Titlebook: Algorithmic Mathematics; Stefan Hougardy,Jens Vygen Textbook 2016 Springer International Publishing Switzerland 2016 algorithms.algorithmi

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Stefan Hougardy,Jens VygenTextbook covering basic mathematical lecture course.Allows readers to develop basic mathematical abilities, in particular those concerning the design and analysis of algorithms as well as their implem

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https://doi.org/10.1007/978-3-319-39558-6algorithms; algorithmic mathematics; C++; elementary data structures; sorting algorithms

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Springer International Publishing Switzerland 2016

Concrete

Representations of the Integers,ore all occurring natural numbers in the data type .. This, however, is in fact not the case. A variable of type . usually corresponds to a sequence of 4?bytes. This clearly enables us to represent no more than 2. different numbers. In this chapter we will learn how integers are stored.

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Computing with Integers,e this assumption, although it is clearly by no means a realistic one for arbitrarily large numbers. Here we will investigate how fast one can actually compute with integers. Here, in a narrower sense, elementary operations only include operations and comparisons restricted to integers in some bounded interval.

Defense

Approximate Representations of the Real Numbers,t the occurrence of rounding errors. The elementary operations are, however, comparatively slow because both numerators and denominators can get very large, even if one always reduces fractions to lowest terms with the Euclidean Algorithm.

KIN

Computing with Errors,not only when inputting data (the number 0.1, for example, has no exact binary representation with finitely many digits; cf. Example?.), but also when using the elementary operations +, ?, ??and ∕. Moreover, the desired answer may be a nonrepresentable number.

Psychogenic

Matchings and Network Flows,networks. It will turn out that the first of these is a special case of the second. Thus it will not come as a surprise that the same basic method, namely augmenting paths, will be the key to solving both.