For example, let's say we have this list:

file 3.txt
file 2.txt
file 10.txt
file 9.txt
file 1.txt

Regular sorting would produce this:

file 1.txt
file 10.txt
file 2.txt
file 3.txt
file 9.txt

But that is not how we humans sort, we'd like to see (called "natural sort"):

file 1.txt
file 2.txt
file 3.txt
file 9.txt
file 10.txt

In case you have seen my QuickSort examples (for example this one - I'll add the code below), you'll see that we often use "StrIcomp" to compare 2 strings to see which one goes first. Unfortunately results in the wrong output I just showed. So I wrote a "drop in" replacement for this "NaturalCompare". Simply replace the StrIcomp with NaturalCompare and the QuickSort will now produce a natural sorted list.

function NaturalCompare(const S1, S2: string): Integer;
var
  I, J: Integer;
  N1, N2: Int64;
  C1, C2: Char;
begin
  I := 1;
  J := 1;

  while (I <= Length(S1)) and (J <= Length(S2)) do
  begin
    C1 := S1;
    C2 := S2;

    // If both characters are digits, compare numbers
    if (C1 in ) and (C2 in ) then
    begin
      N1 := 0;
      while (I <= Length(S1)) and (S1 in ) do
      begin
        N1 := N1 * 10 + Ord(S1) - Ord('0');
        Inc(I);
      end;

      N2 := 0;
      while (J <= Length(S2)) and (S2 in ) do
      begin
        N2 := N2 * 10 + Ord(S2) - Ord('0');
        Inc(J);
      end;

      if N1 <> N2 then
        Exit(N1 - N2);
    end
    else
    begin
      // Case-insensitive character compare
      C1 := UpCase(C1);
      C2 := UpCase(C2);

      if C1 <> C2 then
        Exit(Ord(C1) - Ord(C2));

      Inc(I);
      Inc(J);
    end;
  end;

  // If all equal so far, shorter string comes first
  Result := Length(S1) - Length(S2);
end;                                                           

Example QuickStort procedure:

procedure QuickSort(var A: TStringList);
  procedure Sort(L, R: Integer);
  var
    I, J: Integer;
    Y, X:string;
  begin
    I:= L; J:= R; X:= A;

    repeat
      // was:  while StrIcomp(pchar(A),pchar(X))<0 do inc(I);
      // was:  while StrIComp(pchar(X),pchar(A))<0 do dec(J); 

      while NaturalCompare(pchar(A),pchar(X))<0 do inc(I);
      while NaturalCompare(pchar(X),pchar(A))<0 do dec(J); 

      if I <= J then
        begin
          Y:= A; A:= A; A:= Y;
          inc(I); dec(J);
        end;
    until I > J;

    if L < J then Sort(L,J);
    if I < R then Sort(I,R);
  end;
begin
  Sort(0,A.Count-1);
end;