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Red–black Tree
In computer science, a red–black tree is a self-balancing binary search tree data structure noted for fast storage and retrieval of ordered information. The nodes in a red-black tree hold an extra "color" bit, often drawn as red and black, which help ensure that the tree is always approximately balanced. When the tree is modified, the new tree is rearranged and "repainted" to restore the coloring properties that constrain how unbalanced the tree can become in the worst case. The properties are designed such that this rearranging and recoloring can be performed efficiently. The (re-)balancing is not perfect, but guarantees searching in O(\log n) time, where n is the number of entries in the tree. The insert and delete operations, along with tree rearrangement and recoloring, also execute in O(\log n) time. Tracking the color of each node requires only one bit of information per node because there are only two colors (due to memory alignment present in some programming languag ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Left-leaning Red–black Tree
A left-leaning red–black (LLRB) tree is a type of self-balancing binary search tree, introduced by Robert Sedgewick (computer scientist), Robert Sedgewick. It is a variant of the red–black tree and guarantees the same asymptotic complexity for operations, but is designed to be easier to implement. Properties A left-leaning red-black tree satisfies all the properties of a red-black tree: # Every node is either red or black. # A NIL node is considered black. # A red node does not have a red child. # Every Path (graph theory), path from a given node to any of its descendant NIL nodes goes through the same number of black nodes. # The root is black (by convention). Additionally, the left-leaning property states that: # If a node has only one red child, it must be the left child. The left-leaning property reduces the number of cases that must be considered when implementing search tree operations. Relation to 2–3 and 2–3–4 trees LLRB trees are isomorphic 2–3–4 tr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tree (data Structure)
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 (depending on the type of tree), but must be connected to exactly one parent, except for the ''root'' node, which has no parent (i.e., the root node as the top-most node in the tree hierarchy). These constraints mean there are no cycles or "loops" (no node can be its own ancestor), 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 (parent and children nodes of a node under consideration, if they exist) in a single straight line (called edge or link between two adjacent nodes). Binary trees are a commonly used type, which constrain the number of children for each parent to at most two. Whe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Red-black Trees And 2–3–4 Trees
Red-black or Redblack may refer to: * Ottawa Redblacks, a Canadian football team * Red/black concept, a concept in cryptography * Red-black striped snake, a colubrid snake * Red–black tree In computer science, a red–black tree is a self-balancing binary search tree data structure noted for fast storage and retrieval of ordered information. The nodes in a red-black tree hold an extra "color" bit, often drawn as red and black, wh ..., a type of self-balancing binary search tree used in computer science See also * Black and Red (other) * Red and Black (other) {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Access
Random access (also called direct access) is the ability to access an arbitrary element of a sequence in equal time or any datum from a population of addressable elements roughly as easily and efficiently as any other, no matter how many elements may be in the set. In computer science it is typically contrasted to sequential access which requires data to be retrieved in the order it was stored. For example, data might be stored notionally in a single sequence like a row, in two dimensions like rows and columns on a surface, or in multiple dimensions. However, given all the coordinates, a program can access each record about as quickly and easily as any other. In this sense, the choice of datum is arbitrary in the sense that no matter which item is sought, all that is needed to find it is its address, i.e. the coordinates at which it is located, such as its row and column (or its track and record number on a magnetic drum). At first, the term "random access" was used because th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
In-order Traversal
In computer science, tree traversal (also known as tree search and walking the tree) is a form of graph traversal and refers to the process of visiting (e.g. retrieving, updating, or deleting) 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. Types Unlike linked lists, one-dimensional arrays and other linear data structures, which are canonically traversed in linear order, trees may be traversed in multiple ways. They may be traversed in depth-first or breadth-first order. There are three common ways to traverse them in depth-first order: in-order, pre-order and post-order. Beyond these basic traversals, various more complex or hybrid schemes are possible, such as depth-limited searches like iterative deepening depth-first search. The latter, as well as breadth-first search, can also be use ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proof Of Bounds
Proof most often refers to: * Proof (truth), argument or sufficient evidence for the truth of a proposition * Alcohol proof, a measure of an alcoholic drink's strength Proof may also refer to: Mathematics and formal logic * Formal proof, a construct in proof theory * Mathematical proof, a convincing demonstration that some mathematical statement is necessarily true * Proof complexity, computational resources required to prove statements * Proof procedure, method for producing proofs in proof theory * Proof theory, a branch of mathematical logic that represents proofs as formal mathematical objects * Statistical proof, demonstration of degree of certainty for a hypothesis Law and philosophy * Evidence, information which tends to determine or demonstrate the truth of a proposition * Evidence (law), tested evidence or a legal proof * Legal burden of proof, duty to establish the truth of facts in a trial * Philosophic burden of proof, obligation on a party in a dispute to provide ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
AVL Tree
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. Lookup, insertion, and deletion all take time in both the average and worst cases, where n is the number of nodes in the tree prior to the operation. Insertions and deletions may require the tree to be rebalanced by one or more tree rotations. The AVL tree is named after its two Soviet inventors, Georgy Adelson-Velsky and Evgenii Landis, who published it in their 1962 paper "An algorithm for the organization of information". It is the first self-balancing binary search tree data structure to be invented. AVL trees are often compared with red–black trees because both support the same set of operations and take \text(\log n) time for the basic operations. For lookup-intensiv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logarithmic Growth
In mathematics, logarithmic growth describes a phenomenon whose size or cost can be described as a logarithm function of some input. e.g. ''y'' = ''C'' log (''x''). Any logarithm base can be used, since one can be converted to another by multiplying by a fixed constant.. Logarithmic growth is the inverse of exponential growth and is very slow. A familiar example of logarithmic growth is a number, ''N'', in positional notation, which grows as log''b'' (''N''), where ''b'' is the base of the number system used, e.g. 10 for decimal arithmetic. In more advanced mathematics, the partial sums of the harmonic series :1+\frac+\frac+\frac+\frac+\cdots grow logarithmically. In the design of computer algorithms, logarithmic growth, and related variants, such as log-linear, or linearithmic, growth are very desirable indications of efficiency, and occur in the time complexity analysis of algorithms such as binary search. Logarithmic growth can lead to apparent paradoxes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Height-balanced Binary Search Tree
In computer science, a self-balancing binary search tree (BST) 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.Donald Knuth. ''The Art of Computer Programming'', Volume 3: ''Sorting and Searching'', Second Edition. Addison-Wesley, 1998. . Section 6.2.3: Balanced Trees, pp.458–481. These operations when designed for a self-balancing binary search tree, contain precautionary measures against boundlessly increasing tree height, so that these abstract data structures receive the attribute "self-balancing". For height-balanced binary trees, the height is defined to be logarithmic O(\log n) in the number n 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. Self-balancin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simple Cases
Simple or SIMPLE may refer to: *Simplicity, the state or quality of being simple Arts and entertainment * ''Simple'' (album), by Andy Yorke, 2008, and its title track * "Simple" (Florida Georgia Line song), 2018 * "Simple", a song by Johnny Mathis from the 1984 album ''A Special Part of Me'' * "Simple", a song by Collective Soul from the 1995 album ''Collective Soul'' * "Simple", a song by Katy Perry from the 2005 soundtrack to ''The Sisterhood of the Traveling Pants'' * "Simple", a song by Khalil from the 2017 album ''Prove It All'' * "Simple", a song by Kreesha Turner from the 2008 album '' Passion'' * "Simple", a song by Ty Dolla Sign from the 2017 album ''Beach House 3'' deluxe version * ''Simple'' (video game series), budget-priced console games Businesses and organisations * Simple (bank), an American direct bank * SIMPLE Group, a consulting conglomeration based in Gibraltar * Simple Shoes, an American footwear brand * Simple Skincare, a British brand of soap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Insertion
Insertion may refer to: *Insertion (anatomy), the point of a tendon or ligament onto the skeleton or other part of the body *Insertion (genetics), the addition of DNA into a genetic sequence *Insertion, several meanings in medicine, see ICD-10-PCS *Insertion loss, in electronics *Insertion reaction, a chemical reaction in which one chemical entity interposes itself into an existing bond of a second chemical entity (''e.g.'': + → ) *Insertion sort, a simple computer algorithm for sorting arrays *Local insertion In broadcasting, local insertion (known in the United Kingdom as an opt-out) is the act or capability of a broadcast television station, radio station or cable system to insert or replace part of a network feed with content unique to the local s ..., in broadcasting * Insertion of a character in a string, one of the single-character edits used to define the Levenshtein distance See also * Insert (other) {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
