AVL Trees: Understanding and Application In 1962, Adelson-Velsky and Landis, two Soviet computer scientists, developed AVL Trees, a self-balancing binary search tree. In order to ensure that the heights of each given node's two offspring are approximately identical, this data structure was designed to build an ideal tree. This attribute is crucial because the tree's performance could suffer if the AVL property failed due to changes in the heights of some nodes during tree updating. The implementation and functioning of AVL Trees will be covered in detail in this article, along with how to insert and rebalance nodes correctly to preserve the AVL feature. The Problem with Unbalanced Trees The heights of the nodes along the insertion path may change when a node is added to an AVL Tree, making certain nodes' paths to leaves longer. The AVL property may not hold as a result, in which case the tree would no longer be optimal. Maintaining the AVL Property The tree needs to be rebalanced after each insertion in order to guarantee the AVL property is maintained. The rebalancing algorithm's fundamental concept is as follows: ● As with any other binary search tree, the node is initially added to the tree. ● After that, the rebalance process is carried out, starting at the newly added node and moving up to the root as necessary by using parent pointers. ● The balancing operation determines if there is a height difference of more than one between the left and right children. ● The AVL property is maintained and no further action is required if the difference is less than or equal to 1. ● The tree has to be rearranged if the difference is bigger than 1. The left child must be placed higher up the tree in relation to the right if it is two or more heights taller than the right. It is crucial to remember that a node's left and right children can never differ in height by more than 2, which makes the rebalancing process easier. Rebalancing Rotations To rebalance an AVL Tree, one can apply one of four rotation types: ● ● ● ● Left Rotation Right Rotation Left-Right Rotation Right-Left Rotation Each rotation is used to reorder the tree in a way that corrects the height disparity between a node's left and right children, thereby retaining the AVL property. Left-Right Rotation Right-Left Rotation An essential and effective data structure for maintaining the AVL attribute, AVL Trees guarantee the balance and performance of the tree. For making the most of this data structure, it is essential to comprehend its construction and operation, including how to correctly insert and rebalance nodes.