Download Concrete Abstractions: An Introduction to Computer Science by Max Hailperin PDF

By Max Hailperin

Scheme has been taught to each pupil taking desktop 'science' at MIT for the previous twenty years, and it truly is more and more used during the international to coach that topic. The mainstream languages C++ and visible uncomplicated are thought of to be poorly designed, and C is simply too low point to be a sensible choice in a direction meant to supply a accomplished creation to laptop technological know-how (which is going a ways past what the typical individual calls 'programming').

Scheme is a version of Lisp, that is the second one oldest laptop language, after Fortran. it truly is, notwithstanding, a completely smooth language, and has strongly encouraged the layout of alternative smooth languages like ML and Python.

The publication begins in Scheme, then provides item orientated recommendations and meeting language. It finishes with a transition to Java, that is, after all, just like C++. This process will offer a wider heritage than a regular textual content utilizing C++ or C could.

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1 Recursion 23 To make a chain of length n: 1. If n ϭ 1, (a) Bend a strip around to bring the two ends together, and join them. (b) Proudly deliver to your customer a chain of length 1. 2. Otherwise, (a) Pick up a strip. (b) Ask the person next in line to please make you a chain of length n Ϫ 1. (c) Slip your strip through one of the end links of that chain, bend it around, and join the ends together. (d) Proudly deliver to your customer a chain of length n. Now you know all there is to know about recursion, you have met a bunch of new people, and if you were ambitious enough to make a long chain, you even have a nice decoration to drape around your room.

8 Another type of generalization of sum-of-first can be obtained by varying what is being summed, rather than just the range of summation: a. Write a procedure sum-of-squares that computes the sum of the first n squares, where n is a nonnegative integer. b. Write a procedure sum-of-cubes that computes the sum of the first n cubes, where n is a nonnegative integer. c. Write a procedure sum-of-powers that has two parameters n and p, both nonnegative integers, such that (sum-of-powers n p) computes 1p ϩ 2p ϩ и и и ϩ np .

We broke off a big chunk of each problem (the recursion principle) that was just like the original problem (the self-similarity principle) except that it was smaller. After that chunk was finished, we only had a little work left to do, either by putting in one more link or multiplying by one more 28 Chapter 2 Recursion and Induction Exponents In this book, when we use an exponent, such as the k in xk , it will almost always be either a positive integer or zero. When k is a positive integer, xk just means k copies of x multiplied together.

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