Remarks: In all the algorithms, always explain (more precisely try to prove) the correct- ness of your algorithm You Always Must analyze the running time of any algorithm. The time complexity should be as small as possible. A correct algorithm with large complexity, may not get full credit. Do EVEN THINK OF WRITING PROGRAMS. The Rollo Thomasi legacy: work alone. Question 3: Given an unsorted array, an inversion is a pair of indices i, j so that i A[j]. For example a sorted array has no inversion. An array sorted in reverse has an inversion for any i