Algorithms can be a very difficult subject to understand. They come in varying logic expressed in varying languages, implemented in different syntax for varying purposes. Indeed, there are algorithms that are said to be different but works pretty much the same: the distinction can be drawn upon many parameters, one that is common is the nature of how the logic is implemented and how efficient it is based on some constraints usually determined by time and memory it needs — more generally with respect to finite resources.

In this article, we shall take a general perspective and build our understanding of algorithms. We shall learn the features and characteristics of an algorithm, a criterion to group and organize the family of algorithms, and the manner as to how can we decide to use an algorithm as a response to a given problem.

Content Overview:

• What is an algorithm, and how does it make any sense?
• Features and characteristics of an algorithm.
• How do we classify algorithms? And how do we determine which one to use?

Forest to the trees.

An algorithm describes the ordering of procedures for obtaining specified results.

In the parlance of mathematics and computer science, an algorithm pertains to a finite sequence of well-defined computer-implementable instructions, typically to solve a class of problems or to perform a computation [1–2]. Algorithms are essential for data and information processing in computers. Historically, computers are people that can carry out the process of computations through a series of operations. Thus, the antiquity of algorithms can be traced back to the Babylonian Mathematics of c. 2500 B.C [2] — the division algorithm. Greek mathematicians have used the concept of an algorithm in investigating patterns of numbers such as the Euclidean algorithm which is a method for finding the greatest common divisor given two numbers. And Eratosthenes’ method for finding prime numbers[2].

Broadly speaking, an algorithm is a series of instructions expressed for an agent being capable of carrying through such a process to execute. Further formalizations suggest that an algorithm be expressed by a Turing-complete system [3–4]. A formal system, say a programming language, is said to be Turing-complete is it can emulate the abstract Turing machines. In other words, a Turing-complete language is theoretically capable of expressing all tasks accomplished by computers [5] as Turing machines bear to be the theoretical representation of a computer. Therefore, expressing algorithms in such a manner not only simplifies but also logically formalizes the series of procedures.

On Expressing Algorithms

One can express algorithms in various forms: either in a natural language that we use every day or in an artificial language that is constructed with specified grammatical syntax and vocabularies — e.g. cookbook recipes and methods explained in _English _or Pseudocodes. By the same token, algorithms are independent of languages they are expressed upon. Additionally, there are means as to how we could sort out the representation of algorithms for varying purposes.

In developing a solution for a given problem, one has to follow an iterative development approach — planning, building, testing, and revising. In that sense, a representation of an algorithm, in varying degrees of abstraction, might be helpful for generating solutions. We can categorize these degrees as follows:

• High-level description: a statement that describes an algorithm without necessarily specifying implementation details.
• Implementation description: directives that specify the implementation, plausibly with respect to the language e.g. pseudocodes or C++ code.

In the same way, data structures and algorithms are represented abstractly (which only gets into the essence of the matter) before it can be implemented in a codebase[4]. One has to begin with a high-level (abstract) description to picture the given case: for this inputs what are the expected outputs? What are the key procedures? Among others, Input-Processing-Output (IPO) diagrams might be helpful for thi

#programming #algorithms #computer-science #mathematics #algorithms