Problem Statement

A   set   is a collection (container) of certain values, without any particular order, and no repeated values. It corresponds with a finite set in mathematics. A set can be implemented as an associative array (partial mapping) in which the value of each key-value pair is ignored. Given a set S, the power set (or powerset) of S, written P(S), or 2S, is the set of all subsets of S.

By using a library or built-in set type, or by defining a set type with necessary operations, write a function with a set S as input that yields the power set 2S of S.

For example, the power set of     {1,2,3,4}     is For a set which contains n elements, the corresponding power set has 2n elements, including the edge cases of empty set. The power set of the empty set is the set which contains itself (20 = 1): And the power set of the set which contains only the empty set, has two subsets, the empty set and the set which contains the empty set (21 = 2):

Extra credit: Demonstrate that your language supports these last two powersets.

Let's start with the solution:

MODE MEMBER = INT;

PROC power set = ([]MEMBER s)[][]MEMBER:(
  [2**UPB s]FLEX[1:0]MEMBER r;
  INT upb r := 0;
  r[upb r +:= 1] := []MEMBER(());
  FOR i TO UPB s DO
    MEMBER e = s[i];
    FOR j TO upb r DO
      [UPB r[j] + 1]MEMBER x;
      x[:UPB x-1] := r[j];
      x[UPB x] := e; # append to the end of x #
      r[upb r +:= 1] := x # append to end of r #
    OD
  OD;
  r[upb r] := s;
  r    
);
# Example: #
test:(
  [][]MEMBER set = power set((1, 2, 4));
  FOR member TO UPB set DO
    INT upb = UPB set[member];
    FORMAT repr set = $"("f( upb=0 | $$ | $n(upb-1)(d", ")d$ )");"$;
    printf(($"set["d"] = "$,member, repr set, set[member],$l$))
  OD
)