Python 3: Optimised Bubble Sort

Question

please help. I need to optimize my Bubble Sort algorithm in order to get less total comparisons than the non-optimised bubbleSort. I managed to create just the 'Normal Bubble sort (only travels from left to right):

def bubbleSort(values):
    n = len(values) - 1
    swap = True
    ncomp = 0 # My total comparisons counter
    while swap:
        swap = False
        for i in range(n): # i = 0, 1, 2, ..., n-1
            ncomp += 1
            if values[i] > values[i+1]:
                temp = values[i]
                values[i] = values[i+1]
                values[i+1] =  temp
                swap = True
    return values, ncomp

So basically i dont know how to create an 'optimised bubbleSort', a bubbleSortPlus function in which bubbles travel in both directions: from left to right, immediately followed by a travel from right to left. In theory, in each pass the travel of the bubbles should be shortened (saving in a variable the position of the last swap in a travel, and make the next travel start at that position. I tried so hard but i'm just a python newbie, please help.

Answer 1

I guess it has been optimized... The naive Bubble sort does not include the swap flag. So it will not return until finish all O(n^2) comparisons in any cases. But with swap flag, the number of comparison will be almost linear if the input sequence has been "almost sorted".

Answer 2

Here's some skeleton code that shows how to scan the array forwards and backwards, while shrinking the list on each iteration.

values = 100,101,102,103,104,105

start = 0
stop = len(values)-1

while stop > start:
    for i in range(start, stop):
        print i, "compare", values[i], "with", values[i+1]
    print "moved a large value to index", stop
    print

    stop = stop - 1
    if stop == start:
        break

    for i in range(stop, start, -1):
        print i, "compare", values[i], "with", values[i-1]
    print "moved a small value to index", start
    print

    start = start + 1