1. The file contains all of the integers between 1 and 10,000 (inclusive, with no repeats) in unsorted order. The integer in the ith row of the file gives you the ith entry of an input array.
Your task is to compute the total number of comparisons used to sort the given input file by Quicksort. For this part you should always use the first element of the array as the pivot element.
You should not count comparisons one-by-one. Rather, when there is a recursive call on a subarray of length m, you should simply add m-1 to your running total of comparisons.
2. Compute the number of comparisons (as in Part 1), always using the final element of the given array as the pivot element.
3. Compute the number of comparisons (as in Part 1), using the "median-of-three" pivot rule.
In more detail, you should choose the pivot as follows. Consider the first, middle, and final elements of the given array. If the array has odd length it should be clear what the middle element is. For an array with even length 2k, use the kth element as the middle element. So for the array 4 5 6 7, the middle element is the second one - 5 and not 6. Identify which of these three elements is the median, and use this as your pivot.