Comb Sort

Comb Sort is mainly an improvement over Bubble Sort. Bubble sort always compares adjacent values. So all inversions are removed one by one. Comb Sort improves on Bubble Sort by using gap of size more than 1. The gap starts with a large value and shrinks by a factor of 1.3 in every iteration until it reaches the value 1. Thus Comb Sort removes more than one inversion counts with one swap and performs better than Bubble Sort.

The shrink factor has been empirically found to be 1.3 (by testing Combsort on over 200,000 random lists).
Although, it works better than Bubble Sort on average, worst case remains O(n²).

EXPLANATION:

Let the array elements be
8, 4, 1, 56, 3, -44, 23, -6, 28, 0

Initially gap value = 10
After shrinking gap value => 10/1.3 = 7;

8 4 1 56 3 -44 23 -6 28 0 
-6 4 1 56 3 -44 23 8 28 0 
-6 4 0 56 3 -44 23 8 28 1

New gap value => 7/1.3 = 5;

-44 4 0 56 3 -6 23 8 28 1 
-44 4 0 28 3 -6 23 8 56 1 
-44 4 0 28 1 -6 23 8 56 3

New gap value => 5/1.3 = 3;

-44 1 0 28 4 -6 23 8 56 3 
-44 1 -6 28 4 0 23 8 56 3 
-44 1 -6 23 4 0 28 8 56 3 
-44 1 -6 23 4 0 3 8 56 28

New gap value => 3/1.3 = 2;

-44 1 -6 0 4 23 3 8 56 28 
-44 1 -6 0 3 23 4 8 56 28 
-44 1 -6 0 3 8 4 23 56 28

New gap value => 2/1.3 = 1;

-44 -6 1 0 3 8 4 23 56 28 
-44 -6 0 1 3 8 4 23 56 28 
-44 -6 0 1 3 4 8 23 56 28 
-44 -6 0 1 3 4 8 23 28 56 

no more swaps required (Array sorted)

CODE:

# Python program for implementation of CombSort 
  
# To find next gap from current 
def getNextGap(gap): 
  
    # Shrink gap by Shrink factor 
    gap = (gap * 10)/13
    if gap < 1: 
        return 1
    return gap 
  
# Function to sort arr[] using Comb Sort 
def combSort(arr): 
    n = len(arr) 
  
    # Initialize gap 
    gap = n 
  
    # Initialize swapped as true to make sure that 
    # loop runs 
    swapped = True
  
    # Keep running while gap is more than 1 and last 
    # iteration caused a swap 
    while gap !=1 or swapped == 1: 
  
        # Find next gap 
        gap = getNextGap(gap) 
  
        # Initialize swapped as false so that we can 
        # check if swap happened or not 
        swapped = False
  
        # Compare all elements with current gap 
        for i in range(0, n-gap): 
            if arr[i] > arr[i + gap]: 
                arr[i], arr[i + gap]=arr[i + gap], arr[i] 
                swapped = True
  
  
# Driver code to test above 
arr = [ 8, 4, 1, 3, -44, 23, -6, 28, 0] 
combSort(arr) 
  
print ("Sorted array:") 
for i in range(len(arr)): 
    print (arr[i])

Output:           After sort :
-44 -6 0 1 3 4 8 23 28 56

Time Complexity : Worst case complexity of this algorithm is O(n²) and the Best Case complexity is O(n).

Auxiliary Space : O(1).