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Binary Tree Sort
A tree sort is a sort algorithm that builds a binary search tree from the elements to be sorted, and then traverses the tree ( in-order) so that the elements come out in sorted order. Its typical use is sorting elements online: after each insertion, the set of elements seen so far is available in sorted order. Tree sort can be used as a one-time sort, but it is equivalent to quicksort as both recursively partition the elements based on a pivot, and since quicksort is in-place and has lower overhead, tree sort has few advantages over quicksort. It has better worst case complexity when a self-balancing tree is used, but even more overhead. Efficiency Adding one item to a binary search tree is on average an process (in big O notation). Adding n items is an process, making tree sorting a 'fast sort' process. Adding an item to an unbalanced binary tree requires time in the worst-case: When the tree resembles a linked list ( degenerate tree). This results in a worst case of tim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Sorting Algorithm
In computer science, a sorting algorithm is an algorithm that puts elements of a List (computing), list into an Total order, order. The most frequently used orders are numerical order and lexicographical order, and either ascending or descending. Efficient sorting is important for optimizing the Algorithmic efficiency, efficiency of other algorithms (such as search algorithm, search and merge algorithm, merge algorithms) that require input data to be in sorted lists. Sorting is also often useful for Canonicalization, canonicalizing data and for producing human-readable output. Formally, the output of any sorting algorithm must satisfy two conditions: # The output is in monotonic order (each element is no smaller/larger than the previous element, according to the required order). # The output is a permutation (a reordering, yet retaining all of the original elements) of the input. Although some algorithms are designed for sequential access, the highest-performing algorithms assum ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Comparison Sort
A comparison sort is a type of sorting algorithm that only reads the list elements through a single abstract comparison operation (often a "less than or equal to" operator or a three-way comparison) that determines which of two elements should occur first in the final sorted list. The only requirement is that the operator forms a total preorder over the data, with: # if ''a'' ≤ ''b'' and ''b'' ≤ ''c'' then ''a'' ≤ ''c'' (transitivity) # for all ''a'' and ''b'', ''a'' ≤ ''b'' or ''b'' ≤ ''a'' ( connexity). It is possible that both ''a'' ≤ ''b'' and ''b'' ≤ ''a''; in this case either may come first in the sorted list. In a stable sort, the input order determines the sorted order in this case. Comparison sorts studied in the literature are "comparison-based". Elements ''a'' and ''b'' can be swapped or otherwise re-arranged by the algorithm only when the order between these elements has been established based on the outcomes of prior comparisons. This is the case when ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Haskell (programming Language)
Haskell () is a General-purpose programming language, general-purpose, static typing, statically typed, purely functional programming, purely functional programming language with type inference and lazy evaluation. Designed for teaching, research, and industrial applications, Haskell pioneered several programming language #Features, features such as type classes, which enable type safety, type-safe operator overloading, and Monad (functional programming), monadic input/output (IO). It is named after logician Haskell Curry. Haskell's main implementation is the Glasgow Haskell Compiler (GHC). Haskell's Semantics (computer science), semantics are historically based on those of the Miranda (programming language), Miranda programming language, which served to focus the efforts of the initial Haskell working group. The last formal specification of the language was made in July 2010, while the development of GHC continues to expand Haskell via language extensions. Haskell is used in a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Functional Programming
In computer science, functional programming is a programming paradigm where programs are constructed by Function application, applying and Function composition (computer science), composing Function (computer science), functions. It is a declarative programming paradigm in which function definitions are Tree (data structure), trees of Expression (computer science), expressions that map Value (computer science), values to other values, rather than a sequence of Imperative programming, imperative Statement (computer science), statements which update the State (computer science), running state of the program. In functional programming, functions are treated as first-class citizens, meaning that they can be bound to names (including local Identifier (computer languages), identifiers), passed as Parameter (computer programming), arguments, and Return value, returned from other functions, just as any other data type can. This allows programs to be written in a Declarative programming, d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Total Order
In mathematics, a total order or linear order is a partial order in which any two elements are comparable. That is, a total order is a binary relation \leq on some set X, which satisfies the following for all a, b and c in X: # a \leq a ( reflexive). # If a \leq b and b \leq c then a \leq c ( transitive). # If a \leq b and b \leq a then a = b ( antisymmetric). # a \leq b or b \leq a ( strongly connected, formerly called totality). Requirements 1. to 3. just make up the definition of a partial order. Reflexivity (1.) already follows from strong connectedness (4.), but is required explicitly by many authors nevertheless, to indicate the kinship to partial orders. Total orders are sometimes also called simple, connex, or full orders. A set equipped with a total order is a totally ordered set; the terms simply ordered set, linearly ordered set, toset and loset are also used. The term ''chain'' is sometimes defined as a synonym of ''totally ordered set'', but generally refers to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Adaptive Sort
A sorting algorithm falls into the adaptive sort family if it takes advantage of existing order in its input. It benefits from the presortedness in the input sequence – or a limited amount of disorder for various definitions of measures of disorder – and sorts faster. Adaptive sorting is usually performed by modifying existing sorting algorithms. Motivation Comparison-based sorting algorithms have traditionally dealt with achieving an optimal bound of '' O''(''n'' log ''n'') when dealing with time complexity. Adaptive sort takes advantage of the existing order of the input to try to achieve better times, so that the time taken by the algorithm to sort is a smoothly growing function of the size of the sequence ''and'' the disorder in the sequence. In other words, the more presorted the input is, the faster it should be sorted. This is an attractive feature for a sorting algorithm because sequences that nearly sorted are common in practice. Thus, the performance of exist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Splaysort
In computer science, splaysort is an adaptive comparison sorting algorithm based on the splay tree data structure. Algorithm The steps of the algorithm are: # Initialize an empty splay tree # For each data item in the input order, insert it into the splay tree # Traverse the splay tree inorder to find the sorted order of the data Thus, the algorithm may be seen as a form of insertion sort or tree sort, using a splay tree to speed up each insertion. Analysis Based on the amortized analysis of splay trees, the worst case running time of splaysort, on an input with ''n'' data items, is ''O''(''n'' log ''n''), matching the time bounds for efficient non-adaptive algorithms such as quicksort, heap sort, and merge sort. For an input sequence in which most items are placed close to their predecessor in the sorted order, or are out of order with only a small number of other items, splaysort can be faster than ''O''(''n'' log ''n''), showing that it is an adaptive sort ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Splay Tree
A splay tree is a binary search tree with the additional property that recently accessed elements are quick to access again. Like self-balancing binary search trees, a splay tree performs basic operations such as insertion, look-up and removal in big O notation, O(log ''n'') amortized analysis, amortized time. For random access patterns drawn from a non-uniform random distribution, their amortized time can be faster than logarithmic, proportional to the Entropy (information theory), entropy of the access pattern. For many patterns of non-random operations, also, splay trees can take better than logarithmic time, without requiring advance knowledge of the pattern. According to the unproven dynamic optimality conjecture, their performance on all access patterns is within a constant factor of the best possible performance that could be achieved by any other self-adjusting binary search tree, even one selected to fit that pattern. The splay tree was invented by Daniel Sleator and Rob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Memory Management
Memory management (also dynamic memory management, dynamic storage allocation, or dynamic memory allocation) is a form of Resource management (computing), 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 (computing), 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 Random-access memory, RAM using paging or swapping to secondary storage. The quality of the virtual memory manager can have an extensive effect on overall system C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Heapsort
In computer science, heapsort is an efficient, comparison-based sorting algorithm that reorganizes an input array into a heap (a data structure where each node is greater than its children) and then repeatedly removes the largest node from that heap, placing it at the end of the array in a similar manner to Selection sort. Although somewhat slower in practice on most machines than a well-implemented quicksort, it has the advantages of very simple implementation and a more favorable worst-case runtime. Most real-world quicksort variants include an implementation of heapsort as a fallback should they detect that quicksort is becoming degenerate. Heapsort is an in-place algorithm, but it is not a stable sort. Heapsort was invented by J. W. J. Williams in 1964. The paper also introduced the binary heap as a useful data structure in its own right. In the same year, Robert W. Floyd published an improved version that could sort an array in-place, continuing his earlier research ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Self-balancing 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-bal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Binary Tree Sort(2)
A tree sort is a sort algorithm that builds a binary search tree from the elements to be sorted, and then traverses the tree ( in-order) so that the elements come out in sorted order. Its typical use is sorting elements online: after each insertion, the set of elements seen so far is available in sorted order. Tree sort can be used as a one-time sort, but it is equivalent to quicksort as both recursively partition the elements based on a pivot, and since quicksort is in-place and has lower overhead, tree sort has few advantages over quicksort. It has better worst case complexity when a self-balancing tree is used, but even more overhead. Efficiency Adding one item to a binary search tree is on average an process (in big O notation). Adding n items is an process, making tree sorting a 'fast sort' process. Adding an item to an unbalanced binary tree requires time in the worst-case: When the tree resembles a linked list ( degenerate tree). This results in a worst case of tim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
