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.



Task

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

 {{}, {1}, {2}, {1,2}, {3}, {1,3}, {2,3}, {1,2,3}, {4}, {1,4}, {2,4}, {1,2,4}, {3,4}, {1,3,4}, {2,3,4}, {1,2,3,4}}.
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):


 





P




{\displaystyle {\mathcal {P}}}

(



∅


{\displaystyle \varnothing }

) = { 



∅


{\displaystyle \varnothing }

 }

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):


 





P




{\displaystyle {\mathcal {P}}}

({



∅


{\displaystyle \varnothing }

}) = { 



∅


{\displaystyle \varnothing }

, { 



∅


{\displaystyle \varnothing }

 } }


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




Function Dec2Bin(n)
	q = n
	Dec2Bin = ""
	Do Until q = 0
		Dec2Bin = CStr(q Mod 2) & Dec2Bin
		q = Int(q / 2)
	Loop
	Dec2Bin = Right("00000" & Dec2Bin,6)
End Function
 
Function PowerSet(s)
	arrS = Split(s,",")
	PowerSet = "{"
	For i = 0 To 2^(UBound(arrS)+1)-1
		If i = 0 Then
			PowerSet = PowerSet & "{},"
		Else
			binS = Dec2Bin(i)
			PowerSet = PowerSet & "{"
			c = 0
			For j = Len(binS) To 1 Step -1
				If CInt(Mid(binS,j,1)) = 1 Then
					PowerSet = PowerSet & arrS(c) & ","	
				End If
				c = c + 1
			Next
			PowerSet = Mid(PowerSet,1,Len(PowerSet)-1) & "},"
		End If
	Next
	PowerSet = Mid(PowerSet,1,Len(PowerSet)-1) & "}"
End Function
 
WScript.StdOut.Write PowerSet("1,2,3,4")