Sorting algorithms/Comb sort

You are encouraged to solve this task according to the task description, using any language you may know.

Sorting Algorithm

This is a sorting algorithm.   It may be applied to a set of data in order to sort it.    
For comparing various sorts, see compare sorts.  
For other sorting algorithms,   see sorting algorithms,   or:

O(n logn) sorts
Heap sort |
Merge sort |
Patience sort |
Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort


Task

Implement a   comb sort.



The Comb Sort is a variant of the Bubble Sort.

Like the Shell sort, the Comb Sort increases the gap used in comparisons and exchanges.

Dividing the gap by   



(
1
−

e

−
φ



)

−
1


≈
1.247330950103979


{\displaystyle (1-e^{-\varphi })^{-1}\approx 1.247330950103979}

    works best, but    1.3   may be more practical.



Some implementations use the insertion sort once the gap is less than a certain amount.



Also see

   the Wikipedia article:   Comb sort.


Variants:

 Combsort11 makes sure the gap ends in (11, 8, 6, 4, 3, 2, 1), which is significantly faster than the other two possible endings.
 Combsort with different endings changes to a more efficient sort when the data is almost sorted (when the gap is small).   Comb sort with a low gap isn't much better than the Bubble Sort.


Pseudocode:

function combsort(array input)
    gap := input.size //initialize gap size
    loop until gap = 1 and swaps = 0
        //update the gap value for a next comb. Below is an example
        gap := int(gap / 1.25)
        if gap < 1
          //minimum gap is 1
          gap := 1
        end if
        i := 0
        swaps := 0 //see Bubble Sort for an explanation
        //a single "comb" over the input list
        loop until i + gap >= input.size //see Shell sort for similar idea
            if input[i] > input[i+gap]
                swap(input[i], input[i+gap])
                swaps := 1 // Flag a swap has occurred, so the
                           // list is not guaranteed sorted
            end if
            i := i + 1
        end loop
    end loop
end function



with Ada.Text_IO;
procedure Comb_Sort is
   generic
      type Element_Type is private;
      type Index_Type is range <>;
      type Array_Type is array (Index_Type range <>) of Element_Type;
      with function ">" (Left, Right : Element_Type) return Boolean is <>;
      with function "+" (Left : Index_Type; Right : Natural) return Index_Type is <>;
      with function "-" (Left : Index_Type; Right : Natural) return Index_Type is <>;
   procedure Comb_Sort (Data: in out Array_Type);
 
   procedure Comb_Sort (Data: in out Array_Type) is
      procedure Swap (Left, Right : in Index_Type) is
         Temp : Element_Type := Data(Left);
      begin
         Data(Left)  := Data(Right);
         Data(Right) := Temp;
      end Swap;
      Gap : Natural := Data'Length;
      Swap_Occured : Boolean;
   begin
      loop
         Gap := Natural (Float(Gap) / 1.25 - 0.5);
         if Gap < 1 then
            Gap := 1;
         end if;
         Swap_Occured := False;
         for I in Data'First .. Data'Last - Gap loop
            if Data (I) > Data (I+Gap) then
               Swap (I, I+Gap);
               Swap_Occured := True;
            end if;
         end loop;
         exit when Gap = 1 and not Swap_Occured;
      end loop;
   end Comb_Sort;
 
   type Integer_Array is array (Positive range <>) of Integer;
   procedure Int_Comb_Sort is new Comb_Sort (Integer, Positive, Integer_Array);
   Test_Array : Integer_Array := (1, 3, 256, 0, 3, 4, -1);
begin
   Int_Comb_Sort (Test_Array);
   for I in Test_Array'Range loop
      Ada.Text_IO.Put (Integer'Image (Test_Array (I)));
   end loop;
   Ada.Text_IO.New_Line;
end Comb_Sort;