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English: Analysis of data structures, tree compared to hash and array based structures, height balanced tree compared to more perfectly balanced trees, a simple height balanced tree class with test code, comparable statistics for tree performance, statistics of worst case strictly-AVL-balanced trees versus perfect full binary trees.
BATON* - BAlanced m-ary Tree Overlay Network: A height-balanced m-ary search tree extension of BATON with further links for efficiency, fault-tolerance, and load-balancing. nBATON* - null-BAlanced m-ary Tree Overlay Network: A null-balancey m-ary search tree extension of BATON* with up to 50% better performance w.r.t. required routing hops.
For height-balanced binary trees, the height is defined to be logarithmic () in the number of items. This is the case for many binary search trees, such as AVL trees and red–black trees . Splay trees and treaps are self-balancing but not height-balanced, as their height is not guaranteed to be logarithmic in the number of items.
It depends on the balance factor of the sibling Z (the higher child tree in figure 2) whether the height of the subtree decreases by one –and the retracing needs to continue– or does not change (if Z has the balance factor 0) and the whole tree is in AVL-shape.
The height of a node is the length of the longest downward path to a leaf from that node. The height of the root is the height of the tree. The depth of a node is the length of the path to its root (i.e., its root path). Thus the root node has depth zero, leaf nodes have height zero, and a tree with only a single node (hence both a root and ...
The height of an external node is zero, and the height of any internal node is always one plus the maximum of the heights of its two children. Thus, the height function of an AVL tree obeys the constraints of a WAVL tree, and we may convert any AVL tree into a WAVL tree by using the height of each node as its rank. [1] [2]
In order for a tree to function as a search tree, the key for each node must be greater than any keys in subtrees on the left, and less than any keys in subtrees on the right. [1] The advantage of search trees is their efficient search time given the tree is reasonably balanced, which is to say the leaves at either end are of comparable depths ...
A weight-balanced tree is a binary search tree that stores the sizes of subtrees in the nodes. That is, a node has fields key, of any ordered type; value (optional, only for mappings) left, right, pointer to node; size, of type integer. By definition, the size of a leaf (typically represented by a nil pointer) is zero.