Читать книгу Algorithms For Dummies - John Paul Mueller, John Mueller Paul, Luca Massaron - Страница 45

Gaining insights into precisely how algorithms work is important because otherwise you can’t determine whether an algorithm actually performs in the way you need it to. Also, without good measurements, you can’t perform accurate comparisons to know whether you really do need to discover a new method of solving a problem when an older solution works too slowly or uses too many resources. Knowing the basis to use to compare different solutions and deciding between them is an essential skill when dealing with algorithms.

The issue of efficiency has been part of discovering and designing new algorithms since the concept of algorithms first came into being, which is why you see so many different algorithms competing to solve the same problem. The concept of measuring the size of the functions within an algorithm and analyzing how the algorithm works isn’t new; both Ada Lovelace and Charles Babbage considered the problems of algorithm efficiency in reference to computers as early as 1843 (see https://www.computerhistory.org/babbage/adalovelace/).

Donald Knuth (https://www-cs-faculty.stanford.edu/~knuth/), computer scientist, mathematician, professor emeritus at Stanford University, and author of the milestone, multivolume book The Art of Computer Programming (Addison-Wesley), devoted much of his research and studies to comparing algorithms. He strove to formalize how to estimate the resource needs of algorithms in a mathematical way and to allow a correct comparison between alternative solutions. He coined the term analysis of algorithms, which is the branch of computer science devoted to understanding how algorithms work in a formal way. The analysis measures resources required in terms of the number of operations an algorithm requires to reach a solution or by its occupied space (such as the storage an algorithm requires in computer memory).

Analysis of algorithms requires some mathematical understanding and some computations, but it’s extremely beneficial in your journey to discover, appreciate, and effectively use algorithms. This topic is considerably more abstract than other topics in this book. To make the discussion less theoretical, later chapters present more practicalities of such measurement by examining algorithms together in detail. The following sections give you the basics.