Final answer:
The minimum possible height difference (balance factor) between the left and right subtrees of a node in a balanced AVL tree is 1. Answer (c) is correct. AVL trees use rotations to maintain this balance, ensuring logarithmic height and operation times.
Step-by-step explanation:
In the context of AVL trees, which are a type of balanced binary search tree, the minimum possible height difference (also known as the balance factor) between the left and right subtrees of any node is -1, 0, or +1. This balance factor is used to ensure that the tree remains approximately balanced after each insertion and deletion operation. If the balance factor of any node in an AVL tree becomes less than -1 or greater than +1, rotations are performed to restore the balance of the tree.
The correct answer to the question is: (c) 1. This means that the height of the left subtree and the right subtree for any given node can differ at most by 1 level for the tree to be considered balanced in the context of AVL trees. If the difference is greater than 1, the tree requires rebalancing through rotations.
Understanding the balance factor is crucial for implementing AVL trees and for operations such as insertions, deletions, and rebalancing of the tree. The balance conditions of AVL trees enable them to maintain a height that is logarithmic in the number of nodes, guaranteeing O(log n) search, insert, and delete operations.