By Robert Sedgewick

ISBN-10: 0201066726

ISBN-13: 9780201066722

This booklet is meant to survey crucial algorithms in use on desktops this present day and train the basic suggestions to the transforming into inhabitants attracted to changing into severe laptop clients.

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Extra resources for Algorithms (Addison-Wesley series in computer science)

Example text

For example, the abstract data structure for polynomials in the examples above is the set of coefficients: a user providing input to one of the programs above need not know whether a linked list or an array is being used. Modern programming systems have sophisticated mechanisms which make it possible to change representations easily, even in large, tightly integrated systems. AFUTHAJETIC 31 Exercises 1. Another way to represent polynomials is to write them in the form rc(xrr)(z - r2) . . (X - TN).

These data structures are used by many of the algorithms in this book; in later sections we’ll study some more advanced data structures. Polynomials Suppose that we wish to write a program that adds two polynomials: we would 23 CJUJ’TER 2 24 like it to perform calculations like (1+ 2x - 3x3) + (2 -x) = 3 + x - 3x3. In general, suppose we wish our program to be able to compute r(x) = p(x) + q(x), where p and q are polynomials with N coefficients. maxN] of real; N, i: integer; begin readln (N) ; for i:=O to N-l do read(p[i]); for i:=O to N-l do read(q[i]); for i:=O to N-J do r[i] :=p[i]+q[i]; for i:=O to N-l do write(r[i]); wri teln end.

Give a counterexample to the assertion that the user of an abstract data structure need not know what representation is being used. 3. Random Numbers Our next set of algorithms will bie methods for using a computer to generate random numbers. We will find many uses for random numbers later on; let’s begin by trying to get a better idea of exactly what they are. Often, in conversation, people use the term random when they really mean arbitrary. When one asks for an trrbitrary number, one is saying that one doesn’t really care what number one gets: almost any number will do.