Time left $1$:$41$:$17$

The running time of quicksort, to sort n element, can be improved in practice by taking advantage of the fast running time of insertion sort when its input is "nearly" sorted. When quicksort is called on a subarray with fewer than k elements, let it simply return without sorting the subarray. After the top$-$level call to quicksort returns, run insertion sort on the entire array to finish the sorting process.

Select one or more:

a$.$ The depth of a leaf in the recursion tree is $O(logN)$

b$.$ The total cost of this sorting algorithm is $O(nlogn+nk)$

c$.$ The total cost of this sorting algorithm is $O(nk)$

d$.$ The total cost of this sorting algorithm is $O(nk+nlog(\frac{n}{k}))$