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binary search tree; binary tree; binary tree representation of trees; bingo sort; binomial heap; binomial tree; bin packing problem; bin sort; bintree; bipartite graph; bipartite matching; bisector; bitonic sort; bit vector; Bk tree; bdk tree (not to be confused with k-d-B-tree) [2] block; block addressing index; blocking flow; block search ...
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.
Several extensions to the basic structure have been presented in the literature. To reduce the height of the tree, multiary nodes can be used instead of binary. [2] The data structure can be made dynamic, supporting insertions and deletions at arbitrary points of the string; this feature enables the implementation of dynamic FM-indexes. [4]
A binary heap is a heap data structure that takes the form of a binary tree. Binary heaps are a common way of implementing priority queues. [1]: 162–163 The binary heap was introduced by J. W. J. Williams in 1964 as a data structure for implementing heapsort. [2] A binary heap is defined as a binary tree with two additional constraints: [3]
This unsorted tree has non-unique values (e.g., the value 2 existing in different nodes, not in a single node only) and is non-binary (only up to two children nodes per parent node in a binary tree). The root node at the top (with the value 2 here), has no parent as it is the highest in the tree hierarchy.
Thus at each step one can either go down (append a (, 1) to the end) or go right (add one to the last number) (except the root, which is extra and can only go down), which shows the correspondence between the infinite binary tree and the above numbering; the sum of the entries (minus one) corresponds to the distance from the root, which agrees ...
In computing, a threaded binary tree is a binary tree variant that facilitates traversal in a particular order. An entire binary search tree can be easily traversed in order of the main key, but given only a pointer to a node, finding the node which comes next may be slow or impossible. For example, leaf nodes by definition have no descendants ...
The size of an internal node is the sum of sizes of its two children, plus one: (size[n] = size[n.left] + size[n.right] + 1). Based on the size, one defines the weight to be weight[n] = size[n] + 1. [a] Weight has the advantage that the weight of a node is simply the sum of the weights of its left and right children. Binary tree rotations.