A Simple Algorithm for Generating Subsets of $k$ or Fewer Elements of an $n$-Set

Abstract

Forming all distinct subsets with $k$ or fewer objects from a set with $n$ elements can be accomplished by generating a subset of the binary reflected Gray code. This paper presents a straightforward algorithm that generates the desired Gray codewords by altering the stack which maintains the transition sequence that determines the next codeword position to be altered.