Algorithm

An algorithm is a sequence of steps set out with the aim of solving a problem. It is a way of addressing questions sharing a similar character in a systematic manner. The term is used in computing to describe the essential first step in programming, that is the intuitive understanding of both the nature of a problem and its solution. Because the steps of an algorithm are all simple, in a sense that they do not require great intelligence. Alas, attempts to break philosophical problems down similarly into simple steps have fallen short of the hopes of such as Pascal and Leibniz.

A cooking recipe can be considered an example of an algorithm, although the term is more frequently applied to the information processing instructions used in computer programs. The word is derived from the name of al-Khwarizmi, a mathematician active in Baghdad in the 9th century CE.

Introduction

An algorithm consists of the underlying recipe steps (print the value of X) rather than the actual computer program source code used to execute the steps (PRINT X). When encoded in computer programs, algorithms operate on data values, preferably data maintained in a consistent data structure. Thus an algorithm is the recipe, while the data structure is the well-stored ingredients on which the recipe is designed to operate.

Nicklaus Wirth, the inventor of the programming language Pascal, titled one of his books "Algorithms + Data Structures = Programs" (ISBN 0130224189) to indicate the complementary nature of algorithms and data structures, and their centrality to computing.

Algorithms are usually expressed independently of the programming language, typically in terms of a brief, informal list of commands called pseudocode, or diagrammatically in the form of a flowchart.

Examples of different categories of algorithms used in computer programming include:

• Bounding limit
• Compression
• Conversion
• Encryption
• Fourier transform
• Geometric
• Graphic
• Numeric
• Probabilistic
• Searching
• Sorting
• Text string

Basic algorithm designs

There are several general methods for designing algorithms. Some of the most common are

• Divide and conquer strategies. These typically yield algorithms of $O(n\log n)$ complexity, or better.
• The greedy method.
• Dynamic programming.

Some well known algorithms

• Quicksort
• The fast fourier transform, also known as the fft.
• The Euclidean algorithm, known from number theory.