Design a decrease$-$by$-$one algorithm for generating the power set of a set of n elements.

$($The power set of a set s is the set of all the subsets of s$,$ including the empty set and s itself.$)$

Hint:

Use the fact that all the subsets of an n$-$element set S $=\{$a$1,....$ an$\}$ can be divided into two groups: those that contain an and those that do not.

$($see a more detailed discussion in Section $4\mathrm{.}3)$: