algorithm

algorithm (ăl`gərĭth'əm) or algorism (–rĭz'əm) [for Al-Khowarizmi], a clearly defined procedure for obtaining the solution to a general type of problem, often numerical. Much of ordinary arithmetic as traditionally taught consists of algorithms involving the fundamental operations of addition, subtraction, multiplication, and division. An example of an algorithm is the common procedure for division, e.g., the division of 1,347 by 8, in which the remainders of partial divisions are carried to the next digit or digits; in this case the remainder of 5 in the division of 13 by 8 is placed in front of the 4, and 8 is then divided into 54. The software that instructs modern computers embodies algorithms, often of great sophistication.

---

algorithm

Procedure that produces the answer to a question or the solution to a problem in a finite number of steps. An algorithm that produces a yes or no answer is called a decision procedure; one that leads to a solution is a computation procedure. A mathematical formula and the instructions in a computer program are examples of algorithms. Euclid's Elements (c. 300 BC) contained an algorithm for finding the greatest common divisor of two integers. Manipulation of lists (searching for, inserting, and removing items) can be done efficiently by using algorithms.

---

A set of ordered steps for solving a problem, such as a mathematical formula or the instructions in a program. The terms algorithm and logic are synonymous. Both refer to a sequence of steps to solve a problem. However, an algorithm implies an expression that solves a complex problem rather than the overall input-process-output logic of typical business programs. See encryption algorithm.

---

(algorithm, programming)

algorithm - A detailed sequence of actions to perform to accomplish some task. Named after the Iranian mathematician, Mohammed Al-Khawarizmi. Technically, an algorithm must reach a result after a finite number of steps, thus ruling out brute force search methods for certain problems, though some might claim that brute force search was also a valid (generic) algorithm. The term is also used loosely for any sequence of actions (which may or may not terminate). Paul E. Black's Dictionary of Algorithms, Data Structures, and Problems.