Algorithm

In mathematics or computer science, an algorithm is a sequence of steps for one particular method of solving a problem, similar to the instructions of a recipe when cooking. The word is derived from the name of al-Khwarizmi, a Persian mathematician who was a librarian in Baghdad in the 9th century CE.

Introduction

An algorithm consists of the steps to follow in solving a problem. 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.