(15 pts, 3 pts for each) Consider the quicksort using Hoare's partition method on a set of numbers, 65,70,75,80,85,60,55,50, and 45 . Suppose we use the left most elements as the partition element and, when performing the recursion, we work on the left part first and then the right part. Mark by T(= true ) or F(= false ) each of the following: (1) After the first iteration (partition), the fifth smallest element is found. (2) Suppose that the recursion returns when there is only one element, there are 9 recursive calls during the execution. (3) During the execution, the position of 85 in the sorted result is determined before the position of 70 . (4) The best case in running time for the quicksort using Hoare's partition method occurs when all the numbers are sorted. (5) As we have known that, the lower bound for the sorting problem is O(nlogn), so the quicksort is optimal in worst case