always presents a series of steps and doesn’t necessarily perform these steps to solve a math formula. The scope of algorithms is incredibly large. You can find algorithms that solve problems in science, medicine, finance, industrial production and supply, and communication. Algorithms provide support for all parts of a person’s daily life. Anytime a sequence of actions achieving something in our life is finite, well-defined, and effective, you can view it as an algorithm. For example, you can turn even something as trivial and simple as making toast into an algorithm. In fact, the making toast procedure often appears in computer science classes, as discussed at http://brianaspinall.com/now-thats-how-you-make-toast-using-computer-algorithms/.
Unfortunately, the algorithm on the site is flawed. The instructor never removes the bread from the wrapper and never plugs the toaster in, so the result is damaged plain bread still in its wrapper stuffed into a nonfunctional toaster (see the discussion at http://blog.johnmuellerbooks.com/2013/03/04/procedures-in-technical-writing/ for details). Even so, the idea is the correct one, yet it requires some slight, but essential, adjustments to make the algorithm finite and effective.
One of the most common uses of algorithms is as a means of solving formulas. For example, when working with the GCD of two integer values, you can perform the task manually by listing each of the factors for the two integers and then selecting the greatest factor that is common to both. For example, GCD (20, 25) is 5 because 5 is the largest number that divides evenly into both 20 and 25. However, processing every GCD manually is time consuming and error prone, so the Greek mathematician Euclid created a better algorithm to perform the task. You can see the Euclidean method demonstrated at https://www.khanacademy.org/computing/computer-science/cryptography/modarithmetic/a/the-euclidean-algorithm.
However, a single formula, which is a presentation of symbols and numbers used to express information or ideas, can have multiple solutions, each of which is an algorithm. In the case of GCD, another common algorithm is one created by Derrick Henry Lehmer (https://www.imsc.res.in/~kapil/crypto/notes/node11.html). Because you can solve any formula multiple ways, people spend a great deal of time comparing algorithms to determine which one works best in a given situation. (See a comparison of Euclid to Lehmer at http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.31.693&rep=rep1&type=pdf.)
Because our society and its accompanying technology are changing quickly, we need algorithms that can keep the pace. Scientific achievements such as sequencing the human genome were possible in our age because scientists found algorithms that run fast enough to complete the task. Measuring which algorithm is better in a given situation, or in an average usage situation, is really serious stuff and is a topic of discussion among computer scientists.
When it comes to computer science, the same algorithm can have multiple presentations; why do it one way when you can invent multiple methods just for fun? For example, you can present the Euclidean algorithm in both recursive and iterative forms, as explained at http://cs.stackexchange.com/questions/1447/what-is-most-efficient-for-gcd. In short, algorithms present a method of solving formulas, but it would be a mistake to say that just one acceptable algorithm exists for any given formula or that only one acceptable presentation of an algorithm exists. Using algorithms to solve problems of various sorts has a long history — it isn’t something that has just happened.
Even if you limit your gaze to computer science, data science, artificial intelligence, and other technical areas, you find many kinds of algorithms — too many for a single book. For example, The Art of Computer Programming, by Donald E. Knuth (Addison-Wesley), spans 3,168 pages in four volumes (see http://www.amazon.com/exec/obidos/ASIN/0321751043/datacservip0f-20/) and still doesn’t manage to cover the topic (the author intended to write more volumes). However, here are some interesting uses for you to consider:
Searching: Locating information or verifying that the information you see is the information you want is an essential task. Without this ability, you couldn’t perform many tasks online, such as finding the website on the Internet selling the perfect coffee pot for your office. These algorithms change constantly, as shown by Google’s recent change in its algorithm (https://www.youaretech.com/blog/2021/1/26/webpage-experience-a-major-google-algorithm-update-in-2021nbsp).
Sorting: Determining which order to use to present information is important because most people today suffer from information overload, and putting information in order is one way to reduce the onrush of data. Imagine going to Amazon, finding that more than a thousand coffee pots are for sale there, and yet not being able to sort them in order of price or the most positive review. Moreover, many complex algorithms require data in the proper order to work dependably, so ordering is an important requisite for solving more problems.
Transforming: Converting one sort of data to another sort of data is critical to understanding and using the data effectively. For example, you might understand imperial weights just fine, but all your sources use the metric system. Converting between the two systems helps you understand the data.
Scheduling: Making the use of resources fair to all concerned is another way in which algorithms make their presence known in a big way. For example, timing lights at intersections are no longer simple devices that count down the seconds between light changes. Modern devices consider all sorts of issues, such as the time of day, weather conditions, and flow of traffic.
Graph analysis: Deciding on the shortest path between two points finds all sorts of uses. For example, in a routing problem, your GPS couldn’t function without this particular algorithm because it could never direct you along city streets using the shortest route from point A to point B. And even then, your GPS might direct you to drive into a lake (https://theweek.com/articles/464674/8-drivers-who-blindly-followed-gps-into-disaster).
Cryptography: Keeping data safe is an ongoing battle with hackers constantly attacking data sources. Algorithms make it possible to analyze data, put it into some other form, and then return it to its original form later.
Pseudorandom number generation: Imagine playing games that never varied. You start at the same place; perform the same steps, in the same manner, every time you play. Without the capability to generate seemingly random numbers, many computer tasks become impossible.
Finding algorithms everywhere
The previous section mentions the toast algorithm for a specific reason. For some reason, making toast is probably the most popular algorithm ever created. Many grade-school children write their equivalent of the toast algorithm long before they can even solve the most basic math. It’s not hard to imagine