combinationsnew

CombinationsNew is a term used in programming libraries and mathematical tooling to denote an updated approach for generating combinations from a finite set. It usually refers to a function or class that enumerates k-element subsets from a given collection, with an emphasis on efficiency, flexibility, and streaming output.

Key features typically include lazy evaluation, producing one combination at a time without constructing the full set of combinations; support for multiple generation orders such as lexicographic or Gray-code-like sequences; and the ability to apply constraints such as element predicates or index-based restrictions. Some implementations also support combinations with repetition and provide options to skip symmetric duplicates.

Algorithms behind CombinationsNew generally avoid naive recursive expansion and instead use iterative state machines or combinatorial number systems to advance to the next combination with minimal memory. Many versions maintain low memory usage per yielded combination and incur time proportional to the number of combinations produced.

Usage patterns usually involve calling a constructor or function with a collection and a target size, then iterating over the results. For example, given a set S and k, CombinationsNew(S, k) yields all k-element subsets in a defined order. This pattern is common in combinatorial testing, sampling, and puzzle solving.

CombinationsNew is not a standardized mathematical term; its exact behavior, syntax, and performance depend on the library or language. It relates to concepts such as combinations, combinations with repetition, and generation algorithms.

See also: combinations, combinations with repetition, lexicographic generation, Gray code, Knuth's Art of Computer Programming on generating all subsets.