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The balance factor is a key concept in AVL trees, a type of self-balancing binary search tree. It helps maintain the tree’s height and ensures efficient operations such as search, insertion, and deletion. Understanding how to calculate and apply the balance factor is essential for managing AVL trees effectively.
What is the Balance Factor?
The balance factor of a node in an AVL tree is the difference between the heights of its left and right subtrees. It is calculated as:
Balance Factor = Height of Left Subtree – Height of Right Subtree
A node’s balance factor can be -1, 0, or 1 for the tree to be balanced. If the balance factor exceeds these values, the tree requires rebalancing through rotations.
Calculating the Balance Factor
To determine the balance factor, first find the height of each subtree rooted at the node’s children. The height is the number of edges on the longest path from the node to a leaf. Subtract the height of the right subtree from the height of the left subtree to get the balance factor.
For example, if the left subtree has height 3 and the right subtree has height 1, then the balance factor is 2, indicating the node is unbalanced and needs rotation.
Applications of the Balance Factor
The balance factor is used during insertion and deletion to maintain the AVL tree’s balance. When a node’s balance factor becomes outside the range of -1 to 1, rotations are performed to restore balance. These rotations include:
- Single Right Rotation
- Single Left Rotation
- Left-Right Rotation
- Right-Left Rotation
These operations help keep the tree height minimal, ensuring optimal performance for search operations.