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



 
  // Node 5.4.1 tested implementation (ES6)
  function is_array_sorted(arr) {
      var sorted = true;
      for (var i = 0; i < arr.length - 1; i++) {
          if (arr[i] > arr[i + 1]) {
              sorted = false;
              break;
          }
      }
      return sorted;
  }
 
  // Array to sort
  var arr = [4, 9, 0, 3, 1, 5];
 
  var iteration_count = 0;
  var gap = arr.length - 2;
  var decrease_factor = 1.25;
 
  // Until array is not sorted, repeat iterations
  while (!is_array_sorted(arr)) {
      // If not first gap
      if (iteration_count > 0)
      // Calculate gap
          gap = (gap == 1) ? gap : Math.floor(gap / decrease_factor);
 
      // Set front and back elements and increment to a gap
      var front = 0;
      var back = gap;
      while (back <= arr.length - 1) {
          // If elements are not ordered swap them
          if (arr[front] > arr[back]) {
              var temp = arr[front];
              arr[front] = arr[back];
              arr[back] = temp;
          }
 
          // Increment and re-run swapping
          front += 1;
          back += 1;
      }
      iteration_count += 1;
  }
 
  // Print the sorted array
  console.log(arr);
}