space-complexity

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, m); ------------ (1) mergesort(a, m+1, r); ------------(2) merge(a, l, m, r); a) The time complexity of this Merge Sort is O(nlg(n)). Will parallelizing (1) and (2) give any practical gain ? Theorotically, it appears that after parallelizing them also you would end up in O(nlg(n). But practically can we get any gains ? b) Space complexity of this Merge Sort here is O(n). However, if I choose to perform in-place merge sort using linked lists

I came across the following question. Given an array of n elements and an integer k where k < n . Elements { a 0 ... a k } and { a k +1 ... a n } are already sorted. Give an algorithm to sort in O( n ) time and O(1) space. It does not seem to me like it can be done in O( n ) time and O(1) space. The problem really seems to be asking how to do the merge step of mergesort but in-place. If it was possible, wouldn't mergesort be implemented that way? I am unable to convince myself though and need some opinion. deinst This seems to indicate that it is possible to do in O(lg^2 n) space. I cannot see