Читать книгу Algorithms For Dummies - John Paul Mueller, John Mueller Paul, Luca Massaron - Страница 47

If you thought things were abstract before, this section makes those previous sections seem concrete, but grit your teeth and move on because you really are up to the task! Measuring a series of steps devised to achieve a solution to a problem poses quite a few challenges. The previous section discusses counting time steps (number of operations), but sometimes you also need to compute space (such as the memory an algorithm consumes). You consider space when your problem is greedy for resources. Depending on the problem, you may consider an algorithm to be better when it works efficiently with regard to one of these resource consumption aspects:

 Running time

 Computer memory requirements

 Hard-disk usage

 Power consumption

 Data-transmission speed in a network

Some of these aspects relate to others in an inverse manner, so if, for instance, you want speedier execution time, you can sometimes increase memory or power consumption to get it. Not only can you have different efficiency configurations when running an algorithm, you can also change the hardware characteristics and software implementation to accomplish your goals. In terms of hardware, using a supercomputer or a general-purpose computer does matter, and the software, or language used to write the algorithm, is definitely a game changer. In addition, the quantity and kind of data you feed the algorithm could result in better or worse performance measurements.

RAM simulations count time because when you can employ a solution in so many environments, and its resource usage depends on so many factors, you have to find a way to simplify comparisons so that they become standard. Otherwise, you can’t compare possible alternatives. The solution is, as so often happens with many other problems, to use a single measure and say that one size fits all. In this case, the measure is time, which you make equal to the number of operations, that is, the complexity of the algorithm.

A RAM simulation places the algorithm in a situation that’s both language and machine-agnostic (it’s independent of programming language and computer type). However, explaining how a RAM simulation works to others requires quite an effort. The analysis of algorithms proposes to use the number of operations you get from a RAM simulation and turn them into a mathematical function expressing how your algorithm behaves in terms of time, which is a quantification of the steps or operations required when the number of data inputs grows. For instance, if your algorithm sorts objects, you can express complexity using a function that reports how many operations it needs depending on the number of objects it receives.