In this chapter, we'll discuss how to "think algorithms"—how to design and analyze programs that solve problems. We'll start with a gentle introduction to algorithms and a not-so-gentle introduction to Perl, then consider some of the tradeoffs involved in choosing the right implementation for your needs, and finally introduce some themes pervading the field:
recursion, divide-and-conquer, and dynamic programming.
What Is an Algorithm?
An algorithm is simply a technique—not necessarily computational—for solving a problem step by step. Of course, all programs solve problems (except for the ones that create problems). What elevates some techniques to the hallowed status of algorithm is that they embody a general, reusable method that solves an entire class of problems. Programs are
created; algorithms are invented. Programs eventually become obsolete; algorithms are permanent.
Of course, some algorithms are better than others. Consider the task of finding a word in a dictionary. Whether it's a physical book or an online file containing one word per line, there are different ways to locate the word you're looking for. You could look up a definition with a linear search, by reading the dictionary from front to back until you happen across your word. That's slow, unless your word happens to be at the very beginning of the alphabet. Or, you could pick pages at random and scan them for your word. You might get lucky. Still, there's obviously a better way. That better way is the binary search algorithm, which you'll learncontinue.
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