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:

  1. What is a balance factor in a Binary Search Tree?
  2. How does a left rotation on a node affect the tree structure?
  3. How does a right rotation on a node affect the tree structure?
  4. What are the conditions that necessitate a left-right rotation in a BST?
  5. 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