In mathematics and computer science, an algorithm is a finite sequence of well-defined instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations, data processing, automated reasoning, automated decision-making and other tasks. In contrast, a heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where there is no well-defined correct or optimal result.
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 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 is called the root node.
Insertion sort is a simple sorting algorithm that builds the final sorted array one item at a time. It is much less efficient on large lists than more advanced algorithms such as quicksort, heapsort, or merge sort. However, insertion sort provides several advantages:
In computer science, merge sort is an efficient, general-purpose, and comparison-based sorting algorithm. Most implementations produce a stable sort, which means that the order of equal elements is the same in the input and output. Merge sort is a divide and conquer algorithm that was invented by John von Neumann in 1945. A detailed description and analysis of bottom-up merge sort appeared in a report by Goldstine and von Neumann as early as 1948.
Merge algorithms are a family of algorithms that take multiple sorted lists as input and produce a single list as output, containing all the elements of the inputs lists in sorted order. These algorithms are used as subroutines in various sorting algorithms, most famously merge sort.
In computer science, a sorting algorithm is an algorithm that puts elements of a list into an order. The most frequently used orders are numerical order and lexicographical order, and either ascending or descending. Efficient sorting is important for optimizing the efficiency of other algorithms that require input data to be in sorted lists. Sorting is also often useful for canonicalizing data and for producing human-readable output.
Iteration is the repetition of a process in order to generate a sequence of outcomes. Each repetition of the process is a single iteration, and the outcome of each iteration is then the starting point of the next iteration.
Sorting is any process of arranging items systematically, and has two common, yet distinct meanings:
- ordering: arranging items in a sequence ordered by some criterion;
- categorizing: grouping items with similar properties.
In computer science, divide and conquer is an algorithm design paradigm. A divide-and-conquer algorithm recursively breaks down a problem into two or more sub-problems of the same or related type, until these become simple enough to be solved directly. The solutions to the sub-problems are then combined to give a solution to the original problem.
Leonard Adleman is an American computer scientist. He is one of the creators of the RSA encryption algorithm, for which he received the 2002 Turing Award, often called the Nobel prize of Computer science. He is also known for the creation of the field of DNA computing.
In data mining and statistics, hierarchical clustering is a method of cluster analysis which seeks to build a hierarchy of clusters. Strategies for hierarchical clustering generally fall into two types:
In version control, merging is a fundamental operation that reconciles multiple changes made to a version-controlled collection of files. Most often, it is necessary when a file is modified on two independent branches and subsequently merged. The result is a single collection of files that contains both sets of changes.
Quicksort is an in-place sorting algorithm. Developed by British computer scientist Tony Hoare in 1959 and published in 1961, it is still a commonly used algorithm for sorting. When implemented well, it can be somewhat faster than merge sort and about two or three times faster than heapsort.
In mathematics and computer science, a string metric is a metric that measures distance between two text strings for approximate string matching or comparison and in fuzzy string searching. A requirement for a string metric is fulfillment of the triangle inequality. For example, the strings "Sam" and "Samuel" can be considered to be close. A string metric provides a number indicating an algorithm-specific indication of distance.
In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is proved to be impossible to construct an algorithm that always leads to a correct yes-or-no answer. The halting problem is an example: it can be proven that there is no algorithm that correctly determines whether arbitrary programs eventually halt when run.
In the theory of cluster analysis, the nearest-neighbor chain algorithm is an algorithm that can speed up several methods for agglomerative hierarchical clustering. These are methods that take a collection of points as input, and create a hierarchy of clusters of points by repeatedly merging pairs of smaller clusters to form larger clusters. The clustering methods that the nearest-neighbor chain algorithm can be used for include Ward's method, complete-linkage clustering, and single-linkage clustering; these all work by repeatedly merging the closest two clusters but use different definitions of the distance between clusters. The cluster distances for which the nearest-neighbor chain algorithm works are called reducible and are characterized by a simple inequality among certain cluster distances.
Ross Cohen is the cofounder of BitTorrent Inc. He started the company in 2004 along with his brother Bram Cohen, where among other things he was involved in the Codeville project. He attended Carnegie Mellon University and Stuyvesant High School. He was forced out of the company in 2006.
A hybrid algorithm is an algorithm that combines two or more other algorithms that solve the same problem, and is mostly used in programming languages like C++, either choosing one, or switching between them over the course of the algorithm. This is generally done to combine desired features of each, so that the overall algorithm is better than the individual components.
In computer science, merge-insertion sort or the Ford–Johnson algorithm is a comparison sorting algorithm published in 1959 by L. R. Ford Jr. and Selmer M. Johnson. It uses fewer comparisons in the worst case than the best previously known algorithms, binary insertion sort and merge sort, and for 20 years it was the sorting algorithm with the fewest known comparisons. Although not of practical significance, it remains of theoretical interest in connection with the problem of sorting with a minimum number of comparisons. The same algorithm may have also been independently discovered by Stanisław Trybuła and Czen Ping.
