We assume we have $N$ naturals to sort. Determine the correct running time $($big$-$Oh notation$)$ of each of the following four algorithms: Insertion sort, Heapsort, Mergesort, Quicksort and Quicksort combined to Insertion Sort $($use Quicksort first and then switch to Insertion Sort when the size of the sub arrays is small$),$ in the case of a randomly generated input.

Select one or more:

a$.$ Quicksort runs in $O(logN)$ if the pivot is chosen as the median$-$of$-$three partitioning

b$.$ Insertion Sort runs in $O(logN)$

c$.$ Heapsort runs in $O(N^{2}logN)$

d$.$ Mergesort runs in $O(N^{2}logN)$

e$.$ Heapsort runs in $O(NlogN)$