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# Binary tree

In computer science, a binary tree is a tree data structure in which each node has at most two children, which are referred to as the and the. 

76 relations: AA tree, Ahnentafel, Arborescence (graph theory), Array data structure, AVL tree, B-tree, Bijection, Binary heap, Binary search tree, Binary space partitioning, Breadth-first search, Cantor set, Cardinality of the continuum, Catalan number, Chapman & Hall, Cladogram, Combinatorics, Computer science, Countable set, Data structure, Depth-first search, Dictionary of Algorithms and Data Structures, Directed graph, Donald Knuth, Dyck language, Empty set, Encyclopedia of Mathematics, Family tree, Floor and ceiling functions, Graph (discrete mathematics), Graph theory, Huffman coding, Implicit data structure, Information theory, Irrational number, K-ary tree, Kraft–McMillan inequality, Left-child right-sibling binary tree, Linked list, Lisp (programming language), Locality of reference, Magma (algebra), ML (programming language), Mutator method, National Institute of Standards and Technology, Null pointer, OCaml, Optimal binary search tree, Programming language, Random binary tree, ... Expand index (26 more) »

## AA tree

An AA tree in computer science is a form of balanced tree used for storing and retrieving ordered data efficiently.

## Ahnentafel

An ahnentafel (German for "ancestor table") or ahnenreihe ("ancestor series") is a genealogical numbering system for listing a person's direct ancestors in a fixed sequence of ascent.

## Arborescence (graph theory)

In graph theory, an arborescence is a directed graph in which, for a vertex u called the root and any other vertex v, there is exactly one directed path from u to v. An arborescence is thus the directed-graph form of a rooted tree, understood here as an undirected graph.

## Array data structure

In computer science, an array data structure, or simply an array, is a data structure consisting of a collection of elements (values or variables), each identified by at least one array index or key.

## AVL tree

In computer science, an AVL tree (named after inventors Adelson-Velsky and Landis) is a self-balancing binary search tree.

## B-tree

In computer science, a B-tree is a self-balancing tree data structure that keeps data sorted and allows searches, sequential access, insertions, and deletions in logarithmic time.

## Bijection

In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set.

## Binary heap

A binary heap is a heap data structure that takes the form of a binary tree.

## Binary search tree

In computer science, binary search trees (BST), sometimes called ordered or sorted binary trees, are a particular type of container: data structures that store "items" (such as numbers, names etc.) in memory.

## Binary space partitioning

In computer science, binary space partitioning (BSP) is a method for recursively subdividing a space into convex sets by hyperplanes.

Breadth-first search (BFS) is an algorithm for traversing or searching tree or graph data structures.

## Cantor set

In mathematics, the Cantor set is a set of points lying on a single line segment that has a number of remarkable and deep properties.

## Cardinality of the continuum

In set theory, the cardinality of the continuum is the cardinality or “size” of the set of real numbers \mathbb R, sometimes called the continuum.

## Catalan number

In combinatorial mathematics, the Catalan numbers form a sequence of natural numbers that occur in various counting problems, often involving recursively-defined objects.

## Chapman & Hall

Chapman & Hall was a British publishing house in London, founded in the first half of the 19th century by Edward Chapman and William Hall.

A cladogram (from Greek clados "branch" and gramma "character") is a diagram used in cladistics to show relations among organisms.

## Combinatorics

Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures.

## Computer science

Computer science deals with the theoretical foundations of information and computation, together with practical techniques for the implementation and application of these foundations.

## Countable set

In mathematics, a countable set is a set with the same cardinality (number of elements) as some subset of the set of natural numbers.

## Data structure

In computer science, a data structure is a data organization and storage format that enables efficient access and modification.

## Depth-first search

Depth-first search (DFS) is an algorithm for traversing or searching tree or graph data structures.

## Dictionary of Algorithms and Data Structures

The Dictionary of Algorithms and Data Structures is a dictionary style reference for many of the algorithms, algorithmic techniques, archetypal problems, and data structures found in the field of computer science.

## Directed graph

In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is a set of vertices connected by edges, where the edges have a direction associated with them.

## Donald Knuth

Donald Ervin Knuth (born January 10, 1938) is an American computer scientist, mathematician, and professor emeritus at Stanford University.

## Dyck language

In the theory of formal languages of computer science, mathematics, and linguistics, a Dyck word is a balanced string of square brackets.

## Empty set

In mathematics, and more specifically set theory, the empty set or null set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero.

## Encyclopedia of Mathematics

The Encyclopedia of Mathematics (also EOM and formerly Encyclopaedia of Mathematics) is a large reference work in mathematics.

## Family tree

A family tree, or pedigree chart, is a chart representing family relationships in a conventional tree structure.

## Floor and ceiling functions

In mathematics and computer science, the floor function is the function that takes as input a real number x and gives as output the greatest integer less than or equal to x, denoted \operatorname(x).

## Graph (discrete mathematics)

In mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".

## Graph theory

In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.

## Huffman coding

In computer science and information theory, a Huffman code is a particular type of optimal prefix code that is commonly used for lossless data compression.

## Implicit data structure

In computer science, an implicit data structure or space-efficient data structure is a data structure that stores very little information other than the main or required data: a data structure that requires low overhead.

## Information theory

Information theory studies the quantification, storage, and communication of information.

## Irrational number

In mathematics, the irrational numbers are all the real numbers which are not rational numbers, the latter being the numbers constructed from ratios (or fractions) of integers.

## K-ary tree

In graph theory, a k-ary tree is a rooted tree in which each node has no more than k children.

## Kraft–McMillan inequality

In coding theory, the Kraft–McMillan inequality gives a necessary and sufficient condition for the existence of a prefix code (in Leon G. Kraft's version) or a uniquely decodable code (in Brockway McMillan's version) for a given set of codeword lengths.

## Left-child right-sibling binary tree

Every multi-way or k-ary tree structure studied in computer science admits a representation as a binary tree, which goes by various names including child-sibling representation, left-child, right-sibling binary tree, doubly chained tree or filial-heir chain.

In computer science, a linked list is a linear collection of data elements, whose order is not given by their physical placement in memory.

## Lisp (programming language)

Lisp (historically, LISP) is a family of computer programming languages with a long history and a distinctive, fully parenthesized prefix notation.

## Locality of reference

In computer science, locality of reference, also known as the principle of locality, is a term for the phenomenon in which the same values, or related storage locations, are frequently accessed, depending on the memory access pattern.

## Magma (algebra)

In abstract algebra, a magma (or groupoid; not to be confused with groupoids in category theory) is a basic kind of algebraic structure.

## ML (programming language)

ML (Meta Language) is a general-purpose functional programming language.

## Mutator method

In computer science, a mutator method is a method used to control changes to a variable.

## National Institute of Standards and Technology

The National Institute of Standards and Technology (NIST) is one of the oldest physical science laboratories in the United States.

## Null pointer

In computing, a null pointer has a value reserved for indicating that the pointer does not refer to a valid object.

## OCaml

OCaml, originally named Objective Caml, is the main implementation of the programming language Caml, created by Xavier Leroy, Jérôme Vouillon, Damien Doligez, Didier Rémy, Ascánder Suárez and others in 1996.

## Optimal binary search tree

In computer science, an optimal binary search tree (Optimal BST), sometimes called a weight-balanced binary tree, is a binary search tree which provides the smallest possible search time (or expected search time) for a given sequence of accesses (or access probabilities).

## Programming language

A programming language is a formal language that specifies a set of instructions that can be used to produce various kinds of output.

## Random binary tree

In computer science and probability theory, a random binary tree is a binary tree selected at random from some probability distribution on binary trees.

## Record (computer science)

In computer science, a record (also called a structure, struct, or compound data) is a basic data structure.

## Recursion (computer science)

Recursion in computer science is a method of solving a problem where the solution depends on solutions to smaller instances of the same problem (as opposed to iteration).

## Recursive definition

A recursive definition (or inductive definition) in mathematical logic and computer science is used to define the elements in a set in terms of other elements in the set (Aczel 1978:740ff).

## Red–black tree

A red–black tree is a kind of self-balancing binary search tree in computer science.

## Reference (computer science)

In computer science, a reference is a value that enables a program to indirectly access a particular datum, such as a variable's value or a record, in the computer's memory or in some other storage device.

## Rope (data structure)

In computer programming, a rope, or cord, is a data structure composed of smaller strings that is used to efficiently store and manipulate a very long string.

## Search algorithm

In computer science, a search algorithm is any algorithm which solves the search problem, namely, to retrieve information stored within some data structure, or calculated in the search space of a problem domain.

## Self-balancing binary search tree

In computer science, a self-balancing (or height-balanced) binary search tree is any node-based binary search tree that automatically keeps its height (maximal number of levels below the root) small in the face of arbitrary item insertions and deletions.

## Sentinel node

In computer programming, a sentinel node is a specifically designated node used with linked lists and trees as a traversal path terminator.

## Set theory

Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.

## Singleton (mathematics)

In mathematics, a singleton, also known as a unit set, is a set with exactly one element.

## Sorting algorithm

In computer science, a sorting algorithm is an algorithm that puts elements of a list in a certain order.

## Splay tree

A splay tree is a self-adjusting binary search tree with the additional property that recently accessed elements are quick to access again.

## Stern–Brocot tree

In number theory, the Stern–Brocot tree is an infinite complete binary tree in which the vertices correspond one-for-one to the positive rational numbers, whose values are ordered from the left to the right as in a search tree.

## Strahler number

In mathematics, the Strahler number or Horton–Strahler number of a mathematical tree is a numerical measure of its branching complexity.

## Succinct data structure

In computer science, a succinct data structure is a data structure which uses an amount of space that is "close" to the information-theoretic lower bound, but (unlike other compressed representations) still allows for efficient query operations.

## Tagged union

In computer science, a tagged union, also called a variant, variant record, choice type, discriminated union, disjoint union, or sum type, is a data structure used to hold a value that could take on several different, but fixed, types.

## The Art of Computer Programming

The Art of Computer Programming (sometimes known by its initials TAOCP) is a comprehensive monograph written by Donald Knuth that covers many kinds of programming algorithms and their analysis.

In computing, a threaded binary tree is a binary tree variant that allows fast traversal: given a pointer to a node in a threaded tree, it is possible to cheaply find its in-order successor (and/or predecessor).

## Tree (data structure)

In computer science, a tree is a widely used abstract data type (ADT)—or data structure implementing this ADT—that simulates a hierarchical tree structure, with a root value and subtrees of children with a parent node, represented as a set of linked nodes.

## Tree (graph theory)

In mathematics, and more specifically in graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path.

## Tree structure

A tree structure or tree diagram is a way of representing the hierarchical nature of a structure in a graphical form.

## Tuple

In mathematics, a tuple is a finite ordered list (sequence) of elements.

## Unrooted binary tree

In mathematics and computer science, an unrooted binary tree is an unrooted tree in which each vertex has either one or three neighbors.

## 2–3 tree

In computer science, a 2–3 tree is a tree data structure, where every node with children (internal node) has either two children (2-node) and one data element or three children (3-nodes) and two data elements.

## 2–3–4 tree

In computer science, a 2–3–4 tree (also called a 2–4 tree) is a self-balancing data structure that is commonly used to implement dictionaries.

## References

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