1. Consider this problem: given a list 41, ?? . . ., ????f n distinct positive integers, with n odd for snnplicity, find the item in the list that has the same number of list items smaller than it and larger than it. For example, if the list is 3,5, 2,7,1,8,4, then 4 is the answer, because 4 has three numbers smaller than it (1, 2, and 3) and three numbers larger than it (5, 7, and 8) a. 4 points] Here is a brute force algorithm for this problem: for each aj, go through all the ak in the list and tally how many are less than a, and how many are larger than aj. When you encounter an aj such that these two counts are the same, report aj as the answer and stop. What is the worst-case ? efficiency category for this algorith!n (explain briefly)? [4 points Invent and analyze an algorithm for this problem using the idea of pre-sorting algorithm at the same level of detail as in part a, and then state and Justify the ? efficiency category for the algorithm. b. describe your