Recall & Review
beginner
What is the main purpose of rotations in an AVL tree?
Rotations in an AVL tree are used to restore balance after insertions or deletions, ensuring the tree remains height-balanced for efficient operations.
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intermediate
Describe a single right rotation in an AVL tree.
A single right rotation is performed when a left-heavy subtree causes imbalance. The left child becomes the new root of the subtree, and the original root becomes the right child of the new root.
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intermediate
When is a double rotation (left-right or right-left) needed in an AVL tree?
A double rotation is needed when the subtree is unbalanced in a zig-zag pattern, such as a left-right or right-left case. It combines two single rotations to restore balance.
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beginner
What is the difference between a left rotation and a right rotation in AVL trees?
A left rotation moves the right child up to become the subtree root, fixing right-heavy imbalances. A right rotation moves the left child up, fixing left-heavy imbalances.
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beginner
Explain the balance factor in AVL trees and how it relates to rotations.
The balance factor is the height difference between the left and right subtrees of a node. If it becomes less than -1 or greater than 1, rotations are needed to restore balance.
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What does a balance factor of +2 indicate in an AVL tree node?
✗ Incorrect
A balance factor of +2 means the left subtree is taller by 2 levels, indicating a left-heavy imbalance.
Which rotation fixes a right-right imbalance in an AVL tree?
✗ Incorrect
A right-right imbalance is fixed by a single left rotation.
What type of rotation is used to fix a left-right imbalance?
✗ Incorrect
A left-right imbalance requires a double rotation: first left rotation on left child, then right rotation on the node.
After which operation do AVL tree rotations typically occur?
✗ Incorrect
Rotations occur after insertions or deletions to maintain balance.
What is the maximum allowed balance factor in an AVL tree node before rotation is needed?
✗ Incorrect
The balance factor must be -1, 0, or 1. If it goes beyond ±1, rotations are needed.
Explain the four types of rotations used in AVL trees and when each is applied.
Think about left-heavy and right-heavy imbalances and zig-zag patterns.
You got /5 concepts.
Describe how the balance factor guides the decision to perform rotations in an AVL tree.
Focus on height differences between subtrees.
You got /4 concepts.