Indicate whether the following sorting algorithms are stable and/or in-place. Also, provide their time complexity (with justification if needed). Suppose that the for loop header in line 7 of the Counting Sort algorithm (lecture13.ppt Slide #12) is rewritten to for j leftarrow 1 to n Will the algorithm still sort correctly? Is the modified algorithm a stable sorting algorithm? If yes, prove it. Otherwise provide a counterexample. Study the pseudocode and example of Rand-Select on slides #5-8 in Lecturel4.ppt. Use Slide #8 as a model, illustrate the operation of selecting the 4th smallest element on array A = [6 3 16 11 7 1714 8]. Similar to #8, you can use ordinary Partition rather than Rand-Partition, i.e., you always select the first element as the pivot