Cocktail Sort

Cocktail Sort is a variation of Bubble sort. The Bubble sort algorithm always traverses elements from left and moves the largest element to its correct position in first iteration and second largest in second iteration and so on. Cocktail Sort traverses through a given array in both directions alternatively.

ALGORITHM:

Each iteration of the algorithm is broken up into 2 stages:

1.The first stage loops through the array from left to right, just like the Bubble Sort. During the loop, adjacent items are compared and if value on the left is greater than the value on the right, then values are swapped. At the end of first iteration, largest number will reside at the end of the array.

2. The second stage loops through the array in opposite direction- starting from the item just before the most recently sorted item, and moving back to the start of the array. Here also, adjacent items are compared and are swapped if required.

Let us consider an example array (5 1 4 2 8 0 2)

First Forward Pass:
(5 1 4 2 8 0 2) ? (1 5 4 2 8 0 2), Swap since 5 > 1
(1 5 4 2 8 0 2) ? (1 4 5 2 8 0 2), Swap since 5 > 4
(1 4 5 2 8 0 2) ? (1 4 2 5 8 0 2), Swap since 5 > 2
(1 4 2 5 8 0 2) ? (1 4 2 5 8 0 2)
(1 4 2 5 8 0 2) ? (1 4 2 5 0 8 2), Swap since 8 > 0
(1 4 2 5 0 8 2) ? (1 4 2 5 0 2 8), Swap since 8 > 2
After first forward pass, greatest element of the array will be present at the last index of array.
First Backward Pass:
(1 4 2 5 0 2 8) ? (1 4 2 5 0 2 8)
(1 4 2 5 0 2 8) ? (1 4 2 0 5 2 8), Swap since 5 > 0
(1 4 2 0 5 2 8) ? (1 4 0 2 5 2 8), Swap since 2 > 0
(1 4 0 2 5 2 8) ? (1 0 4 2 5 2 8), Swap since 4 > 0
(1 0 4 2 5 2 8) ? (0 1 4 2 5 2 8), Swap since 1 > 0
After first backward pass, smallest element of the array will be present at the first index of the array.
Second Forward Pass:
(0 1 4 2 5 2 8) ? (0 1 4 2 5 2 8)
(0 1 4 2 5 2 8) ? (0 1 2 4 5 2 8), Swap since 4 > 2
(0 1 2 4 5 2 8) ? (0 1 2 4 5 2 8)
(0 1 2 4 5 2 8) ? (0 1 2 4 2 5 8), Swap since 5 > 2
Second Backward Pass:
(0 1 2 4 2 5 8) ? (0 1 2 2 4 5 8), Swap since 4 > 2
Now, the array is already sorted, but our algorithm doesn’t know if it is completed. The algorithm needs to complete this whole pass without any swap to know it is sorted.
(0 1 2 2 4 5 8) ? (0 1 2 2 4 5 8)
(0 1 2 2 4 5 8) ? (0 1 2 2 4 5 8)

CODE:

def cocktailSort(a): 
    n = len(a) 
    swapped = True
    start = 0
    end = n-1
    while (swapped == True): 
  
        # reset the swapped flag on entering the loop, 
        # because it might be true from a previous 
        # iteration. 
        swapped = False
  
        # loop from left to right same as the bubble 
        # sort 
        for i in range (start, end): 
            if (a[i] > a[i + 1]) : 
                a[i], a[i + 1]= a[i + 1], a[i] 
                swapped = True
  
        # if nothing moved, then array is sorted. 
        if (swapped == False): 
            break
  
        # otherwise, reset the swapped flag so that it 
        # can be used in the next stage 
        swapped = False
  
        # move the end point back by one, because 
        # item at the end is in its rightful spot 
        end = end-1
  
        # from right to left, doing the same 
        # comparison as in the previous stage 
        for i in range(end-1, start-1, -1): 
            if (a[i] > a[i + 1]): 
                a[i], a[i + 1] = a[i + 1], a[i] 
                swapped = True
  
        # increase the starting point, because 
        # the last stage would have moved the next 
        # smallest number to its rightful spot. 
        start = start + 1
  
# Driver code to test above 
a = [5, 1, 4, 2, 8, 0, 2] 
cocktailSort(a) 
print("Sorted array is:") 
for i in range(len(a)): 
    print ("% d" % a[i])

Output:           Sorted array is
0 1 2 2 4 5 8

Time Complexity:
O(n*n) [Worst and Average Case]
O(n) [Best Case– Best case occurs when array is already sorted.]

Auxiliary Space: O(1)

Sorting In Place: Yes

Stable: Yes

Comparison with Bubble Sort: 
Time complexities are same, but Cocktail performs better than Bubble Sort. Typically cocktail sort is less than two times faster than bubble sort. Consider the example (2, 3, 4, 5, 1). Bubble sort requires four traversals of array for this example, while Cocktail sort requires only two traversals