Problem We want to sort n keys with the preconditions stated for each case below. Name ONE algorithm that achieves it; if you name TWO or more or NONE you get 0 pts. The universe is the set of algorithms examined in this course so far (before due date of HW3) (a) (1pt) Fastest sorting algorithm that is in-place and its running time in tight asymptotic notation (b) (1pt) Fastest sorting algorithm that is stable and its running time in tight asymptotic notation (c) (1pt) Fastest sorting algorithm that sorts in-place and is stable and its running time in tight asymptotic notation (d) (2pt) Element Uniqess. We have n keys in array A[1...n]. We want to decide whether each key value appears once and only once in A. If this is so, algorithm returns YES otherwise, if there is a key appearing more than once, algorithm prints NO. Give the running time of an efficient solution in as tight asymptotic notation as possible. No algorithm needs to be described! Problem 2. n Tw)-