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1.6 If you were offered a job with Microsoft and permitted to choose between working on operating systems, database products, or applications products like Word or Excel, which would you choose, and why 1.7 Whom do you believe should be credited as the inventor of the modern computer 1.8 What applications of computing seem to you to be unethical What are some principles you can declare with respect to the ethical and unethical use of computers and software 1.9 List some important ways in which computing has contributed to the welfare of humanity. Which people, if any, have suffered from the advance of computing technology
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DEFINITION OF AN ALGORITHM An algorithm is a method for solving a class of problems. While computer scientists think a lot about algorithms, the term applies to any method of solving a particular type of problem. The repair manual for your car will describe a procedure, which could also be called an algorithm, for replacing the brake pads. The turn-by-turn travel instructions from MapQuest could be called an algorithm for getting from one place to another. EXAMPLE DESIGNING A STAIRCASE You may be surprised, as we were, to know that every staircase must be custom-designed to fit the circumstances of total elevation (total rise ) and total horizontal extent (total run ). Figure 2-1 shows these dimensions. If you search the web, you can find algorithms methods for designing staircases. To make stairs fit a person s natural gait, the relationship of each step s rise (lift height) to its run (horizontal distance) should be consistent with a formula. Some say the following formula should be satisfied: (rise * 2) + run = 25 to 27 inches Others say the following simpler formula works well: rise + run = 17 to 18 inches Many say the ideal rise for each step is 7 in, but some say outdoor steps should be 6 in high because people are more likely to be carrying heavy burdens outside. In either case, for any particular situation, the total rise of the staircase will probably not be an even multiple of 6 or 7 in. Therefore, the rise of each step must be altered to create a whole number of steps. These rules lead to a procedure for designing a staircase. Our algorithm for designing a set of stairs will be to: Divide the total rise by 7 in and round the result to the nearest whole number to get the number of steps. We will then divide the total run by (the number of steps 1) (see Fig. 2-1) to compute the run for each step. We will apply one of the formulas to see how close this pair of rise and run parameters is to the ideal. Then we will complete the same computations with one more step and one less step, and also compute the values of the formula for those combinations of rise and run. 5 We will accept the combination of rise and run that best fits the formula for the ideal. An algorithm is a way of solving a type of problem, and an algorithm is applicable to many particular instances of the problem. A good algorithm is a tool that can be used over and over again, as is the case for our staircase design algorithm.
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Figure 2-1 Staircase dimensions. EXAMPLE FINDING THE GREATEST COMMON DENOMINATOR In mathematics, a famously successful and useful algorithm is Euclid s algorithm for finding the greatest common divisor (GCD) of two numbers. The GCD is the largest integer that will evenly divide the two numbers in question. Euclid described his algorithm about 300 BCE. Without having Euclid s algorithm, how would one find the GCD of 372 and 84 One would have to factor the two numbers, and find the largest common factor. As the numbers in question become larger and larger, the factoring task becomes more and more difficult and time-consuming. Euclid discovered an algorithm that systematically and quickly reduces the size of the problem by replacing the original pair of numbers by smaller pairs until one of the pair becomes zero, at which point the GCD is the other number of the pair (the GCD of any number and 0 is that number). Here is Euclid s algorithm for finding the GCD of any two numbers A and B. Repeat: If B is zero, the GCD is A. Otherwise: find the remainder R when dividing A by B replace the value of A with the value of B replace the value of B with the value of R For example, to find the GCD of 372 and 84, which we will show as: GCD(372, 84) Find GCD(84, 36) because 372/84 > remainder 36 Find GCD(36, 12) because 84/36 > remainder 12 Find GCD(12, 0) because 36/12 > remainder 0; Solved! GCD = 12 More formally, an algorithm is a sequence of computations that operates on some set of inputs and produces a result in a finite period of time. In the example of the algorithm for designing stairs, the inputs are the total rise and total run. The result is the best specification for the number of steps, and for the rise and run of each step. In the example of finding the GCD of two numbers, the inputs are the two numbers, and the result is the GCD. Often there are several ways to solve a class of problems, several algorithms that will get the job done. The question then is which algorithm is best In the case of algorithms for computing, computer scientists have developed techniques for analyzing the performance and judging the relative quality of different algorithms. REPRESENTING ALGORITHMS WITH PSEUDOCODE In computer science, algorithms are usually represented as pseudocode. Pseudocode is close enough to a real programming language that it can represent the tasks the computer must perform in executing the algorithm. Pseudocode is also independent of any particular language, and uncluttered by details of syntax, which characteristics make it attractive for conveying to humans the essential operations of an algorithm.
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