Tableau Sort

2021

In most programming languages, the built-in (standard library) sort() function is the most convenient and efficient way for ordering data. Many software engineers have forgotten (or never knew) the underlying algorithms. In programming contests, almost all of the tasks involving sorting can be solved with only knowing how to use the sort() function. The question might arise in young students: do we need to know how it works if we only need to use it? Also, why should we know multiple efficient sorting algorithms, is not one enough? In this paper, we help the teachers to give the best answers to these questions: some beautiful tasks where the key to the solution lies in knowing a particular sorting algorithm. In some cases, the sorting algorithms are applied as a surprisingly nice idea, for example, in an interactive task or a geometry question.

Almost all computers regularly sort data. Many different sorting algorithms have been proposed. It is known that no sort algorithm based on key comparisons can sort N keys in less than O (N log N) operations and that many perform O(N2 ) operations in the worst case . This paper is aimed at proposing a new sortie tree data structure, which can be used for the sorting of data. This algorithm that implements a sortie tree data structure is a non-comparative sorting algorithm.

2009

The objective of this paper is to review the folklore knowledge seen in research work devoted on synthesis, optimization, and effectiveness of various sorting algorithms. We will examine sorting algorithms in the folklore lines and try to discover the tradeoffs between folklore and theorems. Finally, the folklore knowledge on complexity values of the sorting algorithms will be considered, verified and subsequently converged in to theorems.

2011

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Sorting is the fundamental algorithmic problem in computer science. It is the first step in solving many other algorithmic problems. Donald Knuth, a world famous computer scientist and author of the book "The Art of Computer Programming, Volume 3: Sorting and Searching" ([6]), wrote: "I believe that virtually every important aspect of programming arises somewhere in the context of searching or sorting". Quicksort is a comparison sorting algorithm that, on average, makes O(n log n) comparisons to sort n items. This is as efficient as a comparison sorting algorithm can be ([1]). Quicksort is often faster in practice than other O(n log n) sorting algorithms and it has another advantage-it sorts in place, that is, the items are rearranged within the array, so it does not require a lot of additional space ([1]). Quicksort was invented by a British computer scientist, C.A.R. Hoare, in 1960. Sir Charles Antony Richard Hoare describes how he invented Quicksort in his interview published in [10]. After graduating from the University of Oxford in 1956, Hoare did his national service in the Royal Navy studying Russian. In 1958 he took a course in Mercury Autocode, which was the programming language used on a computer in Oxford University. Later, he was a visiting student at Moscow State University in the Soviet Union for a year. That is when he developed the Quicksort algorithm. The following is a quote from the interview with Hoare ([10]), where he describes his invention of Quicksort: "The National Physical Laboratory was starting a project for the automatic translation of Russian into English, and they offered me a job. I met several of the people in Moscow who were working on machine translation, and I wrote my first published article, in Russian, in a journal called Machine Translation. In those days the dictionary in which you had to look up in order to translate from Russian to English was stored on a long magnetic tape in alphabetical order. Therefore it paid to sort the words of the sentence into the same alphabetical order before consulting the dictionary, so that you could look up all the words in the sentence on a single pass of the magnetic tape. I thought with my knowledge of Mercury Autocode, I'll be able to think up how I would conduct this preliminary sort. After a few moments I thought of the obvious algorithm, which is now called bubble sort, and rejected that because it was obviously rather slow. I thought of Quicksort as the second thing. It didn't occur to me that this was anything very difficult. It was all an interesting exercise in programming. I think Quicksort is the only really interesting algorithm that I ever developed." Hoare described the algorithm in his papers in 1961 and 1962 ([2], [3], [4], [5]). After its invention by Hoare, Quicksort has undergone extensive analysis by Robert Sedgewick in 1975, 1977, 1978 ([7], [8], [9]). Sedgewick in his paper "Implementing Quicksort programs" ([9]) presented "a practical study of how to implement the Quicksort sorting algorithm and its best variants on real computers". The paper contains the original version of Quicksort and presents step-by-step modifications to the algorithm which, as Sedgewick says, make its implementation on real computers more efficient.

PHYSICO-MATHEMATICAL SERIES, 2019

Б а с р е д а к т о р ы ф.-м.ғ.д., проф., ҚР ҰҒА академигі Ғ.М. Мұтанов Р е д а к ц и я а л қ а с ы: Жұмаділдаев А.С. проф., академик (Қазақстан) Кальменов Т.Ш. проф., академик (Қазақстан) Жантаев Ж.Ш. проф., корр.-мүшесі (Қазақстан) Өмірбаев У.У. проф. корр.-мүшесі (Қазақстан) Жүсіпов М.А. проф. (Қазақстан) Жұмабаев Д.С. проф. (Қазақстан) Асанова А.Т. проф. (Қазақстан) Бошкаев К.А. PhD докторы (Қазақстан) Сұраған Д. корр.-мүшесі (Қазақстан) Quevedo Hernando проф. (Мексика), Джунушалиев В.Д. проф. (Қырғыстан) Вишневский И.Н. проф., академик (Украина) Ковалев А.М. проф., академик (Украина) Михалевич А.А. проф., академик (Белорус) Пашаев А. проф., академик (Əзірбайжан) Такибаев Н.Ж. проф., академик (Қазақстан), бас ред. орынбасары Тигиняну И. проф., академик (Молдова) «ҚР ҰҒА Хабарлары. Физика-математикалық сериясы».

2014

Certain sorting procedures derived from ELECTRE TRI such as MR-Sort or the Non-Compensatory Sorting (NCS model) model rely on a rule of the type: if an object is better than a profile on a “sufficient coalition” of criteria, this object is assigned to a category above this profile. In some cases the strength a coalition can be numerically represented by the sum of weights attached to the criteria and a coalition is sufficient if its strength passes some threshold. This is the type of rule used in the MR-Sort method. In more general models such as Capacitive-MR-Sort or NCS model, criteria are allowed to interact and a capacity is needed to model the strength of a coalition. In this contribution, we want to investigate the gap of expressivity between the two models. In this view, we explicitly generate a list of all possible families of sufficient coalitions for a number of criteria up to 6. We also categorize them according to the degree of additivity of a capacity that can model the...

Proceedings of the fourth international conference on Information and knowledge management - CIKM '95, 1995

Much research in information retrieval has focused more on matching results to queries than on browsing those results. After brie y exploring browsing in physical and electronic libraries, we i n troduce SortTables, a new system that focuses on support for browsing. We explore the evolution of the system in light of early implementation experience and formative e v aluation of the interface. Finally, w e brie y review related work, and discuss future directions.