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Flowchart of using successive subtractions to find the greatest common divisor of number r and s. In mathematics and computer science, an algorithm (/ ˈ æ l ɡ ə r ɪ ð əm / ⓘ) is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation. [1]
Computer programming or coding is the composition of sequences of instructions, called programs, that computers can follow to perform tasks. [1] [2] It involves designing and implementing algorithms, step-by-step specifications of procedures, by writing code in one or more programming languages.
Algorithms have become synonymous with something highly technical and difficult to understand, that is either an arbiter of objective truth, or, on the other end of the spectrum, something wholly ...
A computer program written in an imperative language. Imperative languages specify a sequential algorithm using declarations, expressions, and statements: [52] A declaration introduces a variable name to the computer program and assigns it to a datatype [53] – for example: var x: integer; An expression yields a value – for example: 2 + 2 ...
There are several broadly recognized algorithmic techniques that offer a proven method or process for designing and constructing algorithms. Different techniques may be used depending on the objective, which may include searching, sorting, mathematical optimization, constraint satisfaction, categorization, analysis, and prediction.
The word programming referred to the use of the method to find an optimal program, in the sense of a military schedule for training or logistics. This usage is the same as that in the phrases linear programming and mathematical programming , a synonym for mathematical optimization .
The transformation of a linear program to one in standard form may be accomplished as follows. [16] First, for each variable with a lower bound other than 0, a new variable is introduced representing the difference between the variable and bound. The original variable can then be eliminated by substitution. For example, given the constraint
In computer science, program synthesis is the task to construct a program that provably satisfies a given high-level formal specification.In contrast to program verification, the program is to be constructed rather than given; however, both fields make use of formal proof techniques, and both comprise approaches of different degrees of automation.