Subsets Animation

This page illustrates an algorithm for generating all possible subsets of size k taken from the set {1, ..., n}.

Each row is derived from the previous row using the following procedure:

Find the smallest element j such that j+1 is not in the set. Replace j by j+1. (Shown in blue)
If there are any elements to the right of j, leave them where they are. (Shown in gray)
If there are any elements to the left of j, push them as far to the left as possible. (Shown in red)

For more details, see:

Combinatorics: Topics, Techniques, Algorithms by Peter J. Cameron (1994), Algorithm 3.12.3, page 43