Mr. Smith's first program

While I was talking about theory and data structures and best practices, our friend Mr. Smith read everything about polar forests on the internet and then got really bored. In a moment of sheer panic—when he was thinking about watching videos of cute kittens for the whole polar night—he turned to programming. He checked various internet sources and decided that Delphi is the way to go. After all, he could use it to put together a new game for iOS and Android and make lots of money while waiting for the sun to show up!

As he didn't have any programming literature on the Antarctic base, he learned programming from internet resources. Sadly, he found most of his knowledge on Experts Exchange and Yahoo Answers and his programs sometimes reflect that.

As of this moment, he has written one working program (and by working I mean that it compiles), but he is not really sure what the program actually does. He only knows that the program is a bit slow and because of that he named it SlowCode.

His program is a console mode program which upon startup calls the Test method:

procedure Test;
var
  data: TArray<Integer>;
  highBound: Integer;
begin
  repeat
    Writeln('How many numbers (0 to exit)?');
    Write('> ');
    Readln(highBound);
    if highBound = 0 then
      Exit;

    data := SlowMethod(highBound);
    ShowElements(data);
   until false;
end;

That one, at least, is easy to grasp. It reads some number, passes it to something called SlowMethod (hmm, Mr. Smith really should work on naming techniques), and then passes the result (which is of type TArray<Integer>) to a method called ShowElements. When the user types in 0, the program exits.

Let's check the ShowElements function:

function SlowMethod(highBound: Integer): TArray<Integer>;
var
  i: Integer;
  temp: TList<Integer>;
begin
  temp := TList<Integer>.Create;
  try
    for i := 2 to highBound do
      if not ElementInDataDivides(temp, i) then
        temp.Add(i);
    Result := Filter(temp);
  finally
    FreeAndNil(temp);
  end;
end;

The code creates a list of integers. Then it iterates from a value 2 to the value that was entered by the user and for each value calls ElementInDataDivides, passing in the list and the current value. If that function returns True, the current value is entered into the list.

After that, SlowMethod calls the Filter method which does something with the list and converts it into an array of integers which is then returned as a function result:

function ElementInDataDivides(data: TList<Integer>; value: Integer): boolean;
var
  i: Integer;
begin
  Result := True;
  for i in data do
    if (value <> i) and ((value mod i) = 0) then
      Exit;
  Result := False;
end;

The ElementInDataDivides function iterates over all the numbers in the list and checks if any element in the list divides the value (with the additional constraint that this element in the list must not be equal to the value).

Let's check the last part of the puzzle—the Filter function:

function Reverse(s: string): string;
var
  ch: char;
begin
  Result := '';
  for ch in s do
    Result := ch + Result;
end;
function Filter(list: TList<Integer>): TArray<Integer>;
var
  i: Integer;
  reversed: Integer;
begin
  SetLength(Result, 0);
  for i in list do
  begin
    reversed := StrToInt(Reverse(IntToStr(i)));
    if not ElementInDataDivides(list, reversed) then
    begin
      SetLength(Result, Length(Result) + 1);
      Result[High(Result)] := i;
    end;
  end;
end;

This one again iterates over the list, reverses the numbers in each element (changes 123 to 321, 3341 to 1433, and so on) and calls ElementInDataDivides on the new number. If it returns True, the element is added to the returned result in a fairly inefficient way.

I agree with Mr. Smith—it is hard to tell what the program does. Maybe it is easiest to run it and look at the output:

It looks like the program is outputting prime numbers. Not all prime numbers, just some of them. (For example, 19 is missing from the list, and so is 23.) Let's leave it at that for the moment.