What is an Algorithm?
Date: 10/21/2001 at 22:30:52 From: jonathan Subject: Algorithm My teacher wants us to define and explain, including an example, what an algorithm is. I'm having trouble figuring out what one is exactly. Can you help? Thanks.
Date: 10/22/2001 at 13:34:02 From: Doctor Ian Subject: Re: Algorithm Hi Jonathan, An algorithm is a sequence of instructions that, if followed, is guaranteed to reach some goal (or establish for certain that the goal is unreachable). The guarantee is important - it's what distinguishes an algorithm from a heuristic ('rule of thumb'). You can find several examples of mathematical algorithms here: Is Math a Science? http://mathforum.org/dr.math/problems/rouzier.03.18.01.html But sometimes the concept is easier to understand in terms of everyday goals and methods. For example, when you've misplaced something, the normal thing to do is to try to think of where you might have left it, by using various heuristics: Look in the last place you remember having it, check your pockets, check your backpack, look on the dining room table, ask your mom, etc. Sometimes these work, and sometimes they don't. When heuristics fail, you can resort to an algorithm, i.e., For each room in the house, For each item in the room, Pick up the item. If it's the item you're looking for, Terminate the search. Note that this will either find the item, or (if you run out of items and rooms to check) will establish for certain that it isn't in the house. Another important feature of an algorithm is that each step has to be both unambiguous and implementable. Perhaps you've heard the old joke: Q: How do you get four elephants into a Volkswagen? A: Put two in the front seat, and two in the back! This isn't an algorithm, because although the steps are unamibiguous, they aren't implementable. Or consider this 'algorithm' for being elected President of the United States: 1. Declare your candidacy. 2. Campaign. 3. Get more votes than the other candidates. Each of these steps is clearly implementable (someone implements them every four years), but some of them are ambiguous. How do you 'campaign'? How do you 'get votes'? Those steps need to be fleshed out a little! Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.