Search results
Results from the WOW.Com Content Network
In a binary tree the balance factor of a node X is defined to be the height difference ():= (()) (()) [6]: 459 of its two child sub-trees rooted by node X. A node X with () < is called "left-heavy", one with () > is called "right-heavy", and one with () = is sometimes simply called "balanced".
Various height-balanced binary search trees were introduced to confine the tree height, such as AVL trees, Treaps, and red–black trees. [5] The AVL tree was invented by Georgy Adelson-Velsky and Evgenii Landis in 1962 for the efficient organization of information. [6] [7] It was the first self-balancing binary search tree to be invented. [8]
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.
A node is α-weight-balanced if weight[n.left] ≥ α·weight[n] and weight[n.right] ≥ α·weight[n]. [7] Here, α is a numerical parameter to be determined when implementing weight balanced trees. Larger values of α produce "more balanced" trees, but not all values of α are appropriate; Nievergelt and Reingold proved that
A balanced binary tree is a binary tree structure in which the left and right subtrees of every node differ in height (the number of edges from the top-most node to the farthest node in a subtree) by no more than 1 (or the skew is no greater than 1). [22]
A B-tree of depth n+1 can hold about U times as many items as a B-tree of depth n, but the cost of search, insert, and delete operations grows with the depth of the tree. As with any balanced tree, the cost grows much more slowly than the number of elements.
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 ...
Language links are at the top of the page. Search. Search