26_split_Introduction to Algorithms 2nd Edition

26_split_Introduction to Algorithms 2nd Edition - it in the...

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Introduction This part will get you started in thinking about designing and analyzing algorithms. It is intended to be a gentle introduction to how we specify algorithms, some of the design strategies we will use throughout this book, and many of the fundamental ideas used in algorithm analysis. Later parts of this book will build upon this base. Chapter 1 is an overview of algorithms and their place in modern computing systems. This chapter deﬁnes what an algorithm is and lists some examples. It also makes a case that algorithms are a technology, just as are fast hardware, graphical user interfaces, object-oriented systems, and networks. In Chapter 2, we see our ﬁrst algorithms, which solve the problem of sorting a sequence of n numbers. They are written in a pseudocode which, although not directly translatable to any conventional programming language, conveys the struc- ture of the algorithm clearly enough that a competent programmer can implement
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Unformatted text preview: it in the language of his choice. The sorting algorithms we examine are insertion sort, which uses an incremental approach, and merge sort, which uses a recursive technique known as “divide and conquer.” Although the time each requires in-creases with the value of n , the rate of increase differs between the two algorithms. We determine these running times in Chapter 2, and we develop a useful notation to express them. Chapter 3 precisely deﬁnes this notation, which we call asymptotic notation. It starts by deﬁning several asymptotic notations, which we use for bounding algo-rithm running times from above and/or below. The rest of Chapter 3 is primarily a presentation of mathematical notation. Its purpose is more to ensure that your use of notation matches that in this book than to teach you new mathematical concepts....
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