In computational

combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ...

, a loopless algorithm or loopless imperative algorithm is an imperative

algorithm In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algo ...

that generates successive combinatorial objects, such as partitions,

permutation In mathematics, a permutation of a set can mean one of two different things: * an arrangement of its members in a sequence or linear order, or * the act or process of changing the linear order of an ordered set. An example of the first mean ...

s, and

combination In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter (unlike permutations). For example, given three fruits, say an apple, an orange and a pear, there are ...

s, in

constant time In theoretical computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations p ...

and the first object in

linear time In theoretical computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations ...

. The objects must be immediately available in simple form without requiring any additional steps. A loopless functional algorithm is a functional algorithm that takes the form ''unfoldr step • prolog'' where ''step'' takes constant time and ''prolog'' takes linear time in the size of the input. The standard

function Function or functionality may refer to: Computing * Function key, a type of key on computer keyboards * Function model, a structured representation of processes in a system * Function object or functor or functionoid, a concept of object-orie ...

''unfoldr'' is a right-associative

Bird Birds are a group of warm-blooded vertebrates constituting the class (biology), class Aves (), characterised by feathers, toothless beaked jaws, the Oviparity, laying of Eggshell, hard-shelled eggs, a high Metabolism, metabolic rate, a fou ...

unfold.

References

Combinatorial algorithms {{Combin-stub