combination without repetition of N elements without use for..to..do

Question

i want load in a list the combination of N number without repetition, giving to input the elements and group. For example, with 4 elements [1,2,3,4], i have for:

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Answer 1

Here's a rather fun solution reliant on bitsets. As it stands it's limited to sets of size not greater than 32. I don't think that's a practical limitation since there are a lot of subsets for a set of cardinality greater than 32.

The output is not in the order that you want, but that would be easy enough to remedy if it matters to you.

program VisitAllSubsetsDemo;

{$APPTYPE CONSOLE}

procedure PrintBitset(Bitset: Cardinal; Size: Integer);
var
  i: Integer;
  Mask: Cardinal;
  SepNeeded: Boolean;
begin
  SepNeeded := False;
  Write('{');
  for i := 1 to Size do begin
    Mask := 1 shl (i-1);
    if Bitset and Mask<>0 then begin
      if SepNeeded then begin
        Write(',');
      end;
      Write(i);
      SepNeeded := True;
    end;
  end;
  Writeln('}');
end;

procedure EnumerateSubsets(Size: Integer);
var
  Bitset: Cardinal;
begin
  for Bitset := 0 to (1 shl Size)-1 do begin
    PrintBitset(Bitset, Size);
  end;
end;

begin
  EnumerateSubsets(4);
end.

Output

{}
{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}

And here is a variant that just lists the subsets of a specified cardinality:

function SetBitCount(Bitset: Cardinal; Size: Integer): Integer;
var
  i: Integer;
  Mask: Cardinal;
begin
  Result := 0;
  for i := 1 to Size do begin
    Mask := 1 shl (i-1);
    if Bitset and Mask<>0 then begin
      inc(Result);
    end;
  end;
end;

procedure EnumerateSubsets(Size, NumberOfSetBits: Integer);
var
  Bitset: Cardinal;
begin
  for Bitset := 0 to (1 shl Size)-1 do begin
    if SetBitCount(Bitset, Size)=NumberOfSetBits then begin
      PrintBitset(Bitset, Size);
    end;
  end;
end;

begin
  EnumerateSubsets(4, 2);
end.

Output

{1,2}
{1,3}
{2,3}
{1,4}
{2,4}
{3,4}