Bubble_Sort_Documentation.txt

The bubble sort is the oldest and simplest sort in use. Unfortunately, it's also the slowest. 
The bubble sort works by comparing each item in the list with the item next to it, and swapping them if required.
The algorithm repeats this process until it makes a pass all the way through the list without swapping any items (in other words, all items are in the correct order). 
This causes larger values to "bubble" to the end of the list while smaller values "sink" towards the beginning of the list. 
The bubble sort is generally considered to be the most inefficient sorting algorithm in common usage. 
Under best-case conditions (the list is already sorted), the bubble sort can approach a constant O(n) level of complexity. General-case is an abysmal O(n2). 

Example-
The list "5,4,9,7,2,8" needs to be sorted from lowest to highest. The following steps are carried out:
Pass 1 
      First (5) and second (4) elements compared. 4 less than 5 therefore elements inverted. 
      Current list: 4,5,9,7,2,8 
      Second (now 5) and third (9) elements compared. In correct order so no change. 
      Current list: 4,5,9,7,2,8 
      9 and 7 compared and inverted 
      Current list: 4,5,7,9,2,8 
      9 and 2 compared and inverted 
      Current list: 4,5,7,2,9,8 
      9 and 8 compared and inverted 
      Current list: 4,5,7,2,8,9 
Pass 2 
      Same method used in Pass 1 applied to current list (4,5,7,2,8,9)  
      Resultant list: 4,5,2,7,8,9 
Pass 3 
      Resultant list: 4,2,5,7,8,9 
Pass 4 
      Resultant list: 2,4,5,7,8,9 
Pass 5 
No changes would be made in this pass therefore the algorithm has reached its termination point and the list is sorted .