Math Problem Statement
Which operation will height-balance the following BST? 25 / \ 16 42 / \ 9 21 \ 22 also Submit an image of the tree after it's been balanced. If the tree is already balanced, leave the upload area blank. so which option is correct Choice 1 of 5:Left rotation on 16
Choice 2 of 5:Right rotation on 21
Choice 3 of 5:Left-right rotation on 25
Choice 4 of 5:Right-left rotation on 16
Choice 5 of 5:This tree is already balanced.
Solution
The image above shows the balanced BST after performing the left-right rotation on node 25.
Do you have any questions or need further details on the balancing process?
Here are five questions to expand on the information provided:
- What is a balance factor in a Binary Search Tree?
- How does a left rotation on a node affect the tree structure?
- How does a right rotation on a node affect the tree structure?
- What are the conditions that necessitate a left-right rotation in a BST?
- Can you explain how to perform a right-left rotation on a BST?
Tip: When analyzing a tree's balance, always check the balance factor for each node to determine the necessary rotations to balance the tree.
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Math Problem Analysis
Mathematical Concepts
Binary Search Trees
Tree Rotations
AVL Trees
Formulas
Balance Factor = Height(Left Subtree) - Height(Right Subtree)
Theorems
AVL Tree Property
Rotation Theorems in BST
Suitable Grade Level
Grades 10-12
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