Algorithms and Programming: Problems and Solutions by Alexander Shen

By Alexander Shen

Algorithms and Programming is essentially meant for a first-year undergraduate direction in programming. it really is dependent in a problem-solution structure that calls for the coed to imagine throughout the programming method, therefore constructing an figuring out of the underlying idea. even supposing the writer assumes a few reasonable familiarity with programming constructs, the booklet is well readable via a pupil taking a uncomplicated introductory direction in desktop technological know-how. moreover, the extra complicated chapters make the booklet necessary for a path on the graduate point within the research of algorithms and/or compiler construction.

Each bankruptcy is kind of self sustaining, containing classical and famous difficulties supplemented by way of transparent and in-depth reasons. the fabric coated contains such issues as combinatorics, sorting, looking, queues, grammar and parsing, chosen famous algorithms and masses extra. scholars and lecturers will locate this either a great textual content for studying programming and a resource of difficulties for a number of courses.

The ebook is addressed either to bold scholars and teachers searching for attention-grabbing difficulties [and] fulfills this activity completely, particularly if the reader has an exceptional mathematical background.— Zentralblatt MATH

This e-book is meant for college students, engineers, and folks who are looking to increase their desktop skills.... The chapters could be learn independently. in the course of the booklet, invaluable workouts provide readers a sense for a way to use the speculation. the writer presents solutions to the exercises.— Computing Reviews

This publication features a selection of difficulties and their ideas. lots of the difficulties are of the kind that might be encountered in a path on facts constructions or compilers.... The ebook will end up helpful in case you want homework or attempt questions for the parts coated by means of it. the various questions are formulated in any such method that generating variations on them could be performed with ease.... Overall...the publication is easily performed. i like to recommend it to academics and people wishing to sharpen their info constitution and compiler skills.— SIGACT News

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Extra resources for Algorithms and Programming: Problems and Solutions

Example text

If we want this new function to apply to the elements of a list we need to use either the Map function, or the map operator /@. In[213]:= Map[PerfectQ, {6, 10, 28}] PerfectQ /@ {6, 10, 28} 34 1 Number Theory Out[213]= {True, False, True} Out[214]= {True, False, True} Unfortunately, the pattern in our PerfectQ function causes another small problem. Our function is supposed to report whether its argument is a perfect number, but in many cases it does nothing at all. Any argument which is not a positive integer cannot possibly be a perfect number, and so our function should return False in these cases.

Furthermore, if a|n then n = ka for some k ∈ N and so, recalling modular arithmetic, n ≡ 0 mod a. The problem we now try to solve now with Mathematica is to find all the divisors of a number. To begin with, it is helpful to know that Mathematica can perform modular 24 1 Number Theory arithmetic using the Mod function. Simply put, entering Mod[a, b] will calculate the modulus of a (modulo b). 6, we may use it to perhaps make the input a little more intuitive. In this case a ~Mod~ b will compute the modulus of a (modulo b).

This is a form of pattern matching inside of Mathematica which we will later use to restrict the arguments of our functions to particular types of mathematical objects or Mathematica expressions. For the moment, however, we content ourselves with allowing any valid expression for our arguments. Fortunately, our function behaves quite sensibly with a variety of different arguments. In[96]:= p[2] p[4] p[A] p[{2, 4}] Out[96]= 18 Out[97]= 62 16 1 Number Theory Out[98]= − 2 + 4A + 3A2 Out[99]= {18, 62} It is interesting to see that in the last example above that the function was applied to each element of the list we used as our argument.

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