Data structure ( Java Problem )

a) Given the following list of numbers: 90 8 7 56 123 235 9 1 653 trace the execution for: a.1) Selection Sort (only the first 5 steps). a.2) Quicksort (pivot = the first element) a.3) Mergesort. b) The processing time of an algorithm is described by the following recurrence equation (C is a positive constant): T(n) = 3T(n/3) + 2cn: T(1) = 0 What is the running time complexity of this algorithm? Justify. c) You decided to improve insertion sort by using binary search to find the position p where the new insertion should take place. c.1) What is the worst-case complexity of your improved insertion sort if you take account of only the comparisons made by the binary search? Justify. c.2) What is the worst-case complexity of your improved insertion sort if only swaps/inversions of the data values are taken into account? Justify. d) What is the running time complexity of the Quicksort when a elements of the array have the same value? Justify