Insert the integers 1 through 7 into an AVL tree, showing each step and rotation.
Insert the integers 1 through 7 into an AVL tree, showing each step and rotation.
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Question
Insert the integers 1 through 7 into an AVL tree, showing each step and rotation.
Is what I have wrong? If not could provide correct solution?
Transcribed Image Text:The image contains a series of diagrams illustrating binary tree transformations with a focus on the balance factor. The steps are as follows:
1. Start with node 7:
- A node labeled "7" with a left child "3".
2. Add a child node to 3:
- The node "3" gains a left child "2".
3. Balance the tree:
- The node "2" becomes the root with left child "1" and right child "3".
4. Expansion:
- Node "3" gets a right child "7".
- Node "7" becomes a right child to "1".
- A right child "5" is added to "3".
5. Further modifications by adding node "6":
- New node "6" added as a right child of "5".
6. The adjustments are demonstrated through rotations:
- "Left-right" and "right-left" rotations are illustrated.
7. Two different configurations are circled and labeled:
- One labeled as "Final" and the other "root -2->1".
- The steps include annotations about left and right rotations with corresponding balance factor adjustments written as "0-2->-2" and "1 right rot".
- The diagrams illustrate how to maintain balance in a binary search tree through rotations, particularly left-right and right-left rotations.
Expert Solution
Step 1: Defining Introduction
The AVL Trees are BST with height balance property. The balance factor of the nodes should be (-1, 0, or 1). Balance factor is calculated as height of left subtree - height of right subtree (OR) height of right subtree - height of left subtree.
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