finding best and wost case in Insertion Sort

I have a code from mathworks for insertion sort

function sorted = insertion_sort(unsorted)
    array_size = size(unsorted,2);
    for pivot = 2:array_size
        for j = 1:pivot-1
            if (unsorted(j)>unsorted(pivot))
                temp = unsorted(pivot);
                unsorted (j+1:pivot) = unsorted (j:pivot-1);
                unsorted(j) = temp        
            end
        end
    end
  sorted = unsorted; 
end

suppose mu unsorted value is [5 1 2 9 7 3 8 ]

kindly tell how to calculate best worst and average case

Answer 1

[Roger Stafford]

It is not clear what you are asking. With a given array such as the one you describe, there can be no "best" or "worst" case. The amount of processing is exactly determined by that array.

In general the worst cases will occur when the initial array is entirely descending and the best cases would be those in which the initial array is already ascending. That is because the amount of shifting in the line

 unsorted (j+1:pivot) = unsorted (j:pivot-1);

is maximized or minimized in the two respective cases.

However, this sorting algorithm is far from optimum since it is of order n^2 operations with n the length of the array. An efficient algorithm such as "merge" sorting can accomplish a sort operation with only order n*log(n) operations, and for a large array this can be significantly fewer operations.