Algorithms And Data Structures

Algorithms (Алгоритмы) - download pdf or read online

By Robert Sedgewick

ISBN-10: 0201066726

ISBN-13: 9780201066722

Из предисловия к книге
"...The ebook comprises 40 chapters that are grouped into seven significant elements: mathematical algorithms, sorting, looking out, string processing, geometric algorithms, graph algorithms and complex issues. a massive target within the improvement of this publication has been to assemble the basic tools from those assorted parts, in an effort to offer entry to the easiest equipment that we all know for fixing difficulties via laptop for as many of us as possible."

Некоторое время назад на сайте были опубликованы первый и второй тома "Фундаментальных алгоритмов на С++" Роберта Седжвика. Книга Algorithms - одна из ранних публикаций (1983 год) этого автора, на русский язык она не переводилась.

Книга рассчитана на тех, кто уже немного знаком с основами программирования (скорее студентов, нежели школьников), фрагменты программ приведены на языке Pascal, в конце каждой главы имеются упражнения.

Алгоритмы описываются весьма кратко и достаточно простым языком (простота касается и английского языка - чтение книги вряд ли будет более трудным, чем чтение справочной информации в современных системах программирования). Представляется удобным то, что большое количество популярных алгоритмов
собраны под одной обложкой. Это позволяет использовать книгу и в качестве справочника.

Конечно, работу Седжвика трудно сравнивать по фундаментальности и строгости с замечательной книгой "Алгоритмы. Построение и анализ" Кормена, Лейзерсона, Ривеста и Штайна, но знакомство с первой может оказаться полезным при изучении второй.

Скан не мой, был когда-то найден в сети. Как уже говорилось, качество его умеренно хорошее: в некоторых формулах (реже в программах) встречаются ошибки распознавания. Однако в большинстве случаев правильный символ может быть легко "восстановлен".

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This is easier to solve than the one in the previous paragraph. We immediately have I14(2~) = n and, again, it turns out that M(N) z 1gN. Of course, it’s not always possible to get by with such trivial manipulations. For a slightly more difficult example, consider an algorithm of the type described in the previous paragraph which must somehow examine each element before or after the recursive step. The running time of such an algorithm is described by the recurrence M(N) = M(N/2) + N. Substituting N = 2n and applying the same recurrence to itself n times now gives This must be evaluated to get the result I~f(2~) = 2n+1 - 1 which translates to M(N) z 2N for general N.

This method requires recomputation of the powers of x; an alternate method, which requires extra storage, would save the powers of x as they are computed. A simple method which avoids recomputation and uses no extra space is known as Homer’s rule: by alternat:ing the multiplication and addition operations appropriately, a degree-N polynomial can be evaluated using only 45 CHAPTER 4 46 N - 1 multiplications and N additions. The parenthesization P(X) = x(x(x(x + 3) - 6) + 2) + 1 makes the order of computation obvious: Y:=PN; for i:=N-I downto 0 do y:=x*y+p[i]; This program (and the others in this section) assume the array representation for polynomials that we discussed in Chapter 2.

The remaining problem is equivalent to multiplying 2-by-2 matrices. Just as we were able to reduce the number of multiplications required from four to three by combining terms in the polynomial multiplication problem, Strassen was able to find a way to combine terms to reduce the number of multiplications required for the 2-by-2 matrix multiplication problem from 8 to 7. The rearrangement and the terms required are quite complicated. 81. This result was quite surprising when it first appeared, since it had previously been thought that N3 multiplications were absolutely necessary for matrix multiplication.

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Algorithms (Алгоритмы) by Robert Sedgewick

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