this function implements the shell sort algorithm which is slightly faster than its pure implementation this shell sort is implemented using a gap which shrinks by a certain factor each iteration in this implementation the gap is initially set to the length of the collection the gap is then reduced by a certain factor 1 3 each iteration for each iteration the algorithm compares elements that are a certain number of positions apart determined by the gap if the element at the higher position is greater than the element at the lower position the two elements are swapped the process is repeated until the gap is equal to 1 the reason this is more efficient is that it reduces the number of comparisons that need to be made by using a smaller gap the list is sorted more quickly implementation of shell sort algorithm in python param collection some mutable ordered collection with heterogeneous comparable items inside return the same collection ordered by ascending shellsort3 2 1 1 2 3 shellsort shellsort1 1 choose an initial gap value set the gap value to be decreased by a factor of 1 3 after each iteration continue sorting until the gap is 1 decrease the gap value sort the elements using insertion sort implementation of shell sort algorithm in python param collection some mutable ordered collection with heterogeneous comparable items inside return the same collection ordered by ascending shell_sort 3 2 1 1 2 3 shell_sort shell_sort 1 1 choose an initial gap value set the gap value to be decreased by a factor of 1 3 after each iteration continue sorting until the gap is 1 decrease the gap value sort the elements using insertion sort
def shell_sort(collection: list) -> list:
    

    
    gap = len(collection)

    
    
    shrink = 1.3

    
    while gap > 1:
        
        gap = int(gap / shrink)

        
        for i in range(gap, len(collection)):
            temp = collection[i]
            j = i
            while j >= gap and collection[j - gap] > temp:
                collection[j] = collection[j - gap]
                j -= gap
            collection[j] = temp

    return collection


if __name__ == "__main__":
    import doctest

    doctest.testmod()