How does the bubble sort algorithm work with optimized code?

The bubble sort algorithm works by repeatedly swapping adjacent elements if they are in the wrong order.

Bubble sort is a simple sorting algorithm that works by repeatedly stepping through the list to be sorted, comparing each pair of adjacent items and swapping them if they are in the wrong order. The pass through the list is repeated until the list is sorted. The algorithm gets its name from the way smaller or larger elements "bubble" to the top of the list.

In an optimised version of bubble sort, we can introduce a flag to monitor whether any swapping operation took place in the current iteration. If no swapping was done, it means the list is already sorted and there is no need for further iterations. This optimisation reduces unnecessary passes over the list, thus improving the efficiency of the algorithm.

Let's consider an example. Suppose we have a list of five elements: [5, 3, 8, 4, 2]. The bubble sort algorithm starts at the beginning of the list, comparing the first two elements, 5 and 3. Since 5 is greater than 3 and we're sorting in ascending order, these elements are swapped. The algorithm then moves on to the next pair of elements, 5 and 8. Since these are in the correct order, no swap is made. This process continues until the algorithm has gone through the entire list.

After the first pass, the largest number will have 'bubbled up' to the end of the list. The algorithm then starts again from the beginning of the list, but this time it only goes up to the second last element. This is because the last element is already in its correct position. This process is repeated, with each pass going one element less than the previous pass, until no more swaps are needed.

In terms of code optimisation, the bubble sort algorithm is not the most efficient for large data sets due to its high computational complexity. However, it has the advantage of simplicity and ease of implementation. It also performs well for nearly sorted or small data sets. The optimised version with the flag to check for swaps can significantly improve performance in the best-case scenario, where the list is already sorted.