Algorithm design. If its a commonly know algorithm please mention its name.

3. (20pts) Design and analyze an algorithm to find the median, upper quartile and lower quartile from a list of n integers (unordered). Your time complexity should be no more than O(n logn). Can you improve your algorithm if the input list is sorted? If so, design and analyze such an algorithm. If not, justify why no improvement in time/space complexity can exist. a. b. 4. (20pts) a. Algorithm A uses (100n log n) operations, while algorithm B uses n2 operations. b. Are there values of n such that B is better than A? If yes, list the ranges. If not, justify c. Determine the value no such that A is better than B for n 2 no, when B uses n1.5 Determine the value no such that A is better than B for n 2 no. why not. operations