Now implement Merge Sort, Heap Sort, and Quick Sort in C++ and perform the following experiment: 1. Generate an Array A of 108 random numbers. Make its copies B and C. Sort A using Merge Sort, B using Heap Sort, and C using Quick Sort. 2. During the sorting process, count the total number of comparisons between array elements made by each algorithm. You may do this by using a global less-than-or-equal- to function to compare numbers, which increments a count variable each time it is called. 3. Repeat this process 5 times to compute the average number of comparisons made by each algorithm.

Now implement Merge Sort, Heap Sort, and Quick Sort in C++ and perform the following
experiment:
1. Generate an Array A of 108

random numbers. Make its copies B and C. Sort A using
Merge Sort, B using Heap Sort, and C using Quick Sort.
2. During the sorting process, count the total number of comparisons between array

elements made by each algorithm. You may do this by using a global less-than-or-equal-
to

function to compare numbers, which increments a count variable each time it is called.
3. Repeat this process 5 times to compute the average number of comparisons made by
each algorithm.
4. Present these average counts in a table. These counts give you an indication of how the
different algorithms compare asymptotically (in big-O terms) for a large value of n.
(b) Now compare the same algorithms in terms of practical time, i.e. the actual running time.
Simply, repeat the previous example but use the chrono library to compute the actual times
taken by each algorithm, and report the average value of the time for each algorithm.
(c) The sorting algorithm available in the C++ STL is called IntroSort. Here is what Wikipedia
says about it: "Introsort or introspective sort is a hybrid sorting algorithm that provides
both fast average performance and (asymptotically) optimal worst-case performance. It
begins with quicksort, it switches to heapsort when the recursion depth exceeds a level
based on (the logarithm of ) the number of elements being sorted and it switches to insertion
sort when the number of elements is below some threshold." In light of your experiments
above, explain why IntroSort does what it does.