Merge Sort Time and Space Complexity

Question

Let\'s take this implementation of Merge Sort as an example

void mergesort(Item a[], int l, int r) {
if (r <= l) return;
int m = (r+l)/2;
mergesort(a, l,          


        

Answer 1

a) Yes, of course, parallelizing merge sort can be very beneficial. It remains nlogn, but your constant should be significantly lower.

b) Space complexity with a linked list should be O(n), or more specifically O(n) + O(logn). Note that that's a +, not a *. Don't concern yourself with constants much when doing asymptotic analysis.

c) In asymptotic analysis, only the dominant term in the equation matters much, so the fact that we have a + and not a * makes it O(n). If we were duplicating the sublists all over, I believe that would be O(nlogn) space - but a smart linked-list-based merge sort can share regions of the lists.