Algorithm

In mathematics and computer science, an algorithm (ⁱ/ˈælɡərɪðəm/ AL-gə-ri-dhəm) is a self-contained step-by-step set of operations to be performed. Algorithms exist that perform calculation, data processing, and automated reasoning.

The words 'algorithm' and 'algorism' come from the name al-Khwārizmī. Al-Khwārizmī (Persian: خوارزمي‎‎, c. 780-850) was a Persian mathematician, astronomer, geographer, and scholar.

An algorithm is an effective method that can be expressed within a finite amount of space and time and in a well-defined formal language for calculating a function. Starting from an initial state and initial input (perhaps empty), the instructions describe a computation that, when executed, proceeds through a finite number of well-defined successive states, eventually producing "output" and terminating at a final ending state. The transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate random input.

C (programming language)

C (/ˈsiː/, as in the letter c) is a general-purpose, imperative computer programming language, supporting structured programming, lexical variable scope and recursion, while a static type system prevents many unintended operations. By design, C provides constructs that map efficiently to typical machine instructions, and therefore it has found lasting use in applications that had formerly been coded in assembly language, including operating systems, as well as various application software for computers ranging from supercomputers to embedded systems.

C was originally developed by Dennis Ritchie between 1969 and 1973 at AT&T Bell Labs, and used to re-implement the Unix operating system. It has since become one of the most widely used programming languages of all time, with C compilers from various vendors available for the majority of existing computer architectures and operating systems. C has been standardized by the American National Standards Institute (ANSI) since 1989 (see ANSI C) and subsequently by the International Organization for Standardization (ISO).

Bubble sort

Bubble sort, sometimes referred to as sinking sort, is a simple sorting algorithm that repeatedly steps through the list to be sorted, compares each pair of adjacent items and swaps them if they are in the wrong order. The pass through the list is repeated until no swaps are needed, which indicates that the list is sorted. The algorithm, which is a comparison sort, is named for the way smaller elements "bubble" to the top of the list. Although the algorithm is simple, it is too slow and impractical for most problems even when compared to insertion sort. It can be practical if the input is usually in sort order but may occasionally have some out-of-order elements nearly in position.

Analysis

Performance

Bubble sort has worst-case and average complexity both О(n²), where n is the number of items being sorted. There exist many sorting algorithms with substantially better worst-case or average complexity of O(n log n). Even other О(n²) sorting algorithms, such as insertion sort, tend to have better performance than bubble sort. Therefore, bubble sort is not a practical sorting algorithm when n is large.

Flow Chart

Flow Chart is a long poem by the American writer John Ashbery, published in its own volume in 1991.

Structure

Flow Chart is a work of 4,794 lines, divided into six numbered chapters or parts, each of which is further divided into sections or verse-paragraphs, varying in number from seven to 42. The sections vary in length from one or two lines, to seven pages.

Reception

Scott Mahler wrote in the Los Angeles Times: "Ashbery's poetry has been called mysterious, original, difficult, dream-like, Romantic, a part of the continuum of American poetry that includes Walt Whitman, Emily Dickinson, Wallace Stevens and Hart Crane. It's also been called elusive, inauthentic, unmusical and overmannered. Flow Chart is easily all of these things... Ashbery has shown us again that he can go more than the distance we expect of great poets, but neither the terrain he covers nor the course he takes is altogether very exciting. Flow Chart is a great accomplishment, but it sometimes reads more like a big effort than a real tour de force."