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Segment Tree
In computer science, a segment tree, also known as a statistic tree, is a tree data structure used for storing information about intervals, or segments. It allows querying which of the stored segments contain a given point. It is, in principle, a static structure and cannot be modified once built. A similar data structure is the interval tree. A segment tree for a set of ''n'' intervals uses ''O''(''n'' log ''n'') storage and can be built in ''O''(''n'' log ''n'') time. Segment trees support searching for all the intervals that contain a query point in time ''O''(log ''n'' + ''k''), ''k'' being the number of retrieved intervals or segments. Applications of the segment tree are in the areas of computational geometry, geographic information systems and machine learning. The segment tree can be generalized to higher dimension spaces. Definition Description Let ''S'' be a set of intervals, or segments. Let ''p''1, ''p''2, ..., ''pm'' be the list of distinct interval endpoin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Segment Tree
In computer science, a segment tree, also known as a statistic tree, is a tree data structure used for storing information about intervals, or segments. It allows querying which of the stored segments contain a given point. It is, in principle, a static structure and cannot be modified once built. A similar data structure is the interval tree. A segment tree for a set of ''n'' intervals uses ''O''(''n'' log ''n'') storage and can be built in ''O''(''n'' log ''n'') time. Segment trees support searching for all the intervals that contain a query point in time ''O''(log ''n'' + ''k''), ''k'' being the number of retrieved intervals or segments. Applications of the segment tree are in the areas of computational geometry, geographic information systems and machine learning. The segment tree can be generalized to higher dimension spaces. Definition Description Let ''S'' be a set of intervals, or segments. Let ''p''1, ''p''2, ..., ''pm'' be the list of distinct interval endpoin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Tree
In computer science, a binary tree is a k-ary k = 2 tree data structure in which each node has at most two children, which are referred to as the ' and the '. A recursive definition using just set theory notions is that a (non-empty) 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. Some authors allow the binary tree to be the empty set as well. From a graph theory perspective, binary (and K-ary) trees as defined here are arborescences. A binary tree may thus be also called a bifurcating arborescence—a term which appears in some very old programming books, before the modern computer science terminology prevailed. It is also possible to interpret a binary tree as an undirected, rather than a directed graph, in which case a binary tree is an ordered, rooted tree. Some authors use rooted binary tree instead of ''binary tree'' to emphasize the fact that the tree is rooted, bu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trees (data Structures)
In botany, a tree is a perennial plant with an elongated stem, or trunk, usually supporting branches and leaves. In some usages, the definition of a tree may be narrower, including only woody plants with secondary growth, plants that are usable as lumber or plants above a specified height. In wider definitions, the taller palms, tree ferns, bananas, and bamboos are also trees. Trees are not a taxonomic group but include a variety of plant species that have independently evolved a trunk and branches as a way to tower above other plants to compete for sunlight. The majority of tree species are angiosperms or hardwoods; of the rest, many are gymnosperms or softwoods. Trees tend to be long-lived, some reaching several thousand years old. Trees have been in existence for 370 million years. It is estimated that there are some three trillion mature trees in the world. A tree typically has many secondary branches supported clear of the ground by the trunk. This trunk typically co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jon Bentley (computer Scientist)
Jon Louis Bentley (born February 20, 1953) is an American computer scientist who is credited with the heuristic-based partitioning algorithm ''k''-d tree. Education and career Bentley received a B.S. in mathematical sciences from Stanford University in 1974, and M.S. and PhD in 1976 from the University of North Carolina at Chapel Hill; while a student, he also held internships at the Xerox Palo Alto Research Center and Stanford Linear Accelerator Center. After receiving his Ph.D., he joined the faculty at Carnegie Mellon University as an assistant professor of computer science and mathematics. At CMU, his students included Brian Reid, John Ousterhout, Jeff Eppinger, Joshua Bloch, and James Gosling, and he was one of Charles Leiserson's advisors. Later, Bentley moved to Bell Laboratories, where he co-authored an optimized Quicksort algorithm with Doug McIlroy. He found an optimal solution for the two dimensional case of Klee's measure problem: given a set of ''n'' rectangles, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Priority Search Tree
In computer science, a priority search tree is a tree data structure for storing points in two dimensions. It was originally introduced by Edward M. McCreight. It is effectively an extension of the priority queue with the purpose of improving the search time from O(''n'') to O(''s'' + log ''n'') time, where ''n'' is the number of points in the tree and ''s'' is the number of points returned by the search. Description The priority search tree is used to store a set of 2-dimensional points ordered by priority and by a key value. This is accomplished by creating a hybrid of a priority queue and a binary search tree. The result is a tree where each node represents a point in the original dataset. The point contained by the node is the one with the lowest priority. In addition, each node also contains a key value used to divide the remaining points (usually the median of the keys, excluding the point of the node) into a left and right subtree. The points are divided by comparing t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fractional Cascading
In computer science, fractional cascading is a technique to speed up a sequence of binary searches for the same value in a sequence of related data structures. The first binary search in the sequence takes a logarithmic amount of time, as is standard for binary searches, but successive searches in the sequence are faster. The original version of fractional cascading, introduced in two papers by Chazelle and Guibas in 1986 (; ), combined the idea of cascading, originating in range searching data structures of and , with the idea of fractional sampling, which originated in . Later authors introduced more complex forms of fractional cascading that allow the data structure to be maintained as the data changes by a sequence of discrete insertion and deletion events. Example As a simple example of fractional cascading, consider the following problem. We are given as input a collection of ''k'' ordered lists ''Li'' of numbers, such that the total length Σ, ''Li'', of all lists is ''n' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linked List
In computer science, a linked list is a linear collection of data elements whose order is not given by their physical placement in memory. Instead, each element points to the next. It is a data structure consisting of a collection of nodes which together represent a sequence. In its most basic form, each node contains: data, and a reference (in other words, a ''link'') to the next node in the sequence. This structure allows for efficient insertion or removal of elements from any position in the sequence during iteration. More complex variants add additional links, allowing more efficient insertion or removal of nodes at arbitrary positions. A drawback of linked lists is that access time is linear (and difficult to pipeline). Faster access, such as random access, is not feasible. Arrays have better cache locality compared to linked lists. Linked lists are among the simplest and most common data structures. They can be used to implement several other common abstract data types, in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Union (set Theory)
In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection. It is one of the fundamental operations through which sets can be combined and related to each other. A refers to a union of zero (0) sets and it is by definition equal to the empty set. For explanation of the symbols used in this article, refer to the table of mathematical symbols. Union of two sets The union of two sets ''A'' and ''B'' is the set of elements which are in ''A'', in ''B'', or in both ''A'' and ''B''. In set-builder notation, :A \cup B = \. For example, if ''A'' = and ''B'' = then ''A'' ∪ ''B'' = . A more elaborate example (involving two infinite sets) is: : ''A'' = : ''B'' = : A \cup B = \ As another example, the number 9 is ''not'' contained in the union of the set of prime numbers and the set of even numbers , because 9 is neither prime nor even. Sets cannot have duplicate elements, so the union of the sets and is . Multip ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Internal Node
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. 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 in a single straight line. Binary trees are a commonly used type, which constrain the number of children for each parent to exactly two. When the order of the children is specified, this data structure corresponds to an ordered tree in graph theory. A value or pointer to other data may be associated with every node in the tree, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leaf Node
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. 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 in a single straight line. Binary trees are a commonly used type, which constrain the number of children for each parent to exactly two. When the order of the children is specified, this data structure corresponds to an ordered tree in graph theory. A value or pointer to other data may be associated with every node in the tree ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dimension
In physics and mathematics, the dimension of a Space (mathematics), mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any Point (geometry), point within it. Thus, a Line (geometry), line has a dimension of one (1D) because only one coordinate is needed to specify a point on itfor example, the point at 5 on a number line. A Surface (mathematics), surface, such as the Boundary (mathematics), boundary of a Cylinder (geometry), cylinder or sphere, has a dimension of two (2D) because two coordinates are needed to specify a point on itfor example, both a latitude and longitude are required to locate a point on the surface of a sphere. A two-dimensional Euclidean space is a two-dimensional space on the Euclidean plane, plane. The inside of a cube, a cylinder or a sphere is three-dimensional (3D) because three coordinates are needed to locate a point within these spaces. In classical mechanics, space and time are different categ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical disciplines (including the design and implementation of Computer architecture, hardware and Computer programming, software). Computer science is generally considered an area of research, academic research and distinct from computer programming. Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of computational problem, problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and for preventing Vulnerability (computing), security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Progr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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