AVL Tree Basics: Structure and Insertion Rules An AVL tree is a self-balancing binary search tree where the difference in heights between left and right subtrees (balance factor) must be -1, 0, or +1. The insertion process involves placing elements according to binary search rules while maintaining balance after each addition. For instance, inserting values like 15 and then 17 maintains this structure as both are placed correctly based on their value hierarchy.
Maintaining Balance Through Rotations As new elements are added—like 11 or even smaller numbers—the balance of the AVL tree needs constant checking to ensure it remains within acceptable limits. When an imbalance occurs due to insertions that create height differences greater than one between child nodes, rotations may be necessary for rebalancing. This ensures efficient operations such as searching remain optimal.
Complex Insertions Require Strategic Balancing Techniques When adding more complex sequences of numbers like three consecutive inserts leading up from lower values through higher ones requires careful balancing techniques including single or double rotations depending on how far out-of-balance the node becomes during insertion processes.
Restoring Order with Right/Left Rotations 'Right' and 'left' rotation strategies help restore order when imbalances arise post-insertion; these adjustments keep trees balanced by repositioning nodes effectively without losing overall data integrity in terms of hierarchical relationships among inserted items throughout various stages of growth within an AVL framework.