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Unformatted text preview: Lecture Notes CMSC 251 Lecture 2: Analyzing Algorithms: The 2d Maxima Problem (Thursday, Jan 29, 1998) Read: Chapter 1 in CLR. Analyzing Algorithms: In order to design good algorithms, we must first agree the criteria for measuring algorithms. The emphasis in this course will be on the design of efficient algorithm, and hence we will measure algorithms in terms of the amount of computational resources that the algorithm requires. These resources include mostly running time and memory. Depending on the application, there may be other elements that are taken into account, such as the number disk accesses in a database program or the communication bandwidth in a networking application. In practice there are many issues that need to be considered in the design algorithms. These include issues such as the ease of debugging and maintaining the final software through its lifecycle. Also, one of the luxuries we will have in this course is to be able to assume that we are given a clean, fully specified mathematical description of the computational problem. In practice, this is often not the case, and the algorithm must be designed subject to only partial knowledge of the final specifications. Thus, in practice it is often necessary to design algorithms that are simple, and easily modified if problem parameters and specifications are slightly modified. Fortunately, most of the algorithms that we will discuss in this class are quite simple, and are easy to modify subject to small problem variations. Model of Computation: Another goal that we will have in this course is that our analyses be as independent as possible of the variations in machine, operating system, compiler, or programming language. Unlike programs, algorithms to be understood primarily by people (i.e. programmers) and not machines. Thus gives us quite a bit of flexibility in how we present our algorithms, and many lowlevel details may be omitted (since it will be the job of the programmer who implements the algorithm to fill them in). But, in order to say anything meaningful about our algorithms, it will be important for us to settle on a mathematical model of computation. Ideally this model should be a reasonable abstraction of a standard generic singleprocessor machine. We call this model a random access machine or RAM . A RAM is an idealized machine with an infinitely large randomaccess memory. Instructions are exe cuted onebyone (there is no parallelism). Each instruction involves performing some basic operation on two values in the machines memory (which might be characters or integers; let’s avoid floating point for now). Basic operations include things like assigning a value to a variable, computing any basic arithmetic operation ( + , , * , integer division) on integer values of any size, performing any comparison (e.g. x ≤ 5 ) or boolean operations, accessing an element of an array (e.g. A [10] ). We assume that each basic operation takes the same constant time to execute.assume that each basic operation takes the same constant time to execute....
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This note was uploaded on 01/13/2012 for the course CMSC 351 taught by Professor Staff during the Fall '11 term at University of Louisville.
 Fall '11
 Staff

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