In an AVL tree, what is the balance factor of a node?

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Question: In an AVL tree, what is the balance factor of a node?

Options:

Correct Answer: Height of left subtree - height of right subtree

Solution:

The balance factor of a node in an AVL tree is defined as the height of the left subtree minus the height of the right subtree.

In an AVL tree, what is the balance factor of a node?

In an AVL tree, what is the balance factor of a node?

Step 1: Understand what an AVL tree is. It is a type of binary search tree that keeps itself balanced.
Step 2: Know that each node in the AVL tree has two subtrees: a left subtree and a right subtree.
Step 3: Learn about the height of a subtree. The height is the number of edges on the longest path from that subtree to a leaf node.
Step 4: Calculate the height of the left subtree of a node. Count the edges from the node to the deepest leaf in the left subtree.
Step 5: Calculate the height of the right subtree of the same node. Count the edges from the node to the deepest leaf in the right subtree.
Step 6: Find the balance factor by subtracting the height of the right subtree from the height of the left subtree. The formula is: Balance Factor = Height of Left Subtree - Height of Right Subtree.
Step 7: Understand that a balance factor of 0 means the tree is balanced, while positive or negative values indicate the tree is leaning towards one side.

Balance Factor – The balance factor of a node in an AVL tree is calculated as the height of the left subtree minus the height of the right subtree, which helps maintain the tree's balance.