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Min-heap
In computer science, a heap is a specialized tree-based data structure which is essentially an almost complete tree that satisfies the heap property: in a ''max heap'', for any given node C, if P is a parent node of C, then the ''key'' (the ''value'') of P is greater than or equal to the key of C. In a ''min heap'', the key of P is less than or equal to the key of C. The node at the "top" of the heap (with no parents) is called the ''root'' node. The heap is one maximally efficient implementation of an abstract data type called a priority queue, and in fact, priority queues are often referred to as "heaps", regardless of how they may be implemented. In a heap, the highest (or lowest) priority element is always stored at the root. However, a heap is not a sorted structure; it can be regarded as being partially ordered. A heap is a useful data structure when it is necessary to repeatedly remove the object with the highest (or lowest) priority, or when insertions need to be inter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Heap
A binary heap is a 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 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 ( logarithmic time) algorithms are known for the two ope ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Priority Queue
In computer science, a priority queue is an abstract data-type similar to a regular queue or stack data structure in which each element additionally has a ''priority'' associated with it. In a priority queue, an element with high priority is served before an element with low priority. In some implementations, if two elements have the same priority, they are served according to the order in which they were enqueued; in other implementations ordering of elements with the same priority remains undefined. While coders often implement priority queues with heaps, they are conceptually distinct from heaps. A priority queue is a concept like a list or a map; just as a list can be implemented with a linked list or with an array, a priority queue can be implemented with a heap or with a variety of other methods such as an unordered array. Operations A priority queue must at least support the following operations: * ''is_empty'': check whether the queue has no elements. * ''insert_ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dictionary Of Algorithms And Data Structures
The NIST ''Dictionary of Algorithms and Data Structures'' is a reference work maintained by the U.S. National Institute of Standards and Technology. It defines a large number of terms relating to algorithms and data structures. For algorithms and data structures not necessarily mentioned here, see list of algorithms and list of data structures. This list of terms was originally derived from the index of that document, and is in the public domain, as it was compiled by a Federal Government employee as part of a Federal Government work. Some of the terms defined are: __NOTOC__ A * absolute performance guarantee * abstract data type (ADT) * (a,b)-tree * accepting state * Ackermann's function * active data structure * acyclic directed graph * adaptive heap sort * adaptive Huffman coding * adaptive k-d tree * adaptive sort * address-calculation sort * adjacency list representation * adjacency matrix representation * adversary * algorithm * algorithm BSTW * algorithm FGK * ... [...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'' ( values or variables), each identified by at least one ''array index'' or ''key''. An array is stored such that the position 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 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 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 concept of a matrix can be represented as a two-dimensional grid, two-dimensional arrays are also sometimes called "matrices". In some cases the term "vector" is used in com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Implicit Data Structure
In computer science, an implicit data structure or space-efficient data structure is a data structure that stores very little information other than the main or required data: a data structure that requires low overhead. They are called "implicit" because the position of the elements carries meaning and relationship between elements; this is contrasted with the use of pointers to give an ''explicit'' relationship between elements. Definitions of "low overhead" vary, but generally means constant overhead; in big O notation, ''O''(1) overhead. A less restrictive definition is a succinct data structure, which allows greater overhead. Definition An implicit data structure is one with constant space overhead (above the information-theoretic lower bound). Historically, defined an implicit data structure (and algorithms acting on one) as one "in which structural information is implicit in the way data are stored, rather than explicit in pointers." They are somewhat vague in the de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heapsort
In computer science, heapsort is a comparison-based sorting algorithm. Heapsort can be thought of as an improved selection sort: like selection sort, heapsort divides its input into a sorted and an unsorted region, and it iteratively shrinks the unsorted region by extracting the largest element from it and inserting it into the sorted region. Unlike selection sort, heapsort does not waste time with a linear-time scan of the unsorted region; rather, heap sort maintains the unsorted region in a heap data structure to more quickly find the largest element in each step. Although somewhat slower in practice on most machines than a well-implemented quicksort, it has the advantage of a more favorable worst-case runtime (and as such is used by Introsort as a fallback should it 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. This was also the birth of the heap, presented ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stirling's Approximation
In mathematics, Stirling's approximation (or Stirling's formula) is an approximation for factorials. It is a good approximation, leading to accurate results even for small values of n. It is named after James Stirling, though a related but less precise result was first stated by Abraham de Moivre. One way of stating the approximation involves the logarithm of the factorial: \ln(n!) = n\ln n - n +O(\ln n), where the big O notation means that, for all sufficiently large values of n, the difference between \ln(n!) and n\ln n-n will be at most proportional to the logarithm. In computer science applications such as the worst-case lower bound for comparison sorting, it is convenient to use instead the binary logarithm, giving the equivalent form \log_2 (n!) = n\log_2 n - n\log_2 e +O(\log_2 n). The error term in either base can be expressed more precisely as \tfrac12\log(2\pi n)+O(\tfrac1n), corresponding to an approximate formula for the factorial itself, n! \sim \sqrt\left(\frac\r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2–3 Heap
In computer science, a 2–3 heap is a data structure, a variation on the heap, designed by Tadao Takaoka in 1999. The structure is similar to the Fibonacci heap, and borrows from the 2–3 tree. Time costs for some common heap operations are: * ''Delete-min'' takes O(\log(n)) amortized time In computer science, amortized analysis is a method for analyzing a given algorithm's complexity, or how much of a resource, especially time or memory, it takes to execute. The motivation for amortized analysis is that looking at the worst-case .... * ''Decrease-key'' takes constant amortized time. * ''Insertion'' takes constant amortized time. Polynomial of trees A linear tree of size r is a sequential path of r nodes with the first node as a root of the tree and it is represented by a bold \mathbf (e.g. \mathbf is a linear tree of a single node). Product P = ST of two trees S and T, is a new tree with every node of S is replaced by a copy of T and for each edge of S we connect the r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peek (data Type Operation)
In computer science, peek is an operation on certain abstract data types, specifically sequential collections such as stacks and queues, which returns the value of the top ("front") of the collection without removing the element from the collection. It thus returns the same value as operations such as "pop" or "dequeue", but does not modify the data. The name "peek" is similar to the basic "push" and "pop" operations on a stack, but the name for this operation varies depending on data type and language. Peek is generally considered an inessential operation, compared with the more basic operations of adding and removing data, and as such is not included in the basic definition of these data types. However, since it is a useful operation and generally easily implemented, it is frequently included in practices, and in some definitions peek is included as basic, with pop (or analog) defined in terms of peek; see abstract definition. Data types Sequential types for which peek is ofte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
