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:

$ include "seed7_05.s7i";
 
const func array bitset: powerSet (in bitset: baseSet) is func
  result
    var array bitset: pwrSet is [] (bitset.value);
  local
    var integer: element is 0;
    var integer: index is 0;
    var bitset: aSet is bitset.value;
  begin
    for element range baseSet do
      for key index range pwrSet do
        aSet := pwrSet[index];
        if element not in aSet then
          incl(aSet, element);
          pwrSet &:= aSet;
        end if;
      end for;
    end for;
  end func;

const proc: main is func
  local
    var bitset: aSet is bitset.value;
  begin
    for aSet range powerSet({1, 2, 3, 4}) do
      writeln(aSet);
    end for;
  end func;