are inserted into an empty AVL tree, so that it is possible to get the above AVL tree?

Discover how the insertion sequence of nodes can create a balanced AVL tree structure. This problem involves understanding AVL tree rotations and balancing properties, commonly covered in Grades 11-12 or undergraduate-level computer science courses.

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