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In computer science, a binary search tree (BST), also called an ordered or sorted binary tree, is a rooted binary tree data structure with the key of each internal node being greater than all the keys in the respective node's left subtree and less than the ones in its right subtree. The time complexity of operations on the binary search tree is linear with respect to the height of the tree.
In computer science, a binary tree is a tree data structure in which each node has at most two children, referred to as the left child and the right child. That is, it is a k-ary tree with k = 2. A recursive definition using set theory is that a binary tree is a tuple (L, S, R), where L and R are binary trees or the empty set and S is a singleton set containing the root.
In computer science, a B-tree is a self-balancing tree data structure that maintains sorted data and allows searches, sequential access, insertions, and deletions in logarithmic time. The B-tree generalizes the binary search tree, allowing for nodes with more than two children. 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.
In computer science, a tree is a widely used abstract data type that represents a hierarchical tree structure with a set of connected nodes. Each node in the tree can be connected to many children, but must be connected to exactly one parent, except for the root node, which has no parent. These constraints mean there are no cycles or "loops", and also that each child can be treated like the root node of its own subtree, making recursion a useful technique for tree traversal. In contrast to linear data structures, many trees cannot be represented by relationships between neighboring nodes in a single straight line.
A parse tree or parsing tree is an ordered, rooted tree that represents the syntactic structure of a string according to some context-free grammar. The term parse tree itself is used primarily in computational linguistics; in theoretical syntax, the term syntax tree is more common.
Alpha–beta pruning is a search algorithm that seeks to decrease the number of nodes that are evaluated by the minimax algorithm in its search tree. It is an adversarial search algorithm used commonly for machine playing of two-player combinatorial games. It stops evaluating a move when at least one possibility has been found that proves the move to be worse than a previously examined move. Such moves need not be evaluated further. When applied to a standard minimax tree, it returns the same move as minimax would, but prunes away branches that cannot possibly influence the final decision.
A decision tree is a decision support hierarchical model that uses a tree-like model of decisions and their possible consequences, including chance event outcomes, resource costs, and utility. It is one way to display an algorithm that only contains conditional control statements.
In computer science, the treap and the randomized binary search tree are two closely related forms of binary search tree data structures that maintain a dynamic set of ordered keys and allow binary searches among the keys. After any sequence of insertions and deletions of keys, the shape of the tree is a random variable with the same probability distribution as a random binary tree; in particular, with high probability its height is proportional to the logarithm of the number of keys, so that each search, insertion, or deletion operation takes logarithmic time to perform.
In computer science, a tagged union, also called a variant, variant record, choice type, discriminated union, disjoint union, sum type, or coproduct, is a data structure used to hold a value that could take on several different, but fixed, types. Only one of the types can be in use at any one time, and a tag field explicitly indicates which type is in use. It can be thought of as a type that has several "cases", each of which should be handled correctly when that type is manipulated. This is critical in defining recursive datatypes, in which some component of a value may have the same type as that value, for example in defining a type for representing trees, where it is necessary to distinguish multi-node subtrees and leaves. Like ordinary unions, tagged unions can save storage by overlapping storage areas for each type, since only one is in use at a time.
In computer science, tree traversal is a form of graph traversal and refers to the process of visiting each node in a tree data structure, exactly once. Such traversals are classified by the order in which the nodes are visited. The following algorithms are described for a binary tree, but they may be generalized to other trees as well.
In computer science, a 2–3 tree is a tree data structure, where every node with children has either two children (2-node) and one data element or three children (3-node) and two data elements. A 2–3 tree is a B-tree of order 3. Nodes on the outside of the tree have no children and one or two data elements. 2–3 trees were invented by John Hopcroft in 1970.
R-trees are tree data structures used for spatial access methods, i.e., for indexing multi-dimensional information such as geographical coordinates, rectangles or polygons. The R-tree was proposed by Antonin Guttman in 1984 and has found significant use in both theoretical and applied contexts. A common real-world usage for an R-tree might be to store spatial objects such as restaurant locations or the polygons that typical maps are made of: streets, buildings, outlines of lakes, coastlines, etc. and then find answers quickly to queries such as "Find all museums within 2 km of my current location", "retrieve all road segments within 2 km of my location" or "find the nearest gas station". The R-tree can also accelerate nearest neighbor search for various distance metrics, including great-circle distance.
Adaptive Huffman coding is an adaptive coding technique based on Huffman coding. It permits building the code as the symbols are being transmitted, having no initial knowledge of source distribution, that allows one-pass encoding and adaptation to changing conditions in data.
In computer science, a 2–3–4 tree is a self-balancing data structure that can be used to implement dictionaries. The numbers mean a tree where every node with children has either two, three, or four child nodes:
A B+ tree is an m-ary tree with a variable but often large number of children per node. A B+ tree consists of a root, internal nodes and leaves. The root may be either a leaf or a node with two or more children.
In computer science, a radix tree is a data structure that represents a space-optimized trie in which each node that is the only child is merged with its parent. The result is that the number of children of every internal node is at most the radix r of the radix tree, where r = 2x for some integer x ≥ 1. Unlike regular trees, edges can be labeled with sequences of elements as well as single elements. This makes radix trees much more efficient for small sets and for sets of strings that share long prefixes.
An AA tree in computer science is a form of balanced tree used for storing and retrieving ordered data efficiently. AA trees are named after their originator, Swedish computer scientist Arne Andersson.
In cryptography and computer science, a hash tree or Merkle tree is a tree in which every "leaf" node is labelled with the cryptographic hash of a data block, and every node that is not a leaf is labelled with the cryptographic hash of the labels of its child nodes. A hash tree allows efficient and secure verification of the contents of a large data structure. A hash tree is a generalization of a hash list and a hash chain.
In computer science, a leftist tree or leftist heap is a priority queue implemented with a variant of a binary heap. Every node x has an s-value which is the distance to the nearest leaf in subtree rooted at x. In contrast to a binary heap, a leftist tree attempts to be very unbalanced. In addition to the heap property, leftist trees are maintained so the right descendant of each node has the lower s-value.
Hilbert R-tree, an R-tree variant, is an index for multidimensional objects such as lines, regions, 3-D objects, or high-dimensional feature-based parametric objects. It can be thought of as an extension to B+-tree for multidimensional objects.
References
- ↑ "Leafnode 1.12.0". 26 May 2022. Retrieved 2 Sep 2024.
- ↑ "Sourceforge summary page" . Retrieved 7 Apr 2021.
- ↑ "Debian copyright file" . Retrieved 7 Apr 2021.
- ↑ Krasel, Cornelius. "Leafnode FAQ". Leafnode. Retrieved 2006-08-15.
