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Let C be a category with finite products and a terminal object 1. A list object over an object A of C is: an object L A, a morphism o A : 1 → L A, and; a morphism s A : A × L A → L A; such that for any object B of C with maps b : 1 → B and t : A × B → B, there exists a unique f : L A → B such that the following diagram commutes:
The smallest integer m > 1 such that p n # + m is a prime number, where the primorial p n # is the product of the first n prime numbers. A005235 Semiperfect numbers
The Euclidean algorithm is based on the principle that the greatest common divisor of two numbers does not change if the larger number is replaced by its difference with the smaller number. For example, 21 is the GCD of 252 and 105 (as 252 = 21 × 12 and 105 = 21 × 5) , and the same number 21 is also the GCD of 105 and 252 − 105 = 147 .
It was a design choice from the start to only include very simple toy problems, each providing a different kind of programming challenge. [3] This provides users of the Benchmark Game the opportunity to scrutinize the various implementations. [4] binary-trees; chameneos-redux; fannkuch-redux; fasta; k-nucleotide; mandelbrot; meteor-contest; n ...
map function, found in many functional programming languages, is one example of a higher-order function. It takes as arguments a function f and a collection of elements, and as the result, returns a new collection with f applied to each element from the collection.
In mathematics, the floor function is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted ⌊x⌋ or floor(x). Similarly, the ceiling function maps x to the least integer greater than or equal to x , denoted ⌈ x ⌉ or ceil( x ) .
This is a list of notable programming languages with features designed for object-oriented programming (OOP). The listed languages are designed with varying degrees of OOP support. Some are highly focused in OOP while others support multiple paradigms including OOP.
Decomposing a complex programming task into simpler steps: this is one of the two main tools of structured programming, along with data structures; Reducing duplicate code within a program; Enabling reuse of code across multiple programs; Dividing a large programming task among various programmers or various stages of a project