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Interpolation Search
Interpolation search is an algorithm for searching for a key in an array that has been ordered by numerical values assigned to the keys (''key values''). It was first described by W. W. Peterson in 1957. Interpolation search resembles the method by which people search a telephone directory for a name (the key value by which the book's entries are ordered): in each step the algorithm calculates where in the remaining search space the sought item might be, based on the key values at the bounds of the search space and the value of the sought key, usually via a linear interpolation. The key value actually found at this estimated position is then compared to the key value being sought. If it is not equal, then depending on the comparison, the remaining search space is reduced to the part before or after the estimated position. This method will only work if calculations on the size of differences between key values are sensible. By comparison, binary search always chooses the middl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use Conditional (computer programming), conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning). In contrast, a Heuristic (computer science), heuristic is an approach to solving problems without well-defined correct or optimal results.David A. Grossman, Ophir Frieder, ''Information Retrieval: Algorithms and Heuristics'', 2nd edition, 2004, For example, although social media recommender systems are commonly called "algorithms", they actually rely on heuristics as there is no truly "correct" recommendation. As an e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Online Algorithm
In computer science, an online algorithm is one that can process its input piece-by-piece in a serial fashion, i.e., in the order that the input is fed to the algorithm, without having the entire input available from the start. In contrast, an offline algorithm is given the whole problem data from the beginning and is required to output an answer which solves the problem at hand. In operations research Operations research () (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a branch of applied mathematics that deals with the development and application of analytical methods to improve management and ..., the area in which online algorithms are developed is called online optimization. As an example, consider the sorting algorithms selection sort and insertion sort: selection sort repeatedly selects the minimum element from the unsorted remainder and places it at the front, which requires access to the entire input; it is thus a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flashsort
Flashsort is a distribution sorting algorithm showing linear computational complexity for uniformly distributed data sets and relatively little additional memory requirement. The original work was published in 1998 by Karl-Dietrich Neubert. Concept Flashsort is an efficient in-place implementation of histogram sort, itself a type of bucket sort. It assigns each of the input elements to one of ''buckets'', efficiently rearranges the input to place the buckets in the correct order, then sorts each bucket. The original algorithm sorts an input array as follows: # Using a first pass over the input or ''a priori'' knowledge, find the minimum and maximum sort keys. # Linearly divide the range into buckets. # Make one pass over the input, counting the number of elements which fall into each bucket. (Neubert calls the buckets "classes" and the assignment of elements to their buckets "classification".) # Convert the counts of elements in each bucket to a prefix sum, where i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newton's Method
In numerical analysis, the Newton–Raphson method, also known simply as Newton's method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued function. The most basic version starts with a real-valued function , its derivative , and an initial guess for a root of . If satisfies certain assumptions and the initial guess is close, then x_ = x_0 - \frac is a better approximation of the root than . Geometrically, is the x-intercept of the tangent of the graph of at : that is, the improved guess, , is the unique root of the linear approximation of at the initial guess, . The process is repeated as x_ = x_n - \frac until a sufficiently precise value is reached. The number of correct digits roughly doubles with each step. This algorithm is first in the class of Householder's methods, and was succeeded by Halley's method. The method can also be extended t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hash Table
In computer science, a hash table is a data structure that implements an associative array, also called a dictionary or simply map; an associative array is an abstract data type that maps Unique key, keys to Value (computer science), values. A hash table uses a hash function to compute an ''index'', also called a ''hash code'', into an array of ''buckets'' or ''slots'', from which the desired value can be found. During lookup, the key is hashed and the resulting hash indicates where the corresponding value is stored. A map implemented by a hash table is called a hash map. Most hash table designs employ an Perfect hash function, imperfect hash function. Hash collision, Hash collisions, where the hash function generates the same index for more than one key, therefore typically must be accommodated in some way. In a well-dimensioned hash table, the average time complexity for each lookup is independent of the number of elements stored in the table. Many hash table designs also ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ternary Search
A ternary search algorithm is a technique in computer science for finding the minimum or maximum of a unimodal function. The function Assume we are looking for a maximum of f(x) and that we know the maximum lies somewhere between A and B. For the algorithm to be applicable, there must be some value x such that * for all a, b with A \leq a * if f(m_1) = f(m_2), then the search should be conducted in _1; m_2/math>, but this case can be attributed to any of the previous two (in order to simplify the code). Sooner or later the length of the segment will be a little less than a predetermined constant, and the process can be stopped. choice points m_1 and m_2: * m_1 = l + (r - l) / 3 * m_2 = r - (r - l) / 3 ; Run time order : T(n) = T(2n/3) + O(1) = \Theta(\log n) (by the Master Theorem) Recursive algorithm def ternary_search(f, left, right, absolute_precision) -> float: """Left and right are the current bounds; the maximum is between them. """ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponential Search
In computer science, an exponential search (also called doubling search or galloping search or Struzik search) is an algorithm, created by Jon Bentley and Andrew Chi-Chih Yao in 1976, for searching sorted, unbounded/infinite lists. There are numerous ways to implement this, with the most common being to determine a range that the search key resides in and performing a binary search within that range. This takes O(\log i) time, where i is the position of the search key in the list, if the search key is in the list, or the position where the search key should be, if the search key is not in the list. Exponential search can also be used to search in bounded lists. Exponential search can even out-perform more traditional searches for bounded lists, such as binary search, when the element being searched for is near the beginning of the array. This is because exponential search will run in ''O(\log i)'' time, where i is the index of the element being searched for in the list, whereas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interpolated Binary Search
In the mathematical field of numerical analysis, interpolation is a type of estimation, a method of constructing (finding) new data points based on the range of a discrete set of known data points. In engineering and science, one often has a number of data points, obtained by sampling or experimentation, which represent the values of a function for a limited number of values of the independent variable. It is often required to interpolate; that is, estimate the value of that function for an intermediate value of the independent variable. A closely related problem is the approximation of a complicated function by a simple function. Suppose the formula for some given function is known, but too complicated to evaluate efficiently. A few data points from the original function can be interpolated to produce a simpler function which is still fairly close to the original. The resulting gain in simplicity may outweigh the loss from interpolation error and give better performance in ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Search
In computer science, binary search, also known as half-interval search, logarithmic search, or binary chop, is a search algorithm that finds the position of a target value within a sorted array. Binary search compares the target value to the middle element of the array. If they are not equal, the half in which the target cannot lie is eliminated and the search continues on the remaining half, again taking the middle element to compare to the target value, and repeating this until the target value is found. If the search ends with the remaining half being empty, the target is not in the array. Binary search runs in Time complexity#Logarithmic time, logarithmic time in the Best, worst and average case, worst case, making O(\log n) comparisons, where n is the number of elements in the array. Binary search is faster than linear search except for small arrays. However, the array must be sorted first to be able to apply binary search. There are specialized data structures designed fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Search
In computer science, linear search or sequential search is a method for finding an element within a list. It sequentially checks each element of the list until a match is found or the whole list has been searched. A linear search runs in linear time in the worst case, and makes at most comparisons, where is the length of the list. If each element is equally likely to be searched, then linear search has an average case of comparisons, but the average case can be affected if the search probabilities for each element vary. Linear search is rarely practical because other search algorithms and schemes, such as the binary search algorithm and hash tables, allow significantly faster searching for all but short lists. Algorithm A linear search sequentially checks each element of the list until it finds an element that matches the target value. If the algorithm reaches the end of the list, the search terminates unsuccessfully. Basic algorithm Given a list of elements with values ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Search Algorithm
In computer science, binary search, also known as half-interval search, logarithmic search, or binary chop, is a search algorithm that finds the position of a target value within a sorted array. Binary search compares the target value to the middle element of the array. If they are not equal, the half in which the target cannot lie is eliminated and the search continues on the remaining half, again taking the middle element to compare to the target value, and repeating this until the target value is found. If the search ends with the remaining half being empty, the target is not in the array. Binary search runs in logarithmic time in the worst case, making O(\log n) comparisons, where n is the number of elements in the array. Binary search is faster than linear search except for small arrays. However, the array must be sorted first to be able to apply binary search. There are specialized data structures designed for fast searching, such as hash tables, that can be searched ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Three-way Comparison
In computer science, a three-way comparison takes two values A and B belonging to a type with a total order and determines whether A < B, A = B, or A > B in a single operation, in accordance with the mathematical law of trichotomy. It can be implemented in terms of a function (such as strcmp in C), a method (such as compareTo in Java), or an operator (such as the spaceship operator in Perl, PHP and C++). Machine-level computation Many processors have instruction sets that support such an operation on primitive types. Some machines have signed integers based on a sign-and-magnitude or ones' complement representation (see signed number representations), both of which allow a differentiated positive and negative zero. This does not violate trichotomy as long as a consistent total order is adopted: either −0 = +0 or −0 < +0 is valid. Common floating point types, however, have an exception to trichotomy: there is a special value "NaN" ( Not a Number) such that ''x' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
