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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] |
Trie
In computer science, a trie (, ), also known as a digital tree or prefix tree, is a specialized search tree data structure used to store and retrieve strings from a dictionary or set. Unlike a binary search tree, nodes in a trie do not store their associated key. Instead, each node's ''position'' within the trie determines its associated key, with the connections between nodes defined by individual Character (computing), characters rather than the entire key. Tries are particularly effective for tasks such as autocomplete, spell checking, and IP routing, offering advantages over hash tables due to their prefix-based organization and lack of hash collisions. Every child node shares a common prefix (computer science), prefix with its parent node, and the root node represents the empty string. While basic trie implementations can be memory-intensive, various optimization techniques such as compression and bitwise representations have been developed to improve their efficiency. A n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Node (computer Science)
A node is a basic unit of a data structure, such as a linked list or Tree (data structure), tree data structure. Nodes contain data and also may link to other nodes. Links between nodes are often implemented by Pointer (computer programming), pointers. Nodes and trees Nodes are often arranged into tree structures. A node represents the information contained in a single data structure. These nodes may contain a value or condition, or possibly serve as another independent data structure. Nodes are represented by a single parent node. The highest point on a tree structure is called a root node, which does not have a parent node, but serves as the parent or 'grandparent' of all of the nodes below it in the tree. The height of a node is determined by the total number of edges on the path from that node to the furthest leaf node, and the height of the tree is equal to the height of the root node. Node depth is determined by the distance between that particular node and the root node. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Type Theory
In mathematics and theoretical computer science, a type theory is the formal presentation of a specific type system. Type theory is the academic study of type systems. Some type theories serve as alternatives to set theory as a foundation of mathematics. Two influential type theories that have been proposed as foundations are: * Typed λ-calculus of Alonzo Church * Intuitionistic type theory of Per Martin-Löf Most computerized proof-writing systems use a type theory for their foundation. A common one is Thierry Coquand's Calculus of Inductive Constructions. History Type theory was created to avoid paradoxes in naive set theory and formal logic, such as Russell's paradox which demonstrates that, without proper axioms, it is possible to define the set of all sets that are not members of themselves; this set both contains itself and does not contain itself. Between 1902 and 1908, Bertrand Russell proposed various solutions to this problem. By 1908, Russell arrive ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Connectivity (graph Theory)
In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to separate the remaining nodes into two or more Connected component (graph theory), isolated subgraphs. It is closely related to the theory of flow network, network flow problems. The connectivity of a graph is an important measure of its resilience as a network. Connected vertices and graphs In an undirected graph , two vertex (graph theory), vertices and are called connected if contains a Path (graph theory), path from to . Otherwise, they are called disconnected. If the two vertices are additionally connected by a path of length (that is, they are the endpoints of a single edge), the vertices are called adjacent. A Graph (discrete mathematics), graph is said to be connected if every pair of vertices in the graph is connected. This means that there is a Path (graph theory), path between every ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
S-expression
In computer programming, an S-expression (or symbolic expression, abbreviated as sexpr or sexp) is an expression in a like-named notation for nested List (computing), list (Tree (data structure), tree-structured) data. S-expressions were invented for, and popularized by, the programming language Lisp (programming language), Lisp, which uses them for source code as well as data. Characteristics In the usual parenthesized Syntax (programming languages), syntax of Lisp, an S-expression is classically definedJohn McCarthy (1960/2006)Recursive functions of symbolic expressions. Originally published in Communications of the ACM. as # an atom of the form ''x'', or # an Expression (computer science), expression of the form (''x'' . ''y'') where ''x'' and ''y'' are S-expressions. This definition reflects LISP's representation of a list as a series of "cells", each one an ordered pair. In plain lists, ''y'' points to the next cell (if any), thus forming a Linked list, list. The Recursi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Heap
A binary heap is a heap (data structure), heap data structure that takes the form of a binary tree. Binary heaps are a common way of implementing priority queues. The binary heap was introduced by J. W. J. Williams in 1964 as a data structure for implementing heapsort. A binary heap is defined as a binary tree with two additional constraints: *Shape property: a binary heap is a ''complete binary tree''; that is, all levels of the tree, except possibly the last one (deepest) are fully filled, and, if the last level of the tree is not complete, the nodes of that level are filled from left to right. *Heap property: the key stored in each node is either greater than or equal to (≥) or less than or equal to (≤) the keys in the node's children, according to some total order. Heaps where the parent key is greater than or equal to (≥) the child keys are called ''max-heaps''; those where it is less than or equal to (≤) are called ''min-heaps''. Efficient (that is, logarithmic tim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Array Data Structure
In computer science, an array is a data structure consisting of a collection of ''elements'' (value (computer science), values or variable (programming), variables), of same memory size, each identified by at least one ''array index'' or ''key'', a collection of which may be a tuple, known as an index tuple. An array is stored such that the position (memory address) of each element can be computed from its index tuple by a mathematical formula. The simplest type of data structure is a linear array, also called a one-dimensional array. For example, an array of ten 32-bit (4-byte) integer variables, with indices 0 through 9, may be stored as ten Word (data type), words at memory addresses 2000, 2004, 2008, ..., 2036, (in hexadecimal: 0x7D0, 0x7D4, 0x7D8, ..., 0x7F4) so that the element with index ''i'' has the address 2000 + (''i'' × 4). The memory address of the first element of an array is called first address, foundation address, or base address. Because the mathematical conc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Relational Database
A relational database (RDB) is a database based on the relational model of data, as proposed by E. F. Codd in 1970. A Relational Database Management System (RDBMS) is a type of database management system that stores data in a structured format using rows and columns. Many relational database systems are equipped with the option of using SQL (Structured Query Language) for querying and updating the database. History The concept of relational database was defined by E. F. Codd at IBM in 1970. Codd introduced the term ''relational'' in his research paper "A Relational Model of Data for Large Shared Data Banks". In this paper and later papers, he defined what he meant by ''relation''. One well-known definition of what constitutes a relational database system is composed of Codd's 12 rules. However, no commercial implementations of the relational model conform to all of Codd's rules, so the term has gradually come to describe a broader class of database systems, which at a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamic Memory Allocation
Memory management (also dynamic memory management, dynamic storage allocation, or dynamic memory allocation) is a form of resource management applied to computer memory. The essential requirement of memory management is to provide ways to dynamically allocate portions of memory to programs at their request, and free it for reuse when no longer needed. This is critical to any advanced computer system where more than a single process might be underway at any time. Several methods have been devised that increase the effectiveness of memory management. Virtual memory systems separate the memory addresses used by a process from actual physical addresses, allowing separation of processes and increasing the size of the virtual address space beyond the available amount of RAM using paging or swapping to secondary storage. The quality of the virtual memory manager can have an extensive effect on overall system performance. The system allows a computer to appear as if it may have more ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Breadth-first Search
Breadth-first search (BFS) is an algorithm for searching a tree data structure for a node that satisfies a given property. It starts at the tree root and explores all nodes at the present depth prior to moving on to the nodes at the next depth level. Extra memory, usually a queue, is needed to keep track of the child nodes that were encountered but not yet explored. For example, in a chess endgame, a chess engine may build the game tree from the current position by applying all possible moves and use breadth-first search to find a win position for White. Implicit trees (such as game trees or other problem-solving trees) may be of infinite size; breadth-first search is guaranteed to find a solution node if one exists. In contrast, (plain) depth-first search (DFS), which explores the node branch as far as possible before backtracking and expanding other nodes, may get lost in an infinite branch and never make it to the solution node. Iterative deepening depth-first search ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary 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 . A recursive definition using set theory is that a binary tree is a triple , where ''L'' and ''R'' are binary trees or the empty set and ''S'' is a singleton (a single–element set) containing the root. From a graph theory perspective, binary trees as defined here are arborescences. A binary tree may thus be also called a bifurcating arborescence, a term which appears in some early programming books before the modern computer science terminology prevailed. It is also possible to interpret a binary tree as an undirected, rather than 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, but as defined above, a binary tree is always rooted. In ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lowest Common Ancestor
In graph theory and computer science, the lowest common ancestor (LCA) (also called least common ancestor) of two nodes and in a Tree (graph theory), tree or directed acyclic graph (DAG) is the lowest (i.e. deepest) node that has both and as descendants, where we define each node to be a descendant of itself (so if has a direct connection from , is the lowest common ancestor). The LCA of and in is the shared ancestor of and that is located farthest from the root. Computation of lowest common ancestors may be useful, for instance, as part of a procedure for determining the distance between pairs of nodes in a tree: the distance from to can be computed as the distance from the root to , plus the distance from the root to , minus twice the distance from the root to their lowest common ancestor . In a tree data structure where each node points to its parent, the lowest common ancestor can be easily determined by finding the first intersection of the paths from and to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
