mergesort

I know that the running time of merge sort is O(n*lg(n)) and that merge sort is a comparision sort, which also means that it takes Ω(n logn) in the worst case to sort a list. Can I therefore conclude that the running time of merge sort is theta(n*lg n)? If something is O(X) and Omega(X) , this implies it is Theta(X) . And log_b1(...) is the same as log_b2(...) times a conversion factor constant. What you said was (translated): I know that the running time of merge sort is, in the worst case, no worse than n log(n) . [You arrived at this conclusion somehow with math.] But comparison sorts take

Why does memoization not improve the runtime of Merge Sort? I have this question from Assignment task. But as far as I know, Merge Sort uses divide and conquer approach (no overlapping subproblems) but Memoization is based on dynamic programing (with overlapping subproblem). I know the runtime of Merge Sort is O(nlogn) . I even searched on web search engines and there is no result for this question. Is this question wrong? If it sounds wrong but why would a professor give a wrong question in assignment? If the question is not wrong or my understanding about the question, Merge Sort and

(disclaimer: for school) As far as I know, recursively splitting a linked list, then sending it off to another function to merge is O(nlogn) time and O(n) space. Is it possible to do mergesort on linked list with O(nlogn) time and O(1) space complexity? How would you go about doing this? ANY HELP APPRECIATED PS: to make sure that the traditional mergesort is space complexity 0(n), this is an example of 0(n), right? How would it be changed for O(1) space? void sortTrack() { Node merge = this.head; this.head = Node (merge); } public Node mergeSort(Node head){ if ((head == null)||(head.next ==

I've been reading on in place sorting algorithm to sort linked lists. As per Wikipedia Merge sort is often the best choice for sorting a linked list: in this situation it is relatively easy to implement a merge sort in such a way that it requires only Θ(1) extra space, and the slow random-access performance of a linked list makes some other algorithms (such as quicksort) perform poorly, and others (such as heapsort) completely impossible. To my knowledge, the merge sort algorithm is not an in place sorting algorithm, and has a worst case space complexity of O(n) auxiliary. Now, with this taken

Good day SO community, I am a CS student currently performing an experiment combining MergeSort and InsertionSort. It is understood that for a certain threshold, S, InsertionSort will have a quicker execution time than MergeSort. Hence, by merging both sorting algorithms, the total runtime will be optimized. However, after running the experiment many times, using a sample size of 1000, and varying sizes of S, the results of the experiment does not give a definitive answer each time. Here is a picture of the better results obtained (Note that half of the time the result is not as definitive):

So I have a function defined that works great at doing merge sort on a linear array if it is implemented by its lonesome, but if I put it into a class it bugs out. I think it's a great example of what I don't quite understand about how classes work; possibly in regards to namespace management(?). See below: def sort(array): print('Splitting', array) if len(array) > 1: m = len(array)//2 left = array[:m] right = array[m:] sort(left) sort(right) i = 0 j = 0 k = 0 while i < len(left) and j < len(right): if left[i] < right[j]: array[k] = left[i] i += 1 else: array[k] = right[j] j += 1 k += 1 while