Insertion sort vs Bubble Sort Algorithms

Another difference, I didn't see here:

Bubble sort has 3 value assignments per swap: you have to build a temporary variable first to save the value you want to push forward(no.1), than you have to write the other swap-variable into the spot you just saved the value of(no.2) and then you have to write your temporary variable in the spot other spot(no.3). You have to do that for each spot - you want to go forward - to sort your variable to the correct spot.

With insertion sort you put your variable to sort in a temporary variable and then put all variables in front of that spot 1 spot backwards, as long as you reach the correct spot for your variable. That makes 1 value assignement per spot. In the end you write your temp-variable into the the spot.

That makes far less value assignements, too.

This isn't the strongest speed-benefit, but i think it can be mentioned.

I hope, I expressed myself understandable, if not, sorry, I'm not a nativ Britain

In bubble sort in ith iteration you have n-i-1 inner iterations (n^2)/2 total, but in insertion sort you have maximum i iterations on i'th step, but i/2 on average, as you can stop inner loop earlier, after you found correct position for the current element. So you have (sum from 0 to n) / 2 which is (n^2) / 4 total;

That's why insertion sort is faster than bubble sort.

Insertion Sort

After i iterations the first i elements are ordered.

In each iteration the next element is bubbled through the sorted section until it reaches the right spot:

sorted  | unsorted
1 3 5 8 | 4 6 7 9 2
1 3 4 5 8 | 6 7 9 2

The 4 is bubbled into the sorted section

Pseudocode:

for i in 1 to n
    for j in i downto 2
        if array[j - 1] > array[j]
            swap(array[j - 1], array[j])
        else
            break

Bubble Sort

After i iterations the last i elements are the biggest, and ordered.

In each iteration, sift through the unsorted section to find the maximum.

unsorted  | biggest
3 1 5 4 2 | 6 7 8 9
1 3 4 2 | 5 6 7 8 9

The 5 is bubbled out of the unsorted section

Pseudocode:

for i in 1 to n
    for j in 1 to n - i
         if array[j] > array[j + 1]
             swap(array[j], array[j + 1])

Note that typical implementations terminate early if no swaps are made during one of the iterations of the outer loop (since that means the array is sorted).

Difference

In insertion sort elements are bubbled into the sorted section, while in bubble sort the maximums are bubbled out of the unsorted section.