The pseudocode that you’ve posted will correctly balance a tree. That said, it is too inefficient to be practical – notice that you’re recursively exploring the entire tree trying to do rebalancing operations, which will make all insertions and deletions take O(n) time, eating away all the efficiency gains of having a balanced tree. The … Read more
Assuming you may destroy the input trees: remove the rightmost element for the left tree, and use it to construct a new root node, whose left child is the left tree, and whose right child is the right tree: O(log n) determine and set that node’s balance factor: O(log n). In (temporary) violation of the … Read more
AVL trees are intended for in-memory use, where random access is relatively cheap. B-trees are better suited for disk-backed storage, because they group a larger number of keys into each node to minimize the number of seeks required by a read or write operation. (This is why B-trees are often used in file systems and … Read more
To answer your questions: What is the difference between AVL trees and splay trees? Both splay trees and AVL trees are binary search trees with excellent performance guarantees, but they differ in how they achieve those guarantee that performance. In an AVL tree, the shape of the tree is constrained at all times such that … Read more
Part 1 – height As starblue says, height is just recursive. In pseudo-code: height(node) = max(height(node.L), height(node.R)) + 1 Now height could be defined in two ways. It could be the number of nodes in the path from the root to that node, or it could be the number of links. According to the page … Read more
These are basically research topics, and the results are generally given in the form of conclusions, while the statistical data is hidden. One can have statistical analysis on their own data though. For the benchmarks, better go through the implementation details. The 3rd part of the question is a very subjective matter, and the actual … Read more
AVL trees maintain a more rigid balance than red-black trees. The path from the root to the deepest leaf in an AVL tree is at most ~1.44 lg(n+2), while in red black trees it’s at most ~2 lg (n+1). As a result, lookup in an AVL tree is typically faster, but this comes at the … Read more
Take this with a pinch of salt: B-tree when you’re managing more than thousands of items and you’re paging them from a disk or some slow storage medium. RB tree when you’re doing fairly frequent inserts, deletes and retrievals on the tree. AVL tree when your inserts and deletes are infrequent relative to your retrievals.