An algorithm, according to the Random House Unabridged Dictionary, is a set of rules for solving a problem in a finite number of steps.
One of the fundamental problems of computer science is sorting a set of items. The solutions to these problems are known as sorting algorithms and rather ironically, “the process of applying an algorithm to an input to obtain an output is called a computation” [http://mathworld.wolfram.com/Algorithm.html].
The quest to develop the most memory efficient and the fastest sorting algorithm has become one of the great mathematical challenges of the last half century, resulting in many tried and tested algorithms available to the individual who needs to sort a list of data. In fact new sorting algorithms are still being developed today, take for example the Library sort, which was published in 2004.
Of all the popular sorting algorithms, I have chosen to research and explain in detail an algorithm known as the ‘Quicksort’. Quicksort is a popular and speedy sorting algorithm that is the multi-purpose, sorting algorithm of choice for many mathematicians and computer scientists. Though of course the choosing of an algorithm comes down to which algorithm is best suited to the clients needs, and is dependent on the specific set of data to be sorted, Quicksort has proven to fulfill the required criteria on many occasions.
C.A.R. Hoare developed the Quicksort algorithm in the year 1960, while he was working for a small, English scientific computer manufacturer named Elliott Brothers (London) Ltd.
Sorting algorithms are designed to be fast, and efficient. To be able to sort a list of data as quickly as possible, using as little memory as possible. To measure or classify an algorithm according to these two criteria, we measure the algorithm’s computational complexity. The computational complexity of a sorting algorithm is it’s worst, average and best behavior. Sorting algorithms are generally classified by their computational complexity of element comparisons, against the size of the list.
This is represented with what is known as ‘Big O notation’, for example where the ideal behavior is O(n), most algorithm’s behavior is O(nlogn), and bad behavior is O(n²). O(n) behavior means that a sorting algorithm would take ten times longer to sort a list of one hundred elements, than it would to sort a list of one thousand elements. O(n²) behavior is quadratic behavior, and this would take one hundred times longer to sort a list of one hundred elements, than it would to sort a list of one thousand elements.
The Big Sort, written by Bill Bishop and published in 2009, takes an in-depth, wide-ranging look into the ways that American citizens are defining themselves and forming into like-minded groups. The people of the United States are categorizing their life choices, beliefs and practices in such a way that population areas both great and small are becoming alienated and isolated from one another, clustering in particular groups that share the same or similar interests and points of view. Individuals and groups that do not share equivalent ideas or ways of life with other individuals and groups are increasingly at odds, to the point of minimal contact and knowledge with the rest of the world that exists outside of their thought community. As a result of this, people are clumping to opposing ends of spectrums, whether they are political, religious or lifestyle choices and this is causing “sorting”, referring to the book’s title.
Lovelace and Hopper are by no means the only women who have made invaluable contributions to the field of computer science. Without Betty Holberton, who "devised the first sort-merge generator, for UNIVAC I" (AWC, "Frances..."), Grace Hopper would never have been able to design the first compiler. A more contemporary scientist, Dr. Anita Borg, has profoundly influenced the field by "designing and building a fault tolerant UNIX-based operating system" ("Short Biography of Anita Borg"), as well as developing a performance analysis method for high-speed memory systems. However, I've chosen to focus on Lovelace and Hopper because they are probably the most frequently mentioned women in computer science, and they represent two critical historical moments in the field: Lovelace helps to bring the first computer into being, while Hopper forges the start of the modern computer age.
Sorting gained a lot of importance in computer sciences and its applications are in file systems, sequential and multiprocessing computing, and a core part of database systems. A number of sorting algorithms have been proposed with different time and space complexities. There is no one sorting algorithm that is best for each and every situation. Donald Knuth in [1] reports that “computer manufacturers of the 1960s estimated that more than 25 percent of the running time on their computers was spend on sorting, when all their customers were taken into account. In fact, there were many installations in which the task of sorting was responsible for more than half of the computing time.” Sorting is a significant concept whenever we study algorithms. Knuth divides the taxonomy of sorting...
D. Cantone [2002] et.al have proposed a productive and reasonable algorithm for the internal sorting issue. It performs a running time of O(n lg n) in the size n of the input.
Computer engineering started about 5,000 years ago in China when they invented the abacus. The abacus is a manual calculator in which you move beads back and forth on rods to add or subtract. Other inventors of simple computers include Blaise Pascal who came up with the arithmetic machine for his father’s work. Also Charles Babbage produced the Analytical Engine, which combined math calculations from one problem and applied it to solve other complex problems. The Analytical Engine is similar to today’s computers.
In this paper he described a new system for storing and working with large databases. Instead of records being stored in some sort of linked list of free-form records as in Codasyl, Codd's idea was to use a "table" of fixed-length records. A linked-list system would be very inefficient when storing "sparse" databases where some of the data for any one record could be left empty. The relational model solved this by splitting the data into a series of tables, with optional elements being moved out of the main table to where they would take up room only if needed.
Genetic algorithms are a randomized search method based on the biological model of evolution through mating and mutation. In the classic genetic algorithm, problem solutions are encoded into bit strings which are tested for fitness, then the best bit strings are combined to form new solutions using methods which mimic the Darwinian process of "survival of the fittest" and the exchange of DNA which occurs during mating in biological systems. The programming of genetic algorithms involves little more than bit manipulation and scoring the quality of solutions. Genetic algorithms have been applied to problems as diverse as graph partitioning and the automatic creation of programs to match mathematical functions.
Algorithm is a part of discrete mathematics and very useful for the computer science. An algorithm is the ability to carry out the correct steps in the correct order and should always be considered in the context of the certain assumptions. Algorithms of arithmetic, operate with integers which they depend on a digit integer. That was the definition of an algorithm in numerical situation. The connection with the computing science is that in nowadays the algorithms are designed to be used by a machine. So algorithms can be expressed in more languages like natural language , Java, C++. The computer solves a problem by way of a computer program, which as it is mentioned above is a list of orders giving detailed instructions about the action of the computer. Algo...
Over the last so many years, a large amount of data has become available like a large amount of collections of photos, genetic information, and network traffic statistics, modern technologies and cheap storage facilities have made it possible to collect huge datasets. But can we effectively use all this data? The ever increasing sizes of the datasets make it imperative to design new algorithms capable of shifting through this data with extreme efficiency.
To better describe this concept, an article from Software Technology states, “This is like giving a student a set of problems and their solutions and telling that student to figure [it] out …” (2016, Panos Louridas and Christof Eber). The way the computer learns is by grouping data together. This type of method uses two different types of grouping methods to help identify possible outcomes: classification and regression algorithms.
Huss-Lederman, S., Jacobson, E. M., Johnson, J. R., Tsao, A., & Turnbull, T. (1996). Implementation of Strassen's algorithm for matrix multiplication. In Supercomputing, 1996. Proceedings of the 1996 ACM/IEEE Conference on (pp. 32-32). IEEE.
The field of Computer Science is based primarily on computer programing. Programming is the writing of computer programs using letters and numbers to make "code". The average computer programer will write at least a million lines of code in his or her lifetime. But even more important than writting code, a good programer must be able to solve problems and think logicaly.
The history of the computer dates back all the way to the prehistoric times. The first step towards the development of the computer, the abacus, was developed in Babylonia in 500 B.C. and functioned as a simple counting tool. It was not until thousands of years later that the first calculator was produced. In 1623, the first mechanical calculator was invented by Wilhelm Schikard, the “Calculating Clock,” as it was often referred to as, “performed it’s operations by wheels, which worked similar to a car’s odometer” (Evolution, 1). Still, there had not yet been anything invented that could even be characterized as a computer. Finally, in 1625 the slide rule was created becoming “the first analog computer of the modern ages” (Evolution, 1). One of the biggest breakthroughs came from by Blaise Pascal in 1642, who invented a mechanical calculator whose main function was adding and subtracting numbers. Years later, Gottfried Leibnez improved Pascal’s model by allowing it to also perform such operations as multiplying, dividing, taking the square root.
Computer engineering, in short, is the study of the applications and advancement of computer systems. Research in this field includes but is not limited to: making technology more accessible, developing new systems that are faster and more efficient, programming software to work better with existing hardware, and using technology to improve the lives of its users.
There are several elementary and advanced sorting algorithms. Some sorting algorithms are simple and spontaneous, such as the bubble sort. Others, such as the quick sort are enormously complex, but produce super fast results. Some sorting algorithm work on less number of elements, some are suitable for floating point numbers, some are good for specific range, some sorting algorithms are used for huge number of data, and some are used if the list has repeated values. Other factors to be considered in choosing a sorting algorithm include the programming effort, the number of words of main memory available, the size of disk or tape units and the extent to which the list is already ordered [4]. That means all sorting Algorithms are problem specific, meaning they work well on some specific problem and do not work well...