Which specific tree data structure maintains balance by ensuring that for any node, the height difference between its left and right subtrees is at most one?

The specific tree data structure that maintains balance by ensuring that for any node, the height difference between its left and right subtrees is at most one is an AVL tree. An AVL tree is a self-balancing binary search tree, which means it automatically adjusts its structure to maintain balance after modifications. It was the first self-balancing binary search tree, named after its inventors, Adelson-Velsky and Landis. A node is a fundamental unit in the tree containing data and references to its child nodes. A subtree is a portion of a tree that can itself be considered a tree. The height of a subtree is defined as the number of edges on the longest path from its root down to a leaf node. For example, a tree consisting of only a root node has a height of zero. This strict balancing condition, known as the AVL property, ensures that the tree remains relatively compact and efficient. The benefit of this property is that it guarantees that operations such as search, insertion, and deletion will always perform in logarithmic time, denoted as O(log n), where 'n' is the number of nodes in the tree. This prevents the tree from degenerating into a linear structure, like a linked list, in worst-case scenarios, which would lead to much slower linear time operations, O(n). To maintain this balance, each node in an AVL tree stores or can calculate a balance factor, which is the height of its right subtree minus the height of its left subtree. The AVL property mandates that this balance factor must always be -1, 0, or 1 for every node. After any insertion or deletion operation, if the balance factor of any node along the path from the modified node to the tree's root falls outside this range (i.e., becomes less than -1 or greater than 1), the tree performs rotations. Rotations are local structural changes to the tree that reconfigure the nodes to restore the balance factor to its valid range while preserving the fundamental binary search tree (BST) property. The BST property states that for any node, all values in its left subtree are less than the node's value, and all values in its right subtree are greater than the node's value. There are four types of rotations used to rebalance the tree: single left rotation, single right rotation, left-right double rotation, and right-left double rotation.