How to create an in-place sorting algorithm with faster than O (nlogn) time complexity?
A comparison based sort cannot be faster than O(nlogn). Since all the algorithms you mentioned are comparison based, none of them can have better time complexity.
There are algorithms like bucket sort and radix sort that can achieve O(n) in some cases, namely if the input is uniformly distributed.
I was recently asked to create an in-place sorting algorithm in an interview. The follow up was to code it up to make it faster than O(n logn), discuss the time complexity of every loop.
I understand that insertion sort, bubble sort, heap sort, quicksort, and shell sort are all in-place, however which of these can be modified to have better time complexity?