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Often trees have a fixed (more properly, bounded) branching factor , particularly always having two child nodes (possibly empty, hence at most two non-empty child nodes), hence a "binary tree". Allowing empty trees makes some definitions simpler, some more complicated: a rooted tree must be non-empty, hence if empty trees are allowed the above ...
the empty set is an extended binary tree; if T 1 and T 2 are extended binary trees, then denote by T 1 • T 2 the extended binary tree obtained by adding a root r connected to the left to T 1 and to the right to T 2 [clarification needed where did the 'r' go in the 'T 1 • T 2 ' symbol] by adding edges when these sub-trees are non-empty.
The B-tree generalizes the binary search tree, allowing for nodes with more than two children. [2] Unlike other self-balancing binary search trees, the B-tree is well suited for storage systems that read and write relatively large blocks of data, such as databases and file systems.
A B+ tree consists of a root, internal nodes and leaves. [1] The root may be either a leaf or a node with two or more children. A B+ tree can be viewed as a B-tree in which each node contains only keys (not key–value pairs), and to which an additional level is added at the bottom with linked leaves.
Patricia trees are a particular implementation of the compressed binary trie that uses the binary encoding of the string keys in its representation. [23] [15]: 140 Every node in a Patricia tree contains an index, known as a "skip number", that stores the node's branching index to avoid empty subtrees during traversal.
Join: The function Join is on two weight-balanced trees t 1 and t 2 and a key k and will return a tree containing all elements in t 1, t 2 as well as k. It requires k to be greater than all keys in t 1 and smaller than all keys in t 2. If the two trees have the balanced weight, Join simply create a new node with left subtree t 1, root k and ...
Fig. 1: AVL tree with balance factors (green) In computer science, an AVL tree (named after inventors Adelson-Velsky and Landis) is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; if at any time they differ by more than one, rebalancing is done to restore this property.
A tournament tree can be represented as a balanced binary tree by adding sentinels to the input lists (i.e. adding a member to the end of each list with a value of infinity) and by adding null lists (comprising only a sentinel) until the number of lists is a power of two. The balanced tree can be stored in a single array.